加速度计自校准

As a specific force sensor, the tri-axis accelerometer is one of the core instruments in an inertial navigation system (INS). During navigation, its measurement error directly induces constant or alternating navigation errors of the same order of magnitude. Moreover, it also affects the estimation accuracy of gyro drift coefficients during the initial alignment and calibration, which will indirectly result in navigation errors accumulating over time. Calibration can effectively improve measurement accuracy of the accelerometer. Device-level calibration can identify all of the parameters in the error model, and the system-level calibration can accurately estimate part of these parameters. Combining the advantages of both the methods and making full use of the precise angulation of the space-stabilized platform, this paper proposes a three-stage accelerometer self-calibration technique that can be implemented directly in the space-stable INS. The device-level calibration is divided into two steps considering the large amount of parameters. The first step is coarse calibration, which identifies parameters except for the nonlinear terms, and the second step is fine calibration, which not only identifies the nonlinear parameters, but also improves the accuracy of the parameters identified in the first step. The follow-on system-level calibration is carried out on part of the parameters using specific force error and attitude error to further improve the calibration accuracy. Simulation result shows that by using the proposed three-stage calibration technique in the space-stable INS, the estimation accuracy of accelerometer error can reach 1×10−6 g order of magnitude. Experiment results show that after the three-stage calibration, the accuracy of latitude, longitude, and attitude angles has increased by over 45% and the accuracy of velocity has increased by over 22% during navigation.

This research provides the theoretical feasibility study of a novel architecture of a MEMS differential resonant accelerometer, with switchable and tunable electrostatic transmission between the proof mass and the vibrating sensing beams. The same beams are used for sensing of the inertial force, while the transmission is switched ON, and for the device's calibration, when the transmission is OFF. Therefore, the beams'response in the OFF state is affected by the same factors (temperature, electronics, packaging) as in the ON state, with the only exception for the acceleration. This unique ability to physically disconnect the inertial force from the sensing elements opens possibilities for new schemes of the signal processing, including sensitivity tuning, zero-bias correction and on-the-fly self-calibration of the sensor. The device includes a proof mass (PM) and two force-transmitting frames that are attached to the substrate by the suspension springs, such that there is no direct mechanical connection between the PM and the frames. Two identical sensing beams are attached at their ends to the frames and the substrate. When the electrostatic transmission is switched ON by applying a voltage between the PM and frames, the force is transmitted from the PM through the frame to the beams. Disturbance in the electrostatic field, due to the acceleration-dependent displacement of the PM, results in the shift in the beam axial force and, therefore, in its resonant frequency, assuring the device's acceleration sensing. Furthermore, the change in the control voltage tunes the transmission of the input signal, and therefore the scale factor and the dynamic range of the sensor. An analytic model of the generic device is formulated and verified using finite elements analysis. The tunability of the device and the compensation of the scale factor thermal sensitivity are demonstrated using the model.

As a key component in motion state sensing, the accuracy of accelerometers directly affects the performance and safety of their systems. However, their sensitivity can be influenced due to various factors during operation, necessitating both pre-deployment and periodic calibration. Traditional primary calibration methods rely on laser interferometers, yet their trueness and stability are compromised by environmental disturbances affecting the laser wavelength, making on-site traceability challenging. Addressing these issues, this study combines a Cr self-traceable grating with a homodyne Littrow grating interferometer and primary vibration calibration technique. Leveraging the high line density, stability, and traceability of the self-traceable grating, it achieves high accuracy and on-site traceable calibration. In experiments, the effectiveness of this calibration system was validated using commercial accelerometers, achieving a measurement uncertainty of 0.25%. This calibration technique not only enhances the accuracy and environmental adaptability of accelerometer calibration but also addresses the critical issue of on-site traceability, representing the future direction of in-field accelerometer calibration.

The laser self-mixing grating interferometer based on Cr atom lithography gratings has been applied to the primary calibration of accelerometers due to its compact structure, low cost, high accuracy, and direct on-site traceability. However, the high line density of Cr gratings (4700 l/mm) introduces dense outliers in interferometric signals, complicating displacement demodulation via conventional derivative-based methods and causing frequent phase jumps. To address this challenge, we propose a hybrid algorithm integrating the continuous wavelet transform and the Hilbert transform, which enables robust displacement demodulation under high-noise conditions. Experimental validation on a commercial MEMS accelerometer demonstrated exceptional accuracy: 100 consecutive data segments were successfully demodulated with a displacement fitting goodness of R2=0.9964 (), and the derived sensitivity deviated by only 0.1% from the nominal value. This algorithm establishes a paradigm for the high-accuracy dynamic calibration of inertial sensors in field applications.

To enhance the accuracy of consumer-grade accelerometers in low-cost navigation and attitude measurement applications, this article proposes a diversity-driven self-adaptive genetic algorithm (D-SAGA) for high-precision calibration of accelerometer error parameters. A comprehensive error model is first established, accounting for bias, scale factor, and non-orthogonal errors. A static 24-position calibration platform is designed using a 3-D-printed hexahedral structure to acquire high-quality attitude data. Building on the conventional genetic algorithm (GA), D-SAGA incorporates a population diversity metric and adaptive operator adjustment strategy, thereby improving global search capability and convergence stability. To validate the proposed method, experiments were conducted using two accelerometer modules: the consumer-grade MPU6050 and the higher-performance accelerometer in the CMP10A inertial measurement unit (IMU). Comparative evaluations were performed against gradient descent with line search (GD+LS), newton + GD + line search (Newton+GD+LS), particle swarm optimization (PSO), and traditional GA. Results demonstrate that D-SAGA consistently achieves superior calibration accuracy, convergence efficiency, and robustness. For the MPU6050, post-calibration root mean square error (RMSE) was reduced to 1.41 mg, representing a 95.81% error reduction, while CMP10A experiments confirmed the generalizability of the approach. Repeatability experiments with 50 independent runs further verified robustness: D-SAGA achieved a mean RMSE of 1.4254 mg with a standard deviation of only 0.0213 mg, compared to 0.1222 mg for GA. Statistical analyses (two-sample t-tests, p < 0.01) confirmed that the improvements are significant. Overall, the proposed D-SAGA method offers an efficient, stable, and scalable calibration solution for consumer-grade IMUs, with promising applicability for practical engineering use, though further validation in large-scale field scenarios is warranted.

This paper presents a study on the infield self-calibration of two rigidly connected IMUs' intrinsic parameters, without the aid of any external sensors, equipment, or specialized procedures. Specifically, we consider the calibration of gyroscope biases, gyroscope scale factors, and accelerometer biases, using only IMU data and known extrinsics between the two IMUs. We focus on the observability analysis of this system, and show that all gyroscope intrinsic parameters and a portion of accelerometer biases are observable, with information from both IMUs and sufficient motion. Moreover, we identify the additional unobservable directions in the intrinsic parameters that arise from various degenerate motions. Finally, we validate our observability findings through numerical simulations, and assess our system's calibration accuracy using real-world data.

No abstract available

A Built-in Self-Test methodology has been developed for fault diagnostic in MEMS using the interpolation. In this work, a lookup table together with AKIMA interpolation has been used to calibrate the MEMS capacitive accelerometer to identify deficiencies after manufacturing by reevaluate the self test voltage value for the test electrodes. Several faults are carried out to the spring or finger of the sensing with applying GA to calculate the appropriate electrode voltages for the fault compensation. These voltages (after calibration) then stored in the lookup table to be used in the feedback for the proof mass displacement correction. The sensor has a nonlinear behavior of 0.16 % and a bandwidth (BW) of 400 Hz, with just an input range of ±50 g. This result of a sensing element was compared to various stored fault-free outputs computed by GA to determine the updated self-test bias voltage again for purpose of proof MEMS calibration, which served to verify this process.

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High-sensitivity accelerometers are essential for spacecraft micro-vibration monitoring. This study proposes a procedure to facilitate precise on-ground calibration of such accelerometers with a limited operational range by rotating to multiple positions with its input axis mounted along the horizontal tilt axis of a two-axis indexing device. Each single-axis accelerometer unit of a self-developed tri-axial nano-g accelerometer was respectively tested with its various reference axes along the rotation axis for identifying the parameters of their model equations including higher-order terms. The minute tilt axis deviation of the test equipment from the horizontal plane and the accelerometer’s higher-order response to gravity during calibration are corrected for application in the microgravity environment. Errors of accelerometer biases and scale factors are satisfactorily improved, respectively, to ±2% and ±0.01 mg, by at least one order of magnitude. Parameters of all three units of the accelerometer are unified into one coordinate frame defined by the accelerometer mounting surface. Acceleration measured by our accelerometer shows consistency with the other collocated one in a space mission.

During flight, unmanned aerial vehicles (UAVs) need several sensors to follow a predefined path and reach a specific destination. To this aim, they generally exploit an inertial measurement unit (IMU) for pose estimation. Usually, in the UAV context, an IMU entails a three-axis accelerometer and a three-axis gyroscope. However, as happens for many physical devices, they can present some misalignment between the real value and the registered one. These systematic or occasional errors can derive from different sources and could be related to the sensor itself or to external noise due to the place where it is located. Hardware calibration requires special equipment, which is not always available. In any case, even if possible, it can be used to solve the physical problem and sometimes requires removing the sensor from its location, which is not always feasible. At the same time, solving the problem of external noise usually requires software procedures. Moreover, as reported in the literature, even two IMUs from the same brand and the same production chain could produce different measurements under identical conditions. This paper proposes a soft calibration procedure to reduce the misalignment created by systematic errors and noise based on the grayscale or RGB camera built-in on the drone. Based on the transformer neural network architecture trained in a supervised learning fashion on pairs of short videos shot by the UAV’s camera and the correspondent UAV measurements, the strategy does not require any special equipment. It is easily reproducible and could be used to increase the trajectory accuracy of the UAV during the flight.

The principle of compensating size effect by special structure design or structure design value has its limitation. In this article, the internal size effect and the rotation center size effect are considered, and the coupling between them is eliminated by the constraint of virtual point position. Moreover, in order to avoid the influence of other error sources on the size effect error calibration, such as the gyro-accelerometer asynchronous time and quadratic error of the accelerometer are considered in the state equation to develop a 46D Kalman filter self-calibration model. The calibration accuracy of the size effect is better than 1.2 mm by comparing the design values of the high precision inertial measurement unit physical structure dimensions. The navigation experiment shows that the accuracy of velocity can be increased by more than 4.4 times after the size effect error is compensated.

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This paper devises the deployment of an innovative real-time self-calibration algorithm within sensor-integrated computing resources, designed to compensate for time-varying errors due to thermal and mechanical stresses affecting MEMS accelerometers. The proposed approach employs a Radial Basis Function Neural Network (RBF-NN), which was implemented, trained, and tested within the Intelligent Sensor Processing Unit (ISPU) integrated into the LSM6DSO16IS Inertial Measurement Unit (IMU). This IMU also embeds a 3-axis digital gyroscope and a 3-axis digital accelerometer. The RBF-NN does not use the back-propagation algorithm and does not feature a fixed topology and parameter set. The ISPU integrates a low-power instruction set processor with 32 KiB of program RAM and 8 KiB of data RAM, operating at frequencies between 5 and 10 MHz. Both the 32-bit floating-point precision RBF-NN and its 16-bit integer precision counterpart required less than 21 KiB of the 40 KiB of memory available within the ISPU. The floating-point model, on real-time data acquired by the IMU, achieves an average error reduction of between 90.85% and 99.71%, with, on average, a learning time of 10.18 ms and an inference time of 8.82 ms. The 16-bit model achieves an average error reduction of between 92.90% and 98.92%, with, on average, a learning time of 7.64 ms and an inference time of 4.40 ms.

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The calibration of an inertial measurement unit (IMU) is a key technique to improve the preciseness of the inertial navigation system (INS) for missile, especially for the calibration of accelerometer scale factor. Traditional calibration method is generally based on the high accuracy turntable, however, it leads to expensive costs and the calibration results are not suitable to the actual operating environment. In the wake of developments in multi-axis rotational INS (RINS) with optical inertial sensors, self-calibration is utilized as an effective way to calibrate IMU on missile and the calibration results are more accurate in practical application. However, the introduction of multi-axis RINS causes additional calibration errors, including non-orthogonality errors of mechanical processing and non-horizontal errors of operating environment, it means that the multi-axis gimbals could not be regarded as a high accuracy turntable. As for its application on missiles, in this paper, after analyzing the relationship between the calibration error of accelerometer scale factor and non-orthogonality and non-horizontal angles, an innovative calibration procedure using the signals of fiber optic gyro and photoelectric encoder is proposed. The laboratory and vehicle experiment results validate the theory and prove that the proposed method relaxes the orthogonality requirement of rotation axes and eliminates the strict application condition of the system.

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This paper proposes a digital calibration method for electromechanical closed-loop MEMS accelerometer. The method based on a harmonic self-test mechanism, in which the MEMS structure is excited by an on-chip generated electrostatic force and the corresponding harmonic distortion could be captured and analysed as an indicator of structure mismatch. According the harmonic distortion level, the mismatch could be calibrated out by the electrical signal on-chip. The whole exciting and calibrating procedure is realized in digital domain. Thus, not only the area and power consumption are reduced, but also the flexibility and robustness of the procedure is enhanced.

No abstract available

In the field of ultra high accuracy inertial measurement unit (IMU), pendulous integrating gyroscopic accelerometer (PIGA) has become a research hot spot due to its high-end performance. However, PIGA is sensitive to angular velocity, and the calibration process of PIGA-based IMU will be very complicated, which makes online self-calibration difficult to implement. To solve the above problems, we proposed an online self-calibration method utilizing angular velocity observation. The main contributions of this study are twofold: (1) An error analysis of PIGA is conducted in this paper, and the error model has also been simplified to suit the self-calibration model. (2) An improved online self-calibration method utilizing angular observation based on a simplified PIGA error model is proposed in this study. Experimental results show that the self-calibration method proposed in this study can improve the PIGA online calibration accuracy effectively (with the accuracy within 0.02 m/s/pulse), which can improve the dynamic accuracy of the PIGA.

Capacitive MEMS accelerometers have a high thermal sensitivity that drifts the output when subjected to changes in temperature. To improve their performance in applications with thermal variations, it is necessary to compensate for these effects. These drifts can be compensated using a lightweight algorithm by knowing the characteristic thermal parameters of the accelerometer (Temperature Drift of Bias and Temperature Drift of Scale Factor). These parameters vary in each accelerometer and axis, making an individual calibration necessary. In this work, a simple and fast calibration method that allows the characteristic parameters of the three axes to be obtained simultaneously through a single test is proposed. This method is based on the study of two specific orientations, each at two temperatures. By means of the suitable selection of the orientations and the temperature points, the data obtained can be extrapolated to the entire working range of the accelerometer. Only a mechanical anchor and a heat source are required to perform the calibration. This technique can be scaled to calibrate multiple accelerometers simultaneously. A lightweight algorithm is used to analyze the test data and obtain the compensation parameters. This algorithm stores only the most relevant data, reducing memory and computing power requirements. This allows it to be run in real time on a low-cost microcontroller during testing to obtain compensation parameters immediately. This method is aimed at mass factory calibration, where individual calibration with traditional methods may not be an adequate option. The proposed method has been compared with a traditional calibration using a six tests in orthogonal directions and a thermal chamber with a relative error difference of 0.3%.

No abstract available

The navigation accuracy of the inertial navigation system (INS) can be greatly improved when the inertial measurement unit (IMU) is effectively calibrated and compensated, such as gyro drifts and accelerometer biases. To reduce the requirement for turntable precision in the classical calibration method, a continuous dynamic self-calibration method based on a three-axis rotating frame for the hybrid inertial navigation system is presented. First, by selecting a suitable IMU frame, the error models of accelerometers and gyros are established. Then, by taking the navigation errors during rolling as the observations, the overall twenty-one error parameters of hybrid inertial navigation system (HINS) are identified based on the calculation of the intermediate parameter. The actual experiment verifies that the method can identify all error parameters of HINS and this method has equivalent accuracy to the classical calibration on a high-precision turntable. In addition, this method is rapid, simple and feasible.

The scale factor drifts and other long-term instability drifts of Micro-Electro-Mechanical System (MEMS) inertial sensors are the main contributors of the position and orientation errors in high dynamic environments. In this paper, a novel high dynamic micro vibrator, which could provide high acceleration and high angular rate rotation with integrated optical displacement detector, is proposed. Commercial MEMS inertial sensors, including 3-axis accelerometer and 6-axis inertial measurement unit which is about 3 mm * 3 mm * 1 mm with 19 mg, could be bonded on the vibration platform of the micro vibrator to perform in-situ during the self-calibration procedure. The high dynamic micro vibrator is fabricated by a fully-integrated MEMS process, including lead zirconate titanate (PZT) film deposition, PZT and electrodes patterning, and structural ion etching. The optical displacement detector, using vertical-cavity surface-emitting laser (VCSEL) and photoelectric diodes (PD), is integrated on the top of the package to measure the 6-DOF vibrating displacement with the detecting resolution of 150 nm in the range of 500 μm. The maximum out-of-plane acceleration of the z-axis vibrating platform loaded with commercial 3-axis accelerometer (H3LIS331DL) achieves above 16 g and the maximum angular velocity achieves above 720°/s when the driving voltage is ±6 V.

No abstract available

The in-phase error caused by misalignment of comb fingers leads to bias drift of silicon microgyroscopes which is also susceptible to stress. By periodically making the drive loop close and open and sampling the sense mode output while it’s open, the in-phase error term can be canceled. The calibrated bias of gyro is greatly improved and is no longer susceptible to stress. This method is also applicable to silicon accelerometer and provides a solution for enhancing the long-term stability of MEMS inertial devices.

In this paper, we present an accelerometer-based kinematic calibration algorithm to accurately estimate the pose of multiple sensor units distributed along a robot body. Our approach is self-contained, can be used on any robot provided with a Denavit-Hartenberg kinematic model, and on any skin equipped with Inertial Measurement Units (IMUs). To validate the proposed method, we first conduct extensive experimentation in simulation and demonstrate a sub-cm positional error from ground truth data—an improvement of six times with respect to prior work; subsequently, we then perform a real-world evaluation on a seven degrees-of-freedom collaborative platform. For this purpose, we additionally introduce a novel design for a stand-alone artificial skin equipped with an IMU for use with the proposed algorithm and a proximity sensor for sensing distance to nearby objects. In conclusion, in this work, we demonstrate seamless integration between a novel hardware design, an accurate calibration method, and preliminary work on applications: the high positional accuracy effectively enables to locate distributed proximity data and allows for a distributed avoidance controller to safely avoid obstacles and people without the need of additional sensing.

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Abstract This work presents a monolithically integrated CMOS-MEMS capacitive accelerometer that uses background self-calibration in analog mode to compensate for sensor offset. Background analog calibration maintains sensor accuracy at all times, thus improving upon traditional digital calibration methods. When powered on, the calibration process automatically initiates without the need for an external controller like a microcontroller. The design requires no physical trimming techniques on the MEMS structure, and the worst zero-gram offset can be reduced to ±50 ​mg. The single-axis accelerometer was fabricated by the UMC 0.18 ​μm CMOS-MEMS process. The chip area containing the sensors and the integrated circuit is 1.94 ​mm ​× ​1.23 ​mm. Within the sensing range of ±8 ​g, the measured output noise density is around 100 μg/rtHz. This total power consumption from the 1.8 ​V supply voltage is 45 ​μW.

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The accurate identification and characterization of the accelerometer dynamic model parameters play an important role in improving the dynamic performance of the device or system with an accelerometer. To overcome the problem that the traditional single degree of freedom (SDF) dynamic model of the accelerometer cannot describe the dynamic characteristics beyond the first resonant frequency of the accelerometer, a two degree of freedom (TDF) dynamic model of the accelerometer was constructed. On this basis, a parameter identification method for the TDF dynamic model of the accelerometer based on the feature points coordinate estimation and amplitude correction was proposed. First, the zero frequency point coordinates of the accelerometer frequency response were obtained by the Hv method. The first and second resonance point coordinates were estimated by discrete spectrum correction and the least square (DSC-LS) method. Then, the amplitude correction coefficient was applied to eliminate the influence of series coupling on the amplitude. Finally, the TDF dynamic model parameters of the accelerometer were calculated through the feature point coordinates. The experimental results show that the method has high accuracy and can avoid the influence of series coupling on the parameter identification accuracy of the accelerometer’s TDF dynamic model without complex derivation and decoupling operations. The identified TDF dynamic model of the accelerometer can represent the dynamic characteristics with a higher frequency range.

Vibration response of low-frequency cantilever fibre Bragg grating (FBG) accelerometer produced by Euler–Bernoulli model (namely FBG-MM model) is found to be frequency-dependent, unsimilar to SDOF model. Therefore, the sensitivity of the cantilever FBG accelerometer could not be identified using polynomial or basic fitting methods. This paper presents the use of cascade-forward backpropagation neural network (CFB) to predict the sensitivity of the cantilever FBG accelerometer in a "black box", which refers to the behaviour of the deep neuralnetwork. The inputs of the network are maximum base accelerations and forcing frequencies, which was set between 20 and 90 Hz (below than the first fundamental frequency of the proposed FBG accelerometer), while the output is the wavelength shift. The validation results show that the wavelength shift predicted by the trained CFB demonstrates good agreement with the FBG-MM, with the input parameter within the range of that used in training process. In addition, results also show that the trained CFB would be invalid if the input parameter is out of the range of that used in training process. In real acceleration measurement, since the forcing frequency is unknown beforehand, the trained CFB must be re-trained by considering the maximum base accelerations are embedded with forcing frequencies.

No abstract available

The sampling filters used in the National Strong-Motion Observation Network System (NSMONS) of China are linear-phase filters for both real-time transmitted data and locally stored raw data. The performance evaluation of accelerometer is based on human visual assessment through their step calibration response. However, a new re-sampling requirement has been added for the real-time transmitted data of the Earthquake Early Warning System (EEWS) in China, which has a large number of stations. This involves utilizing minimum-phase filters. There are significant challenges in the performance evaluation of accelerometers and the verification of parameter consistency for different data sets within the EEWS in China. Therefore, we propose a method that integrates waveform adaptive identification and analysis of the dynamic characteristics of the accelerometer's step response in the time domain to calculate the overshoot ratio and its changes over time. Our findings indicate that the overshoot ratios of accelerometers, decimated from linear-phase filters and minimum-phase filters, are approximately 7%–9% and 21%–23% respectively under normal sensor operation. Additionally, we reveal the effects of humidity and instrument aging on changes in the transform function of a Force-Balanced Accelerometer (FBA). In practical applications at NSMONS and EEWS in China, the proposed method can automatically identify the starting point of step calibration and detect parameter setting errors and faulty stations. This method has significant generalization potential.

High-g shock accelerometers usually use model-based dynamic calibration to obtain their dynamic characteristics. Starting from the dynamic calibration technology chain, a different model linearization algorithm from ISO16063-43 is used for accelerometer model establishment and parameter identification, and the Monte Carlo method is used to calculate the uncertainty of model parameters. In order to verify the proposed method, simulated signals were constructed under different shock excitation amplitudes, and the parameter identification and uncertainty evaluation were done on the simulated signals to verify the proposed algorithm. At the same time, the algorithm is tested by using the actual shock accelerometer calibration signal. The results show that the algorithm has achieved good results without increasing the amount of calculation, and has practical significance for the dynamic calibration of accelerometers and other sensors in practical engineering applications.

The initial alignment method, including the identification of inertial device error parameters, has always been a key issue in an inertial navigation system (INS). This study focuses on the error caused by the random noise of inertial devices that can be compensated by the reconstruction of gravitational apparent motion in an inertial frame under the condition of swinging motion. Attitude angles and accelerometer bias can also be estimated. However, the analysis and simulation results indicate that the existing methods cannot estimate the gyroscope bias. The accelerometer and the gyroscope bias will change over a long time, which will lead to long-term parameter identification accuracy decline or even failure. In this paper, a parameter identification algorithm based on Newton iterative optimization combined with a window loop calculation is designed to solve these problems. Simulation and turntable tests indicate that the proposed new algorithm can fulfill the initial alignment of strapdown INS under the swinging condition and estimate accelerometer bias effectively. Moreover, the new algorithm improves data utilization, which also has better time sensitivity, and the calculated alignment errors can nearly approach zero.

Owing to the fact that the conventional Temperature Drift Error (TDE) precise estimation model for a MEMS accelerometer has incomplete Temperature-Correlated Quantities (TCQ) and inaccurate parameter identification to reduce its accuracy and real time, a novel TDE precise estimation model using microstructure thermal analysis is studied. First, TDE is traced precisely by analyzing the MEMS accelerometer’s structural thermal deformation to obtain complete TCQ, ambient temperature T and its square T2, ambient temperature variation ∆T and its square ∆T2, which builds a novel TDE precise estimation model. Second, a Back Propagation Neural Network (BPNN) based on Particle Swarm Optimization plus Genetic Algorithm (PSO-GA-BPNN) is introduced in its accurate parameter identification to avoid the local optimums of the conventional model based on BPNN and enhance its accuracy and real time. Then, the TDE test method is formed by analyzing heat conduction process between MEMS accelerometers and a thermal chamber, and a temperature experiment is designed. The novel model is implemented with TCQ and PSO-GA-BPNN, and its performance is evaluated by Mean Square Error (MSE). At last, the conventional and novel models are compared. Compared with the conventional model, the novel one’s accuracy is improved by 16.01% and its iterations are reduced by 99.86% at maximum. This illustrates that the novel model estimates the TDE of a MEMS accelerometer more precisely to decouple temperature dependence of Si-based material effectively, which enhances its environmental adaptability and expands its application in diverse complex conditions.

This paper presents an extended calibration procedure for mode accelerometers, which makes it possible to compare the accuracy of sensors of this type from different manufacturers. This comparison involves determining the upper bound on dynamic error for a given quality criterion, i.e., the integral square error and absolute error. Therefore, this article extends the standard calibration implemented in engineering practice using tests, providing a value for the upper bound on dynamic error as an additional parameter describing the accelerometer under consideration. This paper presents the theoretical basis for this type of solution, which is partly based on measurement data obtained from a standard calibration process and on the results of parametric identification. The charge mode accelerometer is considered here because this type of sensor is commonly used in the energy industry, as it can operate over a wide range of temperatures. The calculation results presented in this paper were obtained using MathCad 5.0 software, and the tests were carried out using an accelerometer of type 357B21. In the experimental part of this article (Results of Extended Calibration section), values for the upper bound of the dynamic error were determined for two error criteria and constrained simulation signals related to these errors. The impact of interference on the results of accelerometer tests was omitted in this paper.

The aim of this study was to conduct an advanced analysis of the MEMS sensor, including both experimental tests and numerical simulations, in order to determine its mechanical properties and operational dynamics in detail. It is challenging to find publications in the literature that are not based on theoretical assumptions or general manufacturer data, which do not reflect the actual microstructural characteristics of the sensor. This study uses a numerical model developed in MATLAB/Simulink, which allows the experimentally determined material characteristics to be combined with predictive dynamic modelling. The model takes into account key mechanical parameters such as stiffness, damping and response to dynamic loads, and the built-in optimisation algorithm allows the structural parameters of the MEMS accelerometer to be estimated directly from experimental data. In addition, SEM microscopic studies and EDS chemical composition analysis provided detailed information on the sensor’s microstructure, allowing its impact on mechanical properties and dynamic parameters to be assessed. The integration of advanced experimental methods with numerical modelling has resulted in a model whose response closely matches the measurement results, which is an important step towards further research on design optimisation and improving the reliability of MEMS sensors in diverse operating conditions.

To evaluate the fabricated error in the MEMS resonant accelerometer and reduce the test cost, it is necessary to measure the key parameters of the MEMS chips at the wafer level. This paper proposes a method for scale factor identification for batch measurement at the wafer level with electrostatic excitation. An equivalent acceleration is generated by electrostatic force. which is qualified by both excitation voltage and comb drive actuators. By measuring the frequency response of differential resonators, the scale factor is established. The realization of measurement circuits is described in this paper, and the batch measurements of the scale factor of a wafer are performed. The experimental results show that the measurement error is less than 3%, compared with the scale factor obtained by earth’s gravitational field tumble experiments. The test time for a single chip is 10 s, and the test time for the 6-inch wafer is less than 1.2 hours.

Accelerometer bias and scale factor are important parameters of the accelerometer. The accuracy of calibration of bias and scale factor will directly affect navigation accuracy. This paper studies the calibration of accelerometers under out-door conditions. In some applications, the inertial measurement unit (IMU) cannot rotate with any angle due to the restriction of equipment and site. The pitch and roll rotation range is -45° to 45°, and the yaw is -180° to 180°. In this paper, the bias and scale factor identification equations under different positions are derived based on the inertial navigation error equation. The results show that when the IMU rotates around the pitch axis, as long as there are three pitch positions, the bias and scale factor of the y-direction and z-direction accelerometers can be calibrated. When the IMU rotates 45° around the roll axis and then rotates 90° around the yaw axis, the x-direction accelerometer scale factor can be calibrated. If the bias and scale factor of the y-direction and z-direction accelerometer are known, the bias of the x-direction accelerometer can also be calibrated. Then, several simulations are conducted which are consistent with the theoretical results. At last, optimized calibration path is designed. Within 20 min, the calibration accuracy of bias is better than 5 mGal, and the calibration accuracy of scale factor is better than 5 ppm.

No abstract available

The Inertial Navigation System (INS) is a navigation system that determines the position, velocity, and orientation of a moving object without the aid of outside references. It does this by using gyroscopes and accelerometers. The most severe errors of INS are Direct Current (DC) offset or bias drift and scale factor variation. The estimate and correction of these limitations are necessary for accurate navigation. While measuring these errors measurement noise and process noise are the error sources that affect the measurement. The proposed method for measuring the bias from the accelerometer uses a Kalman filter. Estimation is done by using the Kalman filter, which has the predict and update stages, a recursive filter that uses state space techniques. Three accelerometer output is used for analyzing the bias factors of all three axes of INS. Accelerometer output is filtered using a Kalman filter to get the noisy free output. The proposed method effectively filters out the noises which present in the measurement and can estimate the accelerometer bias without the help of a turntable.

In recent years, navigation technology has rapidly developed. System-level calibration technology for inertial navigation system (INS) has been widely used because it does not rely on high-precision equipment. However, INS introduces a bad coupling error in high-precision ring laser gyroscope (RLG) scale-factor error estimation, accompanied by a large accelerometer-slope bias error. To solve this problem, an improved system-level fitting calibration method is proposed, which changes the 90° rotation increment to 450°, while maintaining the original calibration sequence. Compared with the traditional system-level calibration method, the calibration error of the gyroscope scale-factor error is reduced to 0.2 times, under simulation conditions, without affecting the calibration accuracy of the other parameters. The extreme difference of the gyroscope scale-factor calibration error on multiple experiments reduces from 4.75 to 1.40 ppm under experimental-verification conditions. The mean values of the gyroscope scale factor were closer to the real reference values (no more than 2 ppm). The integral calibration results meet the requirements of a high-precision RLG INS. The proposed method maintains the original calibration sequence and exhibits small changes with high practicability. The proposed method is suitable for applications with high requirements for gyroscope scale factor accuracy, such as highly dynamic aircraft.

No abstract available

Micro-electromechanical system (MEMS) sensors are widely used in various navigation applications because of their cost-effectiveness, low power consumption, and compact size. However, their performance is often degraded by temperature hysteresis, which arises from internal temperature gradients. This paper presents a calibration method that corrects temperature hysteresis without requiring any additional hardware or modifications to the existing MEMS sensor design. By analyzing the correlation between the external temperature change rate and hysteresis errors, a mathematical calibration model is derived. The method is experimentally validated on MEMS accelerometers, with results showing an up to 63% reduction in hysteresis errors. We further evaluate bias repeatability, scale factor repeatability, nonlinearity, and Allan variance to assess the broader impacts of the calibration. Although minor trade-offs in noise characteristics are observed, the overall hysteresis performance is substantially improved. The proposed approach offers a practical and efficient solution for enhancing MEMS sensor accuracy in dynamic thermal environments.

The errors can accumulate over time when microelectromechanical system (MEMS) accelerometers are in use, it is necessary to perform autocalibration to remove the systematic error effect. However, little research has been done on simultaneously considering the non-orthogonality and misalignment effect in MEMS triaxial accelerometer calibration. To enhance the calibration accuracy and extend the autocalibration methods, this paper proposed a new autocalibration method for MEMS triaxial accelerometers base on a PID-based search algorithm. Non-orthogonality and misalignment error factors were integrated into the error model and a PID-based search algorithm was developed to identify the optimal error factors, minimizing the difference between the actual accelerometer output and the local gravity. The proposed calibration method was tested through simulations, with results showing that the errors in scale factor, bias, non-orthogonality, and misalignment are within 1.5865×10-4, 2.0060×10-4, 5.0621×10-4, and 6.8104×10-4, respectively. The proposed method was also compared with the existing calibration methods, with the maximum errors of the proposed method within 0.41% and those of the others exceeding 0.80%. Simulation and comparison results verified the effectiveness and improvement of the proposed method. The average time of the autocalibration is 13.22 s, offering practical value for MEMS triaxial accelerometers.

This paper addresses accelerometer array calibration, focusing on determining the errors between multiple sensors. Micro-electromechanical system (MEMS) based triaxial accelerometers, key components of Inertial Measurement Units (IMUs), are used in localization, robotics, and navigation systems. The requirements of these applications necessitate low-cost sensors, which makes MEMS IMUs a reasonable choice. However, these low-cost IMUs are significantly affected by systematic (i.e., bias, misalignment, scale-factor) and random errors. Achieving reliable sensor output depends on the precision of the executed calibration method. While traditional laboratory-based sensor calibration using specialized equipment (i.e., three-axis turntable) is accurate, it is time-consuming and costly. In contrast, in-field calibration techniques, which can be performed using a mechatronic actuator or a robotic arm, have gained popularity. These techniques involve comparing sensor measurements to established reference values. The MEMS sensors are increasingly being used in multi-sensor applications, which demands not only individual sensor error calibration but also important to determine the axis misalignment between the used sensors. During calibration process, various optimization algorithms (e.g., GA, PSO) can also be used to find the error parameters. The proposed measurement system allows for individual calibration of misalignment, bias, and scale factor of the sensor array, and eliminates between-sensor misalignment errors.

Abstract To realise the overall calibration of the error model coefficients of accelerometers in an inertial combination and to improve the navigation accuracy of the inertial navigation system, a norm-observation method is applied to the calibration, especially for the quadratic coefficient of the accelerometer. The Taylor formula is used to expand the solution of the acceleration model, and the intermediate variables with error model coefficients are obtained using the least square method. The formulas for calculating the quadratic term coefficient, scale factor and bias of the accelerometer are given. A 20-position method is designed to calibrate the accelerometer combination, the effectiveness of the method is verified by simulation, and the effects of installation misalignment and rod-arm error on calibration accuracy are analysed. The results show that the installation misalignments and rod-arm errors have little influence on the coefficient calibration, less than 10−8, and can be neglected in a practical calibration process.

Addressing issues such as low testing efficiency, easy introduction of installation errors, and turntable errors in the gravity field testing of the JN-06 quartz flexure accelerometer, a contact-type testing method based on a turntable is proposed. This method utilizes probes to achieve contact connections between the test device and the terminals of the accelerometer, enabling non-destructive and simultaneous testing of multiple accelerometer. Additionally, a reference accelerometer is introduced to ensure consistency between testing conditions and calibration conditions. To verify the feasibility of this method, both contact-type testing experiments and traditional testing experiments were conducted on 11 JN-06D-01 accelerometer. The root mean square errors of zero-bias and scale factor measured by the two experiments are 2.90474E-05 g and 0.00493 P/100s/g respectively. Therefore, the contact-type testing method has higher credibility and verified the feasibility of the testing method.

The error coefficients of the pendulous integrating gyroscopic accelerometer (PIGA) mainly include the bias, scale factor, and nonlinear error. Previous works have fully studied and suppressed the bias and scale factor of PIGAs. At present, the nonlinear error is the most critical factor restricting the measurement accuracy of PIGAs. To address this barrier, a study on the analysis and suppression of the nonlinear error of PIGAs at the instrument level was carried out. Firstly, the error model of a PIGA is established by kinematics and dynamics analyses. Then, nonlinear error is analyzed based on the established model. Finally, a suppression method for the nonlinear error is proposed based on the analysis results. The nonlinear error analysis found that (1) the nonlinear error includes a quadratic term error caused by unequal inertia and the inertia product, cross-coupling error is caused by lateral accelerations, and error is caused by unequal stiffness; (2) unequal inertia and the inertia product were the most critical factors resulting in nonlinear error. Based on the results in the nonlinear error analysis, the suppression method for error focuses on unequal inertia and the inertia product. The proposed method of analysis and suppression was validated experimentally as the quadratic term coefficient was reduced by an order of magnitude from 1.9 × 10−6/g0 to 1.91 × 10−7/g0.

Aligning a robot's trajectory or map to the inertial frame is a critical capability that is often difficult to do accurately even though inertial measurement units (IMUs) can observe absolute roll and pitch with respect to gravity. Accelerometer biases and scale factor errors from the IMU's initial calibration are often the major source of inaccuracies when aligning the robot's odometry frame with the inertial frame, especially for low-grade IMUs. Practically, one would simultaneously estimate the true gravity vector, accelerometer biases, and scale factor to improve measurement quality but these quantities are not observable unless the IMU is sufficiently excited. While several methods estimate accelerometer bias and gravity, they do not explicitly address the observability issue nor do they estimate scale factor. We present a fixed-lag factor-graph-based estimator to address both of these issues. In addition to estimating accelerometer scale factor, our method mitigates limited observability by optimizing over a time window an order of magnitude larger than existing methods with significantly lower computational burden. The proposed method, which estimates accelerometer intrinsics and gravity separately from the other states, is enabled by a novel, velocity-agnostic measurement model for intrinsics and gravity, as well as a new method for gravity vector optimization on $S^{2}$. Accurate IMU state prediction, gravity-alignment, and roll/pitch drift correction are experimentally demonstrated on public and self-collected datasets in diverse environments.

With the increase in the application of micro-electromechanical system (MEMS) accelerometers, their accurate calibration is increasingly essential to reduce the application error. Aiming at the high accuracy calibration requirements of scale factor, bias, and nonorthogonalities, we propose a novel calibration method to obtain highly accurate parameters, especially in the scenario without turntable. First, a 12-parameter model of accelerometer output data is used for analysis. The static data characteristics of the six specified positions of the accelerometer were then analyzed. Finally, based on these characteristics, a novel calibration method performed using an iterated parameter correction process is proposed. Repeatable simulations under different biases show that the calibration accuracy of the proposed method is not affected by the bias value to be calibrated, and that the calibration results have consistent accuracy. The estimation error of bias and relative error of scale factor are less than 0.5 mg and 0.05%, respectively, and the accuracy of the nonorthogonal elements of the calibration matrix $S$ and $K$ are 0.003 and 0.006, respectively. In addition, the calibration results of the laboratory MEMS accelerometer and the triaxial accelerometer in ADIS16488 demonstrate the effectiveness of the proposed method.

The application of MEMS capacitive accelerometers is limited by its thermal dependence, and each accelerometer must be individually calibrated to improve its performance. In this work, a light calibration method based on theoretical studies is proposed to obtain two characteristic parameters of the sensor’s operation: the temperature drift of bias and the temperature drift of scale factor. This method requires less data to obtain the characteristic parameters, allowing a faster calibration. Furthermore, using an equation with fewer parameters reduces the computational cost of compensation. After studying six accelerometers, model LIS3DSH, their characteristic parameters are obtained in a temperature range between 15 °C and 55 °C. It is observed that the Temperature Drift of Bias (TDB) is the parameter with the greatest influence on thermal drift, reaching 1.3 mg/°C. The Temperature Drift of Scale Factor (TDSF) is always negative and ranges between 0 and −400 ppm/°C. With these parameters, the thermal drifts are compensated in tests with 20 °C of thermal variation. An average improvement of 47% was observed. In the axes where the thermal drift was greater than 1 mg/°C, the improvement was greater than 80%. Other sensor behaviors have also been analyzed, such as temporal drift (up to 1 mg/h for three hours) and self-heating (2–3 °C in the first hours with the corresponding drift). Thermal compensation has been found to reduce the effect of the latter in the first hours after power-up of the sensor by 43%.

The calibration accuracy of the accelerometer, a key device in an inertial navigation system, directly affects the navigation accuracy. In our study, a novel calibration method for a triaxial accelerometer was presented with automatic online calibration. A robotic arm was used to set different orientations for the accelerometer. The error parameters, including the scale factor and bias, were estimated using a particle swarm optimization (PSO) and differential evolution (DE) hybrid algorithm with adjustable inertia weight. The effectiveness of the new algorithm was validated using simulated data with or without noise in simulation. Simulation results showed that the hybrid algorithm increased the measurement accuracy by many orders of magnitude and outperformed the single PSO and DE algorithms in terms of convergence speed and global searchability. The new algorithm was applied to a real accelerometer experiment. The experiment results demonstrate that proper calibration parameters can be obtained without a precise turntable.

This paper provides a method for the overall calibration of the accelerometer combined error model coefficients. The calibration of the accelerometer error coefficients is achieved by using the Norm-observation method. It is important to achieve the calibration of the quadratic coefficient of the accelerometer. First, the Tylor series is used to expand the solution of the acceleration model, the nonlinear equations to be solved are obtained by using the least square method and Norm-observation method. Finally using 1stOpt platform of global optimization algorithm for the solution of equations for quadratic order coefficient, scale factor and zero bias. A 12-position method is designed to calibrate the accelerometer combination, the effectiveness of the method is verified by simulation.

To improve the temperature performance of accelerometer, this paper studied the temperature characteristics of MEMS accelerometer, investigated calibration methods of accelerometer and the error compensation model. We proposed a novel interpolation-based least square fitting compensation method, which firstly uses the interpolation method to predict temperature-zero bias and temperature-scale factor data, then compensating doubled data by the least square method. We carried out a compensation experiment and verified the effectiveness of each step in the proposed method. Testing results show that in the range of - 40°C to 60°C, through the use of the least square fitting method based on interpolation, the extreme difference of the scale factor and zero bias errors are reduced by 83.6%, 93.5% respectively. Meanwhile, the root means square error of the scale factor and zero bias errors are reduced 86.2% and 95.1% respectively. After temperature compensation, the fluctuation range of the upright placed accelerometer is reduced from 0.038g to 0.003g. It is proved that this method can reduce the measurement cost and obtain high precision compensation results, which is suitable for engineering applications.

This paper presents a high dynamic range CMOS-MEMS capacitive accelerometer. An array of small masses enables the accelerometer to survive and measure high-G (kG) acceleration. A fine-grain offset compensation technique suppresses the offset due to sense capacitance mismatch. The key idea is to employ two out of 184 accelerometer cells to tune out the charge imbalance, which ensures 90X improved tuning resolution (sub-aF offset). Multiple temperature sensors are integrated on the same accelerometer chip to improve the accelerometer long-term bias instability. The prototype is fabricated in standard 0.18 μm CMOS process and then post-processed to release the accelerometer sensing structures. Measurement results demonstrate that the accelerometer achieves 5.06μV/G transducer scale factor, sub-aF offset, 4.4 μG√hr velocity random walk (VRW), and 5.2 mG bias instability. The sensor array gun-launched at 50 kG and has demonstrated high-shock survivability. Offset measurement results demonstrate 90X better offset tuning resolution than conventional technique.

Dual-axis rotational inertial navigation system (DRINS) can achieve self-calibration of error parameters through a reasonable rotation scheme. However, the traditional self-calibration methods rely on the external reference information, which fail in global navigation satellite system (GNSS)-denied environments. In long-endurance marine navigation applications, carriers are usually equipped with multiple sets of DRINS. The geometric relationship between the DRINSs can serve as constraint observation for error parameter estimation. Therefore, this article proposes a collaborative calibration method with the navigation information fusion of dual DRINSs in GNSS-denied environments. Considering scale factor error, installation error, gyro drift, accelerometer bias, and accelerometer size-effect error introduced by the rotation of dual DRINSs, a 66-D Kalman filter is established based on the geometric constraint observation. Then, a novel collaborative calibration scheme is designed through analyzing the principles of error state observability for dual DRINSs. Simulations and experiments show that all error parameters can be precisely estimated by the proposed method with the designed calibration scheme and the calibration accuracy could satisfy the demand of long-endurance marine navigation.

This article proposes a novel calibration method to improve the calibration accuracy of microelectromechanical system (MEMS) triaxial accelerometers in directional drilling tools. First, a comprehensive sensor error model is established, including scale factor, bias, nonorthogonality, and misalignment. To identify these error factors, a 12-position data collection procedure is designed to acquire raw accelerometer data. Based on this model, a new calibration framework which aims at simultaneously minimizing both spatial attitude angle errors and accelerometer output errors is developed. An improved PID-based search algorithm (PSA) is then employed to solve this optimization problem. Simulation and experimental results demonstrate the superiority of the proposed method. Compared to existing approaches, the maximum output errors are reduced to 0.41%, whereas those of other methods exceed 0.80%. Additionally, the inclination and toolface angle errors are less than 0.1° and 0.3°, respectively, while those of other methods exceed 0.5° and 0.6°, respectively. These results verify the effectiveness and accuracy improvement of the proposed method. With its enhanced performance, this method provides a viable solution for improving attitude measurement for MEMS triaxial accelerometers in directional drilling tools.

The technology has enabled the widespread use of multisensory integration such as inertia sensors for the localization of inertia and navigation systems. The accuracy of the measurement is a key factor that must be maintained and is influenced by default sensor errors (scale factor, misalignment and bias). Thus, this study focuses on proper calibration (complementary filter) to minimize the invalidation of sensor data. The proposed calibration system applies correction of the accelerometer and gyroscope bias data to the x, y, and z axes. Application to the motion of each axis was carried out on the data surface of a robot arm by adjusting the expected axis in the positive or negative areas. For bias correction or compensated distortion of the accelerometer, low pass filter to eliminate deviation and noise was applied into Arduino software. While, for bias correction or compensated distortion of the gyroscope used high-pass filter via software to allow short-term signals and prevents long-term fluctuations. Consequently, this proposed Inertia Measurement Unit (IMU) calibration system demonstrates a high accuracy at estimating the offset of an object. As a result, the accelerometer data of uncalibration and calibration are [14,29 17,38  –22,57] and [1,56 -4,26 -1,91], respectively, while gyroscope resulted uncalibration data [-4,78 0,72 -3,39] and calibration data are [-0.15 0,64 -0,39].  The results highlight the importance of the calibration process for precise sensor data.

The quartz flexible accelerometer (QFA) is a critical component in navigation-grade strapdown inertial navigation systems (SINS) due to its bias error, which significantly impacts the overall navigation accuracy of SINS. Temperature variations induce dynamic changes in the bias and scale factor of QFA, leading to a degradation of the navigation accuracy of SINS. To address this issue, this paper proposes a temperature error compensation method based on a non-uniform mutation strategy genetic algorithm (NUMGA) and a polynomial curve model (PCF). Firstly, the temperature bias mechanism of QFA output is analyzed, and a polynomial temperature error model is established. Then, the NUMGA is utilized to identify the model parameters using the −20–40 °C test data, seeking the optimal parameters for the polynomial. Finally, the compensation parameters are used for cold start static test verification. The results demonstrate that the temperature compensation model based on NUMGA-PCF can automatically select the optimal parameters, which enable the model to exhibit a stable decreasing trend on the adaptation curve without multiple fluctuations. Compared to the traditional GA temperature compensation model, the compensation errors in the three axes of QFA in SINS are reduced by 612.24 μg, 60.82 μg, and 875.82 μg, respectively. Before the 20th generation, there are no decrease in convergence speed observed with the in-crease of population diversity. Within the −20–40 °C temperature range, the average values and standard deviations of QFA for the three optimized axes can be maintained below 0.1 μg by using this compensation model.

No abstract available

Motion errors pose a significant challenge to moving-base gravity gradient measurement applications. To eliminate those errors, model-based compensation methods are commonly employed. However, those compensation results are strongly influenced by the motion error model correctness. This article proposes a postprocessing compensation method, which can solve that problem, for the rotating accelerometer gravity gradiometer (RAGG). Two experiments are carefully designed to validate the different components of the linear motion error model. Using a six-degree-of-freedom (6-DOF) platform, sinusoidal excitations are employed for motion error coefficients calibration. The experimental results show that the R-squared value of the fitting ( ${R} ^{2}$ ) exceeded 0.995, confirming the accuracy of the RAGG linear motion error coefficients calibration. Additionally, using the calibrated motion error coefficients, an aircraft motion excitation is also applied on the RAGG for postprocessing compensation. The compensated outputs indicate that the motion errors can be reduced from the micro-g ( $\mu $ g) level to the order of nano-g (ng). The power spectral density (PSD) of the results after compensation show an excellent accordance with those of the RAGG self-noise in static measurement. These results provide a guidance for noise reduction and motion error compensation in RAGG systems.

A novel in-field calibration method for micro-electromechanical system (MEMS) triaxial accelerometers was proposed to simplify the data collection procedure and improve the calibration accuracy in this article, considering cross-axis sensitivities without the need for external equipment. MEMS accelerometers were placed at six positions on a simple platform, in contrast to the at least 12 positions required by other in-field calibration methods. To enhance calibration accuracy, the cross-axis sensitivities were introduced into the sensor error model comprising 18 calibration parameters. The proposed calibration method was verified by simulations and real experiments, and the errors of scale factor, zero offset, misalignment factor, and cross-axis sensitivity are within 0.002%, 0.07 mg, <inline-formula> <tex-math notation="LaTeX">$4\times 10^{-{4}}$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$8\times 10^{-{4}}$ </tex-math></inline-formula>, respectively. Compared with the existing in-field calibration methods, the P<sc>roposed method</sc>’s output modulus errors are less than 0.51% whereas the others exceed 0.80%. The test results demonstrate that the attitude angle error obtained by the new method is less than 0.2°, confirming the effectiveness of the proposed method. The new method offers higher calibration accuracy and does not depend on external high-precision equipment, making it suitable for in-field calibration of MEMS triaxial accelerometers.

The common error calibration model of a linear accelerometer usually cannot meet the accuracy requirement without considering the influence of misalignments in the precision centrifuge test. In order to improve the calibration accuracy, a series of coordinate systems is established and precise accelerations along the input axes of the accelerometers are deduced first. Then, by analyzing the mechanisms of the main error sources, the revised error calibration model is established which includes the misalignments, the radius errors, and the nonlinearity error terms. Then, the measurement methods are proposed to estimate the initial angular misalignments, the installation angular misalignments, and the installation radius misalignments by a theodolite and the accelerometer themselves in the different modes of the centrifuge, respectively. Finally, the experimental measurement results show that the initial angular misalignments are estimated accurately and less than 0.5' after adjustment. Further investigation shows that the adequacy of the common error calibration model decline obviously and the calibration accuracies are lower than 6 × 10-3g/g without considering the misalignments. After compensating for the misalignments in the revised model, the error coefficients are identified precisely, and the calibration accuracies are higher than 1.5 × 10-3g/g.

This article proposes a sensitivity calibration method for triaxial accelerometers, aiming to eliminate calibration errors caused by the transverse effects of the calibration device on the accelerometers. First, we establish a matrix model that relates the triaxial acceleration excitation loads to the sensor voltage sensitivity. Next, we introduce an orthogonal calibration method based on the Hopkinson bar. Using three laser Doppler velocimeters (LDVs), we simultaneously measure the 3-D orthogonal excitation acceleration at the end of the calibration device. We then calculate the impact of the transverse coupling effect between the elastic rod and the anvil on the accelerometer calibration. Finally, we perform calibration experiments on triaxial high-g accelerometers using the proposed and conventional methods. The sensitivity matrices for each method were computed using the least squares method. We evaluate the calibration accuracy using relative error and root mean square error (RMSE) metrics. The results demonstrate that the proposed orthogonal calibration method reduces the average relative error by 60.3% and the RMSE by 64.3% compared with the conventional calibration method. The proposed orthogonal calibration method achieves higher precision and better reflects the sensitivity characteristics of triaxial accelerometers.

No abstract available

Accurate calibration of micro-electromechanical systems (MEMS) accelerometers is crucial for enhancing the performance of low-cost inertial measurement units (IMUs). This paper introduces a novel calibration technique that leverages artificial neural networks (ANNs) combined with data from multiple IMUs to increase the accuracy of the calibration. The proposed method involves a calibrated UR robot, which enables the data acquisition of ground truth data for an effective calibration of IMUs. It enhances the calibration accuracy by utilizing the collective measurements from five IMUs within an accelerometer array. Fourteen sets of measurement data were established in dynamic environments using the robotic arm. The ANN-based approach was trained using ten datasets of dynamic measurements, where the trained model is validated against four unseen test data. The ANN-based calibration performance is evaluated by comparing it to standard methods such as ellipsoid fitting method and arithmetic averaging of the sensor outputs. Results demonstrate that the proposed method achieves superior calibration accuracy, with an improvement of 18.2% over the ellipsoid fitting technique and 23.3% over the averaging method. It also shows that fusing accelerometer measurements with Euler angles calculated from acceleration as input data for the ANN provided the best results for the calibration. The findings suggest that integrating ANN models with data fusion from multiple sensors significantly improves the calibration accuracy of MEMS accelerometers, thereby enhancing their potential for use in precise motion sensing applications.

Inertial navigation systems (INSs) can continuously provide the attitude, velocity, and position of the vehicle with high accuracy. However, the accelerometer scale factor asymmetry and the temperature-related accelerometer errors can cause significant navigation errors. To solve this problem, in this article, a novel system-level calibration method is proposed, which achieves simultaneous compensation of accelerometer asymmetric errors and second-order temperature-related errors. First, the error model including accelerometer asymmetry and temperature-related errors is constructed. Then, a 51-D Kalman filter is applied to estimate all error factors of accelerometers including biases, scale factor errors, installation errors, scale factor asymmetry, and first- and second-order temperature-related error coefficients at the same time. The effectiveness of the calibration method is proved by both simulation and experiment. The pure inertial navigation experiment results illustrated that, compared with the traditional 30-D calibration, our method can reduce the root mean squares of radial position error and radial velocity error by 50% and 39%, respectively, which indicates that the proposed method can be used to improve the navigation performance of ground or aerial vehicles.

Measurement while drilling (MWD) tools include accelerometers, magnetometers and temperature sensors. The accuracy of these sensors are highly important in measuring inclination and Azimuth angle parameters in a directional well. These factors can increase costs when drilling a directional well. During the past years, many efforts have been made to increase the accuracy of these tools. Accuracy of accelerometer and magnetometer sensors are influenced by scale, bias and non-orthogonal errors. Considering that MWD systems work in a wide range of temperatures (for example 0 °C–150 °C), the temperature parameter should also be added to the factors affecting the errors. Here, after making a sample of MWD tool, a method to calibrate the tool using mathematical model based on total field calibration algorithm, least square method and the transfer matrix is presented. Calibrated parameters at ambient temperature are calculated with acceptable speed. Then, a method for calculating temperature coefficients in the desired range is provided. Compared to the case where temperature coefficients are not considered, the obtained results show a significantly increased accuracy of Inclination and Azimuth parameters through the use of these coefficients.

Abstract This paper presents a new method for in-field calibration of accelerometers to address the problems of low efficiency and high cost associated with traditional calibration methods. A nonlinear mathematical model of the accelerometer is established, and the cost function is analysed and deduced the cost function. Then, an adaptive Northern Goshawk Optimisation (NGO) algorithm based on prior knowledge enhancement is introduced. A method of collecting multi-position data with a hand-held accelerometer is introduced, and the proposed algorithm is used to in-field calibrate nine parameters of the accelerometer’s nonlinear error model. In addition, simulation is used to compare the results of calibrating the accelerometer using the proposed algorithm and the original algorithm, demonstrating the superiority of the proposed algorithm. Finally, experimental results confirm that the proposed method can rapidly calibrate accelerometer error parameters without relying on complex equipment and with greater accuracy than traditional methods.

With the continuous improvement of measurement accuracy requirements for inertial devices, how to accurately calibrate nonlinear error coefficients of accelerometer components has become an important factor affecting the accuracy of the inertial navigation system. Centrifuge calibration method can continuously provide a specific force greater than 1 g, which can fully excite the nonlinear errors of accelerometer components and is a commonly used method for calibrating nonlinear error coefficients. However, on the one hand, traditional centrifuge speeds are often selected based on empirical experience, lacking a scientific determination method. This can lead to a decrease in the calibration accuracy of nonlinear error coefficients. On the other hand, the inability to accurately model the highly complex and time-varying test errors during actual calibration further reduces the calibration accuracy. Therefore, a high-precision calibration method for nonlinear error coefficients is proposed. Firstly, by introducing G-optimal experimental design criterion to minimize the maximum scaled prediction variance of output prediction values, the optimal speed combination is designed to achieve the highest accuracy in estimating nonlinear error coefficients. Based on the idea of semi-parametric regression, system errors caused by calibration test errors are treated as parameters to be estimated, and a high-precision nonlinear error coefficient calibration model is established. Then the influence of calibration test errors is eliminated by estimating and compensating the system errors. Centrifuge calibration test results show compared with the traditional method, the ranges and standard deviations of the repeated calibration results of the proposed method are reduced by more than 80.37% and 63.01%. This indicates that the proposed method can effectively eliminate the influence of calibration test errors and achieve high-precision calibration of nonlinear error coefficients.

By applying a parameterized 2-DOF model to an Endevco type 2270 B2B sensor for the transfer of the unit shock sensitivity SSh, the drawback of the systematic spectral influence to SSh of shock exciters with different spectral composition can be compensated in the frequency domain. The method and first results are presented.

This paper presents a new calibration method of the accelerometer tested on a precision centrifuge to further enhance the calibration accuracy of the high-order error model coefficients. To eliminate the influence of dynamic and static error sources of precision centrifuge on calibration accuracy, nine coordinate systems are established considering the errors of a centrifuge, which are propagated by homogeneous transformation, and the accurate specific forces acting on three axes of the tested accelerometer are obtained. Based on the error model and the accurately computed input specific forces of the accelerometer, the indicated outputs of the tested accelerometer are derived, and with the combinations of indicated outputs of six calibration position pairs, a calibration model of the accelerometer is established. By designing a test plan of 12 positions under three mounting modes and using the least-squares method, all the high-order error model coefficients of the tested accelerometer are calibrated accurately. In the calibration method, the dynamic errors of precision centrifuge are introduced into the observation vectors, and the static errors are introduced into the vectors to be identified; the influence of centrifuge errors is automatically eliminated. Error analysis implies that the calibration accuracy is improved greatly.

A method for calibrating a three-axis accelerometer unit of the navigation accuracy class is proposed. It is based on measuring the modulus of the gravity acceleration vector. The method provides the determination of twelve passport coefficients (including six separate values of non-orthogonality angles) of the linear metrological model of a stationary accelerometer unit under operating conditions. The developed method makes it possible to calculate the acceleration value with an acceptable error using non-precision equipment for calibration. The problem is solved by forming a system of linear nonhomogeneous algebraic equations for the desired differences of unknown actual (real) values and the passport values of an accelerometer unit's metrological model coefficients. The passport coefficients are considered to be determined during bench calibration at the manufacturer. The system of equations is formed by placing the accelerometer in at least nine calibration positions relative to the gravity vector. The solution of this system, with consideration of the limitations formed by the six additional calibration positions of the accelerometer unit, allows determining the actual values of the metrological coefficients of the accelerometer unit and using them as passport values. By reducing the reliance on expensive and complex calibration equipment, the developed method offers a cost-effective solution for maintaining the long-term accuracy and performance of the accelerometer unit over its operational lifetime. The versatility of this calibration approach enables its integration into existing manufacturing processes, ensuring consistent and reliable performance of accelerometer units across different batches, thereby enhancing the overall quality and reliability of navigation systems and related technologies.

Currently, there is no robust method that could calibrate the accelerometer output without explicitly deriving the error model of the device and estimate the nonlinear parameters of the model. This article presents a methodology to approximate the output of two-axis thermal accelerometers based on neural networks (NNs) for calibration and nonlinear correction. This method uses the output of the accelerometer and the Earth’s gravitational acceleration expected at a static position as data for training. The proposed method uses different optimization methods (adaptive moment estimation (ADAM), gradient descent, and gradient descent with momentum) to find the best solution using half mean squared error (HMSE) as the cost functions for evaluation. Experiments are conducted and presented to validate the NN-based calibration method using 2800 unseen data points.

Most small drone accelerometer calibration methods are relatively simple, but their accuracy is not high. In order to improve the accuracy of calibration without increasing the difficulty of operation, a calibration method based on smooth filtering and Levenberg-Marquardt algorithm is proposed. Firstly, the accelerometer error model is established. Then the smoothing filter is used to filter the accelerometer measurement data in different attitudes. Finally, the Levenberg-Marquardt algorithm is used to solve the zero offset of the accelerometer, the scale factor and the tri-axial non-orthogonal error. Experimental results show that the algorithm can quickly calibrate the accelerometer and improve the measurement accuracy of the accelerometer. It is suitable for application in the drone system.

In view of the large thermal drift of microelectromechanical system (MEMS) triaxial accelerometer and the high cost of traditional calibration schemes, this article proposes a low-cost and efficient thermal drift calibration scheme combining the parameter-correction method and the proposed least squares method based on the nine-parameter model. In this scheme, first, the parameter-correction method is applied to the data collected under the heating condition to obtain the thermal drift of calibrated parameters with constant error. The least squares method is then used to obtain the parameters at a temperature <inline-formula> <tex-math notation="LaTeX">$T_{c}$ </tex-math></inline-formula>. Then, the two sets of parameters are combined, and the constant offset error is removed. Finally, higher precision thermal drift curves of the parameters are obtained after smoothing and filtering. One thousand simulations show that the previously proposed parameter-correction method has consistent accuracy and can obtain accurate drift trends of the triaxial accelerometer parameters. The actual triaxial accelerometer thermal drift calibration experiment shows that when the temperature rises by 22 °C, the sensor data converted by the parameters obtained by the proposed scheme can effectively reduce the drift. The drifts of <inline-formula> <tex-math notation="LaTeX">$x$ </tex-math></inline-formula>- and <inline-formula> <tex-math notation="LaTeX">$y$ </tex-math></inline-formula>-axes are reduced from −19.2 and 11.6 mg to −0.7 and −0.6 mg, respectively. The <inline-formula> <tex-math notation="LaTeX">$Z$ </tex-math></inline-formula>-axis drift is reduced from −23.9 to 3.5 mg. This proves the feasibility of the method and scheme proposed in this article.

No abstract available

At present, the design and manufacturing technology of mechanically dithered ring laser gyroscope (MDRLG) have matured, the strapdown inertial navigation systems (SINS) with MDRLG have been widely used in military and business scope. When the MDRLG is working, high-frequency dithering is introduced, which will cause the size effect error of the accelerometer. The accelerometer signal has a time delay relative to the system, which will cause the accelerometer time delay error. In this article, in order to solve the above-mentioned problem: (1) we model the size effect error of the mechanically dithering of the MDRLG and perform an error analysis for the size effect error of the mechanically dithering of the MDRLG; (2) we model the time delay error of accelerometer and perform an error analysis for the time delay error of accelerometer; (3) we derive a continuous linear 43-D SINS error model considering the above-mentioned two error parameters and expand the temperature coefficients of accelerometers, inner lever arm error, outer lever arm error parameters to achieve high-precision calibration of SINS. We use the piecewise linear constant system (PWCS) method during the calibration process to prove that all calibration parameters are observable. Finally, the SINS with MDRLG is used in laboratory conditions to test the validity of the calibration method.

The sensitivity parameters or mathematical model of sensor are obtained through traditional shock accelerometer under calibration test, and then the measurement signal is restored through compensation and correction. As the shock signal with complex components is used in a harsh environment, it is very difficult to accurately restore the measured signals. In the meantime, the deconvolution process of signal recovery is an inverse problem in mathematical physics, which has ubiquitously ill-posed problems, thereby bringing great challenges to the accuracy and precision of the solution. Thus, we propose a depth calibration network based LSTM, which can be used to learn the mapping relationship between the calibrated sensor signal and the standard signal. The measured signal can be restored through a data-driven sequence-to-sequence calibration network, which is trained and verified through the exclusive open-source data set of shock signals. The test results proved the superior performance of the network in shock signal calibration.

Micro-electro-mechanical system (MEMS) accelerometer-based inclinometers are widely used to measure deformations of civil structures. To further improve the measurement accuracy, a new calibration technique was proposed in this paper. First, a single-parameter calibration model was constructed to obtain accurate angles. Then, an image-processing-based method was designed to obtain the key parameter for the calibration model. An ADXL355 accelerometer-based inclinometer was calibrated to evaluate the feasibility of the technique. In this validation experiment, the technique was proven to be reliable and robust. Finally, to evaluate the performance of the technique, the calibrated MEMS inclinometer was used to measure the deflections of a scale beam model. The experimental results demonstrate that the proposed technique can yield accurate deformation measurements for MEMS inclinometers.

No abstract available

Traditional calibration method is usually performed with expensive equipments such as three-axis turntable in a laboratory environment. However in practice, in order to ensure the accuracy and stability of the inertial navigation system (INS), it is usually necessary to recalibrate the inertial measurement unit (IMU) without external equipment in the field. In this paper, a new in-field recalibration method for triaxial accelerometer based on beetle swarm antenna search (BSAS) algorithm is proposed. Firstly, as a new intelligent optimization algorithm, BSAS algorithm and its improvements based on basic beetle antennae search (BAS) algorithm are introduced in detail. Secondly, the nonlinear mathematical model of triaxial accelerometer is established for higher calibration accuracy, and then 24 optimal measurement positions are designed by theoretical analysis. In addition, the calibration procedures are improved according to the characteristics of BSAS algorithm, then 15 calibration parameters in the nonlinear method are optimized by BSAS algorithm. Besides, the results of BSAS algorithm and basic BAS algorithm are compared by simulation, which shows the priority of BSAS algorithm in calibration field. Finally, two experiments demonstrate that the proposed method can achieve high precision in-field calibration without any external equipment, and meet the accuracy requirements of the INS.

No abstract available

This paper is devoted to the construction and operation of precision inclinometer with the automatic compensation of bias, and also presents the results of prototype studies. The inclinometer is intended for use in laboratory conditions to control the movement of surfaces on which the calibration and testing of sensitive elements of navigation systems is carried out. According to this task, the inclination measurement range for each axis is ±600 arc sec. The sensitive element of the inclinometer is a pendulum accelerometer of compensating type. The rotating platform allows performing two-axis measurements and also provides auto-compensation of the sensitive element bias during long-term operation of the inclinometer. On the basis of a series of experimental data, the instability of the inclinometer during long-term operation (about 15 hours) was analyzed, so the error contributed by the rotating platform drive was assessed and the operation of sensitive elements with different ranges of acceleration measurement was compared.

In Engineering Geodesy, most coordinate frames are aligned with the local vertical. For many measurement tasks, it is therefore necessary to manually (or arithmetically) align sensors or equipment with the local vertical, which is a common source of errors and it is very time consuming. Alternatively, accelerometer triads as part of inertial measurement units (IMUs) are used in several applications for horizon leveling. In this contribution we analyze and develop a method to use accelerometer triads for pole tilt compensation with total stations. Several triad sensor models are investigated and applied in a calibration routine using an industrial robot arm. Furthermore a calibration routine to determine the orientation of the IMU mounted on the pole is proposed. Using variance based sensitivity analysis we investigate the influence of different model parameters on leveling and pole tilt compensation. Based on this inference the developed calibration routines are adjusted. The final evaluation experiment shows an RMS of 2.4 mm for the tilt compensated measured ground point with tilts up to 50 gon.

Low-cost micro inertial measurement unit (MIMU) generally has low accuracy, and needs to be calibrated beforehand in practical engineering applications. Aiming at the problems of separate calibration of accelerometers and gyroscopes, complicated steps, and difficulties in batch calibration in traditional calibration methods, firstly, by analyzing the common features of the accelerometer and gyroscope error model, a unified calibration model based on the principle of least squares is established, which can be used to calibrate the accelerometers and gyroscopes at the same time, and finally a batch calibration test was carried out on several MIMUs, and the accuracy after calibration is comparable to that obtained by the traditional calibration method, which meets the requirements of engineering applications.

No abstract available

No abstract available

MEMS accelerometer, the key component of the Inertial Navigation System (INS), has been widely applied in various electronic consumption fields such as mobile phones and unmanned vehicles. However, it suffers from the scale factor errors, constant biases, and misalignment errors. These calibration errors which are not fully compensated may remain in the initial alignment of the INS, and result in attitude errors. In order to address this problem, this paper presents an efficient calibration method of MEMS accelerometer based on Kaiser filter and the ellipsoid fitting. At first, the raw data from the output of the accelerometer will be filtered by using the Kaiser filter. In the second stage, the mathematical error model of the accelerometer is constructed via ellipsoid fitting. Subsequently, the calibration scheme will be given. The experimental results show that the output of the calibrated tri-axis MEMS accelerometer is close to the standard value, and the absolute error of the pitch angle calculated by the accelerometer is reduced from 4.431 degrees (before compensation) to 0.735 degrees (after calibration). Compared with the traditional six-position calibration method, the accuracy of the MEMS accelerometer is significantly improved more than 36% by applying the proposed algorithm. Therefore, it is feasible and advantageous to apply the presented calibration algorithm for improving the measurement accuracy of the MEMS accelerometer.

The inclinometer for coal mine is limited by the downhole drilling conditions, it usually composed of magnetic sensor and MEMS accelerometer, and the drilling trajectory parameters can be solved through the principle of inclination principle. However, in fact, due to the existence of various errors, before the inclinometer is used, it must be calibrated to correct the error. The traditional method is ellipsoid fitting, which can quickly meet the error compensation of three-dimensional space, but there is a problem of algorithm instability caused by constraint matrix singularity during solution, and the compensation effect is limited. In this paper, an improved ellipsoid fitting calibration algorithm is proposed to solve the above problems and to Secondary compensate for the remaining angle error. The result is that the root mean square error of azimuth angle is reduced from 9.72° to 0.86°, which shows that the improved ellipsoid fitting method has significantly improved the measurement accuracy of the inclinometer.

No abstract available

This paper presents an innovative calibration technique for low-cost MEMS accelerometers, using an Adaptive Neuro-Fuzzy Inference System (ANFIS) optimized by a Genetic Algorithm (GA). The proposed method aims to enhance accuracy in inertial measurement units (IMUs), which are prone to errors such as biases, misalignments, and scalefactor variances. Employing a UR5 robotic arm for performing the motions for the calibration enabled gathering the groundtruth information simultaneously with the sensor readings. The method calibrates IMU data in 3D space using dynamic motions, eliminating the need for high-cost rotation rigs. Separate ANFIS models were trained for each sensor axis using both triaxial accelerometer data and Euler angles, achieving significant error reductions compared to the traditional ellipsoid fitting method. Improvement of 11.34 % could be gained using the ANFIS models compared to the ellipsoid fitting. Experimental results confirm that the proposed ANFIS-GA method effectively compensates deterministic and stochastic errors, enhancing sensor reliability for applications in navigation and motion tracking.

Tilt measurement is commonly achieved by sensing the gravity, its accuracy heavily depends on the calibration procedure. This article investigates accelerometer calibration scheme of a drilling inclinometer and proposes a novel piecewise in-plane calibration scheme to update the calibration coefficients from the results of the ellipsoid fitting (EF) and the plane fitting (PF). According to the motions rotating around the inclinometer frame, the proposed scheme utilizes the maximum likelihood to estimate the adjustment for calibration coefficient, as a modification to the EF + PF scheme. The simulation and experimental results demonstrate that, compared to existing methods in drilling applications, the proposed scheme significantly reduces the error of tilt measurement. Specifically, the proposed inclinometer system achieves an error of less than <inline-formula> <tex-math notation="LaTeX">$- 0.0011^{\circ }~\pm ~0.0108^{\circ }$ </tex-math></inline-formula> (<inline-formula> <tex-math notation="LaTeX">$1\sigma \text {)}$ </tex-math></inline-formula> for the axial tilt angle and less than <inline-formula> <tex-math notation="LaTeX">$- 0.0931^{\circ }~\pm ~0.0735^{\circ }$ </tex-math></inline-formula> (<inline-formula> <tex-math notation="LaTeX">$1\sigma \text {)}$ </tex-math></inline-formula> for the tool face angle.

No abstract available

Smartphones are built with a wealth of sensors, which are characterized by small size, lightweight and low cost, etc. With the popularity of smartphones, developments and applications using smartphone's built-in sensors have attracted increasingly research interest in recent years. However, low-cost sensors have inherent disadvantages, such as low measurement accuracy and poor measurement stability. Therefore, in practical applications, the errors of smartphone's built-in sensors cannot be simply ignored. To estimate the sensor errors, this paper analyzes the error characteristics of low-cost accelerometer, gyroscope and magnetometer respectively, and calibrates each sensor by using improved six-position method, Allan variance method and ellipsoid fitting method. Experimental results of sensor error estimation demonstrate the effectiveness of the calibration methods on the built-in micro-electro-mechanical system (MEMS) sensors of smartphones.

A nonlinear least squares optimization method based on time series has been proposed to address the issue of errors in the Inertial Measurement Unit (IMU) accelerometer under high-frequency operating conditions during bead frame and nozzle attitude following monitoring. By combining the trajectory of the rigid body and the curve of acceleration data, a nonlinear model of the acceleration data curve is first fitted using the Lomb-Scargle method; then, the nonlinear least squares optimization method is used to obtain the optimal nonlinear model; finally, the acceleration values derived from the model are used to calculate the attitude of the rigid body. The experimental results shown that, compared to the traditional method of error compensation for acceleration data, the method of fitting the acceleration data curve can effectively avoid the impact of noise and data drift on the acceleration data, while also improving the precision and stability of the calculated attitude angle.

The existing UAV triaxial accelerometer calibration method is complicated. In order to simplify the operation and ensure the accuracy of the accelerometer, a calibration method based on LM (Levenberg-Marquardt) algorithm is proposed. The error model of UAV triaxial accelerometer system is established. The LM algorithm is used to solve the multi-position data of the accelerometer, and the calibration coefficient of the accelerometer is obtained. The experimental results show that the method can reduce the attitude of the three-axis accelerometer in the calibration process, and can quickly calibrate the three-axis accelerometer to improve the measurement accuracy.

This paper provides a reliable practical implementation of the MEMS gyroscope on the base of MPU-6050 universal triaxial inertial measuring unit with a gyroscope sensor and accelerometer and the microcontroller ATmega328. Presented interconnection of functional modules on the base of I2C protocol has allowed to improve the calibration process and make a zero offset for all orthogonal sensors in gyroscope that in return reduce the additive measurement error. Analysis of electromechanical properties of universal gyroscope has shown different properties of vibrating systems. Sensitive elements signal processing common with developed error model, that includes nonlinearity of sensors characteristics, has allowed to reduce the total measurement error of MEMS gyroscope up to 1%.

Precise geomagnetic azimuth measurement is essential for automation and intelligent operations in deep-Earth and deep-sea resource exploration. However, during drilling, the main sources of azimuth error include the inherent distortion of triaxial accelerometer and triaxial magnetometer, which requires prior calibration. To address this issue, we focus on static azimuth measurements by analyzing the error propagation relationship, developing a comprehensive error correction model, and proposing a correction method that combines piecewise polynomial fitting and improved interpolation. Finally, the proposed algorithm was experimentally validated using a high-precision inclinometer calibration platform. The experiment compared the error correction effects of the three-step combination method and the proposed method. At a confidence level of <inline-formula> <tex-math notation="LaTeX">$p = 0.95$ </tex-math></inline-formula> and an axial tilt of <inline-formula> <tex-math notation="LaTeX">$I = 0.594$ </tex-math></inline-formula>, dA decreased from (<inline-formula> <tex-math notation="LaTeX">$3.1^{\circ }~\pm ~0.9^{\circ }$ </tex-math></inline-formula>) to (<inline-formula> <tex-math notation="LaTeX">$1.8^{\circ }~\pm ~0.5^{\circ }$ </tex-math></inline-formula>) and (<inline-formula> <tex-math notation="LaTeX">$7\times 10^{\mathbf {-4}}~\pm ~3.7\times 10^{\mathbf {-2}}$ </tex-math></inline-formula>) for the traditional and proposed method, respectively. The proposed method demonstrates good performance in azimuth reconstruction and meets the practical engineering demands of azimuth calibration in measurement-while-drilling (MWD) system.

Most current human activity recognition algorithms only focus on a single dimension of either local features or temporal features, and face challenges in balancing high accuracy and real-time performance. In this study, a chest-worn triaxial accelerometer is used as the data source. First, the coordinate origin and gravitational acceleration are corrected through static calibration of the device, and normalization preprocessing is performed on the resultant acceleration. Then, 1D-CNN is utilized to extract local motion features, RNN (LSTM) is employed to model the temporal dependencies of behaviors, and a decision tree is adopted to achieve interpretable classification. Experimental results show that the overall accuracy of the algorithm reaches 94.75% and the precision reaches 95.3%, which is an improvement compared with existing algorithms, and the false alarm rate is lower. This algorithm is lightweight and anti-interference, suitable for wearable devices, and provides reliable technical support for scenarios such as workplace health reminders and sports recording.

This article presents a sensitivity calibration method aimed at minimizing installation, misalignment, and measurement errors, as well as reducing the mutual coupling interference of the sensitive axes of the accelerometer. The proposed method is based on a triaxial shock calibration device consisting of three orthogonal Hopkinson bars and relies on a measurement array of three laser Doppler velocimeters (LDVs). Based on the triaxial shock calibration device, we propose using three sensitivity matrices to characterize the three sensitive axes of the accelerometer. The experimental results show that this method achieves an average relative error of 3.2% and a maximum relative error of 8.1% in solving the excitation acceleration. This method significantly outperforms the other two methods that use a single sensitivity matrix. The results demonstrate the high calibration accuracy and reliability of the proposed method.

Aiming at the error compensation of the accelerometer in drilling, an online accelerometer error compensation method based on a magnetic inertial shark optimizer (MISO) is proposed. First, the error compensation model is established by analyzing the error of accelerometer. Then, the objective function is constructed according to the relationship between the local gravitational acceleration and the theoretical mode value, and the constraint conditions of gravity angle and magnetic-gravity angle are designed by the gyroscope and magnetometer, respectively. In MISO, a magnetometer observation gravity vector model is constructed to predict the optimal solution position; with this position as the center, a fixed-point explosion strategy is proposed to improve the global search ability of error parameters and design a gravity-oriented factor based on the local gravity vector and the fitness value of the current solution to dynamically control the local search. Additionally, an intelligent escape optimal solution search behavior is designed to distinguish whether it is trapped in the local optimal according to the dispersion degree of the historical position of the current solution, and the success rate and speed of escaping the local optimal are improved by position updating simplification and optimal region mutation. Finally, the experimental results show that compared with the Genghis khan shark optimizer (GKSO), the convergence speed of MISO is increased by about 26%, and the average absolute error of inclination is reduced from 3.6° to 0.7°, which improves the measuring accuracy of the accelerometer in drilling.

In this article, the problem of accelerometer error compensation in measurement while drilling (MWD) is addressed by introducing a novel method based on the drilling spider algorithm (DSA) for identifying accelerometer error parameters. First, the output model of the micro electro mechanical system (MEMS) accelerometer is established and the error parameters are organized into a solution vector. Design the objective function of DSA through a nonlinear error function, set adaptive upper and lower bounds dimension by dimension, and simultaneously perform global and local updates to identify the error parameters. Introduce a fast oscillation deviation learning based on the centroid at each update to prevent the algorithm from falling into local optima. Finally, apply the DSA algorithm to identify the error parameters of the accelerometer. The results show that after compensation by DSA, the acceleration error is significantly reduced, the range of the well deviation angle is reduced by about 45%, and the root mean square (rms) error is reduced from 1.6° to 0.6°. Compared with particle swarm optimization (PSO) and Portia spider algorithm (PSA) algorithms, DSA has higher accuracy in identifying the error parameters of MEMS accelerometer.

The rotating accelerometer gravity gradiometer (RAGG) is a gravity gradient measuring instrument designed for moving bases, and as such, the primary technical challenge in RAGG development lies in compensating for motion error. Nevertheless, the existing open research is limited in number and exhibits several limitations: a lack of systematic design for monitoring systems, inadequate model interpretability, missing parameters, and lack of experimental validation, among others. To address these issues, this article proposes a novel approach for compensating RAGG motion error, which encompasses two key contributions: 1) development of a multiparameter compensation model for RAGG motion errors based on the motion transfer mechanism and accelerometer output model; and 2) by leveraging RAGG’s internal accelerometers, only four external sensors are utilized to achieve six-degree-of-freedom motion monitoring, thereby streamlining the motion monitoring system. Furthermore, a six-degree-of-freedom movement platform is utilized to construct an experimental test platform, validating the method’s effectiveness and practical applicability through real experiments. The proposed method is also subjected to comparative experimentation with existing approaches. The experimental results demonstrate that the method presented in this study exhibits superior performance, achieving over three orders of magnitude of compensation capability within the 0.35–0.65-Hz bandwidth, and attaining a motion error compensation level of 99.91%.

The electrostatic accelerometer is the key payload of many space missions, such as satellite gravity measurements, space gravitational experiments, with a typical precision requirement from nano-g to femto-g. The measurement error model analysis is an important issue for the electrostatic accelerometer with numerous error sources. The traditional method by theoretical analysis is complicated to evaluate the complete measurement error models quantitatively especially when the machining and assembly errors of the sensor head are considered. Limited by the earth gravity and seismic noise which is much higher than the intrinsic noise, the complete error model of electrostatic accelerometers can also hardly be tested on ground. In this paper, the method by using finite element analysis of the sensor head is studied. The simulation model for an electrostatic accelerometer sensor head is built, and the multi-conductor capacitance matrix data is simulated. The accuracy of the capacitance simulation is evaluated in three ways including the convergence check of the capacitance with the mesh size, the symmetry verification, and the sensitivity comparison with the theoretical model. Finally, the accelerometer measurement model is analyzed based on the simulation data, using the case of rotating installation misalignment of the upper electrode as an example. The measurement model and error items of one horizontal axis and one rotating axis are quantitatively evaluated. The method proposed in this paper provide a new effective approach to the measurement model analysis of the electrostatic accelerometers in complex working scenarios both in orbit and on ground, which could be helpful to enhance the performance and the efficiency of application.

No abstract available

The algorithm for error correction in the Q-flex accelerometer signal based on the support vector machine (SVM) method is proposed. This method uses the temperature and accelerometer output measured in real time as input parameters. The algorithm is characterized by simple implementation and high speed of processing on computing equipment due to the elegance of the method in linear and nonlinear regression problems. Regularization in SVM eliminates the multicollinearity and reduces the set of coefficients in overfitting. Regularization is equivalent to introducing a priori distribution in the space of coefficients of the approximating model. The results of the compensation of the model obtained by the SVM are presented.

The construction of tilt parameters transducers, the types of primary sensors used, and the angles of spatial orientation that are determined are discussed. The various types of accelerometric sensors that are commonly employed in these transducers are explored. The mathematical models that are used in accelerometer-based three-axis tilt parameters transducers are obtained. These models will help us to understand the sources of instrumental errors that may affect the accuracy of the measured signals. Using these mathematical models, it is possible to implement software and algorithmic methods to correct these errors. This correction process leads to a higher level of accuracy in determining the desired spatial orientation parameters, specifically the zenith angle $\theta$ and roll angle $\boldsymbol{\varphi}$, for both stationary and moving objects.

No abstract available

No abstract available

Micro Electro-Mechanical Systems (MEMS) accelerometers are utilized in safety-critical applications, including airbags, aircraft, medical devices, as well as various consumer electronic applications. Despite providing highly accurate results, they require calibration during production and periodic recalibration due to potential degradation over time. The National Institutes of Standards and Technology (NIST) stipulates that the accuracy of motion sensors used in safety-critical applications must be maintained within a 1% error margin. In our research, we propose an electrical stimulus-based calibration method for sensors during production and in-field use. In-field electrical stimulation and calibration can facilitate prolonged sensor operation without the need to remove the sensor from its environment. Although electrical stimulation has been suggested as a replacement for physical stimulation to reduce testing costs for sensors, it has not yet demonstrated the ability to meet the 1% error requirement mandated by NIST safety standards. We propose an incremental sensor-based model that can correlate sensor sensitivity degradation and process variation to its electrical response for in-field monitoring. Simulations demonstrate that the model can forecast sensitivity changes within a 1% error margin. Additionally, we have developed a cost-effective rotating test platform for calibrating and measuring accelerometer sensitivity. This method utilizes wireless technology to transmit accelerometer data to a computer, eliminating the necessity for lengthy cables. The rotating platform can produce various accelerations at different distances along the radius by spinning at different RPMs, leveraging centripetal force to apply a fixed acceleration at a set RPM.

Accelerometers are versatile devices employed in a variety of areas. However, depending on the application, requirements for accuracy and reliability vary substantially. For instance, stand-alone inertial navigation requires high quality sensors, while integrated navigation can be implemented using inferior - but less costly - accelerometers, especially MEMSs (Microeletromechanical Systems). Nevertheless, such sensors can often have the performance improved by a procedure known as calibration, which estimates and compensate for their systematic errors. As main contribution of this study, we adapt and implement a calibration methodology originally designed for magnetometers in a consumer-grade, MEMS, triaxial accelerometer. The technique, called extended two-step, is based on a pseudo least squares estimation, and is suitable for in-field implementation. Since it is both simple and efficient, it is worth using the methodology for accelerometers as well. This is only possible because, instead of using the Earth's local magnetic field vector, local gravity is employed as reference. In this version, the sensor must be rotated to multiple orientations and kept static, while data is acquired. Biases, scale factors and the nonorthogonalities between the sensors' axes are estimated. Calibration with simulated and real data is conducted in order to validate the adaptation.

Highlights What are the main findings? A comprehensive on-field calibration method for HRG SINS is developed, incorporating hexahedral structural errors. The proposed 24-position accelerometer calibration and 48-rotation gyro calibration schemes enable simultaneous identification of sensor biases, scale factor errors, installation misalignments, and fixture-induced errors. What are the implications of the main findings? The method significantly improves calibration accuracy of both accelerometers and HRGs compared to traditional approaches. It relaxes the mechanical precision requirements of the hexahedral fixture, reducing the cost and complexity of on-field calibration. Abstract On-field calibration for SINS often uses right hexahedron, but the influence of the structure errors, such as mutual position tolerances towards parallelism or the perpendicularity of two arbitrary planes of the hexahedron, on the calibration accuracy is often neglected. In this paper, a hexahedron structure error model and a comprehensive corresponding SINS calibration error model are developed based on hemispherical resonator gyroscope (HRGs). The proposed method introduces the comprehensive hexahedron errors through defining the normal vectors of the exterior surfaces of the hexahedron. A 24-position calibration scheme is designed to identify accelerometer-related errors, while a 48-rotation scheme is developed to identify gyro-related errors. The complete calibration procedure enables simultaneous identification of hexahedron structure errors, installation misalignments, scale factor errors, and biases. Experimental validation is conducted using a high-precision three-axis turntable, which simulates the hexahedron structure errors. The results show that the proposed method significantly improves the calibration accuracy of both accelerometers and HRGs compared with traditional methods. Furthermore, it reduces the accuracy requirements for the hexahedron structure, thus lowering the cost of SINS on-field calibration.

The paper is devoted to the measurement errors investigation that arise due to the influence of MEMS accelerometers' nonlinear characteristics. They appear at large inclination angles of the antenna system support-rotary platform, as well as in the presence of a magnetic inclination, which is due to the peculiarity of the Earth's magnetic field for the magnetometer. The study was conducted to assess the possibility of using such devices to increase the accuracy of a satellite antenna control with a classic rotary platform. The experimental setup for researching the parameters of MEMS sensors allows comparison of measurement results with data obtained from precision optical encoder. The experimental results show the main sources of MEMS sensors errors. An accuracy increasing method of antenna system angular position determining using a triaxial accelerometer and a magnetometer is proposed. The main advantage of the proposed estimation vector determining approach using the least squares method is the possibility of carrying out the calibration procedure without reference to the coordinate system. The method makes it possible to get rid of the zero offset error, as well as compensate for the non-unit scale of the sensor axes and the error of the magnetometer angular orientation. This method can be used for many applications including robotics, design of unmanned aerial vehicles and many other technical systems. The proposed method makes it possible to increase the reliability and reduce the cost of such systems.

No abstract available

With the increasing requirements for accuracy of pendulous integrating gyroscopic accelerometer (PIGA), the key to the development of accuracy of PIGA is the advanced calibration methods. This paper focuses on the calibration method of the main error coefficients of PIGA on the indexing head table. The precise input accelerations and angular velocities are deduced and the complete error calibration model is established based on the corresponding coordinate systems. Then, the orthogonal 4-pose calibration method of dual PIGAs is proposed to identify the harmonic term coefficients of angle error. The calibration uncertainty and efficiency of equal angle sequency and equal acceleration sequency calibration schemes are analyzed. Then, the optimal calibration method is proposed and the complete test process is designed, which can accurately and efficiently calibrate PIGA by compensating with the angle error and combining the two different sequency schemes. Simulation results show that 22-position equal acceleration sequency scheme can calibrate bias and scale factor more accurately and the test cost of equal angle sequency scheme is lower. After compensation with angle error, the magnitudes of calibration uncertainties are decreased from 10−6 to 10−7 and the maximum value of relative fitting accuracy is decreased from 6.6 × 10−5 to 2.7 × 10−5 g by the proposed 22-position optimal calibration method.

No abstract available

The Mercury Orbiter Radio Science Experiment onboard the European Space Agency/Japan Aerospace Exploration Agency (JAXA) BepiColombo mission aims at determining the gravity field and the rotational state of the planet to provide insight into its internal structure and at performing tests of general relativity. The experiment will rely on accurate radiometric data provided by the onboard Ka-band transponder and on measurements of the nonconservative perturbations acting on the spacecraft, provided by the Italian Spring Accelerometer. This paper presents a software implementation of a pseudo-drag-free system which includes the accelerometer measurements in the orbit determination process. Numerical simulations focus on the identification of a suitable calibration strategy to fulfill the experiment goals pertaining to geodesy and geophysics. The achievement of the expected scientific results will depend meaningfully on the quality of the accelerometer data. Perturbative analysis aided in the identification of a calibration strategy for the accelerometer data processing that allows obtaining an unbiased solution and compensating for accelerometer errors.

The rotating accelerometer gravity gradiometer (RAGG) is currently the only practical type of moving-base gravity gradiometer. It is carried by a vehicle along a specific survey path to measure the gravity field of a target region. RAGGs play an important role in resource exploration and auxiliary navigation. The dynamic performance of a RAGG is the key to actual gravity gradient measurement. In order to analyze the dynamic performance of a self-developed RAGG, a calibration test was conducted by mounting the RAGG on a displacement platform with a speed of 1 mm s−1. The measurement results exhibited significant drift and impulse noise, which seriously affect the measurement accuracy and limit the application of conventional methods. In order to suppress the measurement noise of the RAGG, a Laplace distribution model of the measurement noise was established. Combined with maximum likelihood estimation, estimation of the least absolute deviation was proposed to fit and cancel the drift noise and a specific weighted median filter was designed to eliminate the impulse noise. These methods successfully reduced the root mean square error of the RAGG calibration measurement from 76 E to 31 E (where ‘E’ is a unit of gravity gradient), representing a 42% improvement compared with the conventional method and effectively enhancing the measurement accuracy of the self-developed RAGG.

This work is focused on developing a self-calibration algorithm for an orientation estimation of cattle movements based on a quaternion Kalman filter. The accelerometer signals in the earth’s frame provide more information to confirm that the cow is performing a jump to mount another cow. To obtain the measurements in the earth’s frame, we propose a self-calibration method based on a strapdown inertial navigation system (SINS), which does not require intervention by the user once deployed in the field. The self-calibration algorithm uses a quaternion-based Kalman filter to predict the angular orientation with bias correction, and update it based on the measurements of accelerometers and magnetometers. The paper also depicts an alternate update to adjust the inclination using only the accelerometer measurements. We conducted experiments to compare the accuracy of the orientation estimation when the body moves similarly to cow mount movements. The comparison is between the proposed self-calibration algorithm with the IvenSense MPU9250 and Bosch BNO055 and the quaternion attitude estimation provided in the BNO055. The auto-calibrating algorithm presents a mean error of 0.149 rads with a mean consumption of 308.5 mW, and the Bosch algorithm shows an average error of 0.139 rads with a mean consumption of 307.5 mW. When we executed this algorithm in an MPU9250, the average error was 0.077 rads, and the mean consumption was 277.7 mW.

This article proposes a technique to calibrate a low-cost inertial measurement unit (IMU) in the field without relying on expensive laboratory-based equipment. The main parameters to be calibrated in any IMU are misalignment factors, sensitivity scale factors, and gyro and accelerometer biases, all of which are temperature-dependent. Usually, IMU manufacturers have highly accurate and expensive rate tables and centrifuges that can provide high-resolution angular rates to the equipment under test but require costly regular maintenance and highly trained technicians. We propose an alternative method of performing this calibration by hand in the field, using a special Kalman filter that benefits from zero-velocity measurement updates. The performance of the proposed calibration technique is evaluated and validated via extensive simulations and real experiments.

This paper presents a scale factor calibration method based on virtual accelerations generated by electrostatic force. This method uses a series of voltage signals to simulate the inertial forces caused by the acceleration input, rather than frequent and laborious calibrations with high-precision instruments. The error transfer model of this method is systematically analyzed, and the geometrical parameters of this novel micromachined resonant accelerometer (MRA) are optimized. The experimental results demonstrate that, referring to the traditional earth’s gravitational field tumble calibration method, the error of the scale factor calibration is 0.46% within ±1 g by using our method. Moreover, the scale factor is compensated by virtual accelerations. After compensation, the maximum temperature drift of the scale factor decreases from 2.46 Hz/g to 1.02 Hz/g, with a temperature range from 40 °C to 80 °C.

Micro Inertial Measurement Unit (MIMU) is the core component of the micro inertial navigation system. To obtain motion parameters such as the carrier’s high-precision attitude, speed, and position, MIMU often needs to be calibrated and compensated. The traditional high-precision turntable MIMU calibration is complex and the test equipment is expensive. Aiming at the need of low cost and high precision field calibration of MIMU, an improved genetic algorithm was proposed for MIMU error calibration for turntable free. Firstly, the random noise in the MIMU measurement output is pretreated by wavelet denoising method, then the error function is constructed by designing the MIMU multi-position rotation scheme to stimulate the correlation error, and the genetic algorithm is introduced with the error function as the optimization objective function. Finally, the calibration error parameters in the objective function are searched and optimized to identify the deterministic error of the gyroscope and accelerometer in the MIMU, so as to achieve the field calibration of MIMU without relying on other test equipment. Simulation results show that the proposed algorithm has a high MIMU calibration accuracy, with a calibration error of about 4%.

Inertial Measurement Units are widely used in various applications and, hardware-wise, they primarily consist of a tri-axial accelerometer and a tri-axial gyroscope. For low-end commercial employments, the low cost of the device is crucial: this makes MEMS-based sensors a popular choice in this context. However, MEMS-based transducers are prone to significant, non-uniform and environmental-condition-dependent systematic errors, that require frequent re-calibration to be eliminated. To this end, identification methods that can be performed in-field by non-expert users, without the need for high-precision or costly equipment, are of particular interest. In this paper, we propose an in-field identification procedure based on the Total Least Squares method for both tri-axial accelerometers and gyroscopes. The proposed identification model is linear and requires no prior knowledge of the parameters to be identified. It enables accelerometer calibration without the need for specific reference surface orientation relative to Earth’s gravity and allows gyroscope calibration to be performed independently of accelerometer data, without requiring the sensor’s sensitive axes to be aligned with the rotation axes during calibration. Experiments conducted on NXP sensors FXOS8700CQ and FXAS21002 demonstrated that using parameters identified by our method reduced cross-validation standard deviations by about two orders of magnitude compared to those obtained using manufacturer-provided parameters. This result indicates that our method enables the effective calibration of IMU sensor parameters, relying only on simple 3D-printed equipment and significantly improving IMU performance at minimal cost.

Nano- $g$ accelerometers are widely used in space exploration and measurement of the earth’s gravitational field. It is essential to precisely evaluate error effects at high orders such as cross-coupling for applications in a dynamic environment. Nevertheless, it remains challenging to meet the precision requirements using conventional calibration measures. In this article, we propose a method to separate the cross-coupling coefficients of a linear single-axis accelerometer by mounting it on a steadily rotating rate table that is tilted at a fixed deviation angle with respect to the horizontal plane. The gravity component is periodically modulated along the input axis per revolution. Simultaneously, a series of centripetal acceleration is applied along the cross axis in sequence while adjusting the rotation frequency of the rate table by steps. Thus, the cross-coupling coefficient can be separated by its dependence both on the modulated gravity acceleration and the centripetal acceleration. In comparison to the static multipoint angular rotation test on a tilted dividing head, the proposed dynamic modulation method demonstrates improved robustness against corruption from bias drift, with an improved uncertainty. This method to separate the cross-coupling coefficient is suitable for testing high-resolution accelerometers, without requiring high bias stability or sensitive response sustaining at ultralow frequency.

We show that the calibration of tri-axis accelerometers based on the device’s intrinsic properties alleviates the uncertainty due to mounting misalignment in comparison to the use of the sensitivity matrix. The intrinsic properties of a tri-axis accelerometer are based on a (u, v, w) coordinate system that represent the direction of maximum sensitivities of each of the three accelerometers (U, V, W) and are assumed not to be perfectly orthogonal to each other. The calibration procedure requires rotation of the device in the gravitational field around each of the Cartesian coordinate (x, y, z) axes. One component in driving down the uncertainty of laboratory comparisons and calibration repeats relates to misalignment in mounting the device onto the calibration instrument. We show that the uncertainty of the cross-axis terms of the sensitivity matrix is a dominating factor affecting uncertainty down to a 0.01° misalignment at a 100 µV noise level. The misalignment component can be exacerbated when calibrating modern microelectromechanical systems (MEMS)-based accelerometers, which are typically a few millimeters in dimension.

In the field of vibration monitoring and control, the use of low-cost multicomponent accelerometer sensors is nowadays increasingly widespread. Low-cost multicomponent sensors allow implementing monitoring systems and networks (even very extensive ones) supported by a very large number of sensors, with low management costs, low power consumption, light weight and small size. In many advanced engineering applications, such as defects prevention and malfunctioning of systems, smart industries development, automation and machine learning managing, it is often necessary to “densify” the spatial resolution of the surveys, to detect more in detail the occurring dynamic phenomena, under investigation. However, for the monitoring systems to provide trustworthy and actually meaningful data, the reliability of sensors is an essential requirement. As a consequence, traceable calibration methods for multicomponent accelerometer sensors, including the appropriate uncertainty evaluation, are necessary to guarantee the reliability in the frequency domain of data provided. Proper metrological characterizations and calibration of these sensors allows to define the reliability in terms of sensitivity, with respect to mechanical reference standards, traceable to SI units. At present, the sensitivity parameters provided by the manufacturers are not traceable and often referred to static conditions only: dynamic response, as a function of frequency, is often barely known or completely disregarded. In this paper, a dynamic calibration procedure is applied to provide the sensitivity parameters of a low-cost multicomponent accelerometer sensor prototype, designed, developed and realized at the University of Siena, conceived for rolling-bearings vibration monitoring, in a broad frequency domain, from 10 Hz up to 20 kHz. The calibration procedure is performed by comparison to a reference transducer (in analogy to ISO Standard 16063–21).

The paper describes a robust technique implemented into the inclinometer based on Lookup Table (LUT) Filter. The filter memorizes the acceleration data corresponding to the angle of inclination as an ideal curve graph of Microelectromechanical Systems (MEMS) accelerometer. This technique works as not only acceleration calibration but also a powerful tool of inclination measurement. A high precision robust setup for inclinometer calibration and metrology was built. The proposed method is applied to two axis-inclinometer with a maximum error of 0.2 degrees. For industrial applications, Control Area Network open (CANopen) is used as an embedded network communication system. The experiment includes both static and dynamic procedures to justify the accuracy as well as the stability of the operating system. The project was carried out at the ‘Sensor System’ in Italy, which is an industrial company in the inclinometer field.

This report presents the results of the APMP comparison in the area of 'vibration', which here refers to the calibration of the accelerometer standards set in compliance with method 1 or method 3 as recommended in the international standard ISO 16063-11:1999.The participants have reached a consensus and considered the most appropriate method, then referred to CCAUV.V-K3 report, the weighted mean and the degrees of equivalence were evaluated for this particular comparison. The calculation of the key weighted mean was in accordance with the Guidelines for CIPM key comparisons.The "linking" procedure was applied to establish the relationship between the results of the participants and those of the CIPM comparison in the field of vibration, which was CCAUV.V-K3. Only one pilot laboratory, NIM, acted as the linking laboratory. The linking factors were defined as the ratio and difference for magnitude and phase shift respectively through the NIM results in CCAUV.V-K3 and APMP.AUV.V-K3.1. Using the linking factors, this RMO results of six participants were directly compared with the results of CCAUV.V-K3. To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database https://www.bipm.org/kcdb/. The final report has been peer-reviewed and approved for publication by the CCAUV, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

No abstract available

In order to quickly complete the calibration of the micro-accelerometer, improve the calibration accuracy and reduce calculation amount, a Newton iterative-particle swarm optimization algorithm (NI-PSO) combining the Newton iteration and the PSO algorithm in the intelligent algorithm is proposed. The algorithm completes the modulus observation calibration of the micro-accelerometer without turntable. Based on the theory of modulus observation, this scheme transforms the calibration problem of the three-axis micro accelerometer into a non-linear function extreme optimization problem. Then, apply the PSO algorithm to solve the nonlinear extreme optimization problem. After reaching certain accuracy, switch to classic Newton iteration algorithm, and use the optimal result as the initial value of the Newton iteration. The proposed method solves the problem of the sensitivity of Newton iterative algorithm to the initial value and the problem that the convergence speed of the PSO algorithm decreases after a certain number of iterations. The simulation results show that the method proposed in this paper avoids the stringent requirements of conventional accelerometer calibration for experimental equipment, and the calibration accuracy is improved by 2 orders of magnitude relative to the Newton iteration, and 1 order of magnitude higher than that of the PSO algorithm The new NI-PSO based calibration method of micro-acceleration provides a valuable reference for engineering application.

Field calibration is an important method to guarantee the accuracy of a strapdown inertial navigation system. Zero velocity update based on the zero-velocity constraint when the carrier is without translational motion is a typical system-level calibration method. In zero velocity update, there is a coupling between biases and horizontal misalignment angles. The accuracy of horizontal misalignment angles is determined by the equivalent accelerometer biases in horizontal directions, which means that improving the accuracy of horizontal angles needs accurate calibration of accelerometer biases. Meanwhile, alignment with gravitational apparent motion is widely used taking advantages of its alignment ability in a swinging condition. But it is an analytical method and cannot calibrate sensor biases and is always dealt as a coarse alignment method. In order to calibrate accelerometer biases and utilize advantages of the alignment method with gravitational motion, a method to estimate accelerometer biases based on an iterative optimization method and gravitational apparent motion is presented in this paper. First, accelerometer biases are introduced to calculate apparent acceleration and an objective function is constructed. Then, Newton's iteration is applied to iteratively optimize the parameters describing gravitational apparent motion and accelerometer biases. As revealed by the theoretical analysis and experimental results, different patterns of gravity and accelerometer biases will be generated when the carrier exhibits a swinging motion; thus, the convergence of the proposed algorithm will be ensured. After accelerometer biases are removed, initial alignment performed with the gravitational apparent motion reconstructed by the estimated parameters gives nearly zero horizontal misalignment angles.

In recent years, the calibration method of Strapdown gravimeter has become the bottleneck of relative gravity measurement accuracy. Based on this situation, this thesis studies the parameter iterative calibration method of SGA-WZ03 strapdown gravimeter to break the bottleneck of relative gravity measurement and further improve the measurement accuracy of relative gravimeter in flight experiment through the improvement of calibration method Degree. The parameter iterative estimation algorithm is based on the pulse output model of a single accelerometer to establish the linear pulse output model of the accelerometer components. Using the idea of parameter separation, the two-step iterative estimation of the model parameters and the tilt vector can complete the calibration of the linear model and the secondary model of the accelerometer. Compared with the traditional 24 bit calibration method, the parameter estimation iterative estimation calibration method has better stability than the traditional method.

No abstract available

A simple systematic calibration method based on acceleration and angular rate measurements is introduced for the fiber-optic gyro strapdown inertial navigation system in this paper. Meanwhile, a unified mathematical framework and an iterative calculation method are designed for the systematic calibration method. Using this method, one can estimate the fiber-optic gyro inertial measurement unit (FOG IMU) parameters both at a manufacturer's facility and in the field. In order to get all FOG IMU parameters, a procedure adopted based on this approach consists of two stages: First, FOG IMU raw data (accelerometer and gyro readouts) are accumulated in 19 specified FOG IMU positions. Second, the accumulated data are processed by special software to estimate all FOG IMU parameters. In addition, observability analysis of the method in 19 specified FOG IMU positions is done without the limitation of FOG IMU's initial orientation, and this analysis provides theoretical support for the application in a complex terrain. Moreover, the influence of gravity disturbance is analyzed for the first time. The analysis and experiment results show that the systematic calibration method provided by this work can meet the requirement of FOG IMU calibration.

No abstract available

Accelerometers are increasingly used to observe human behavior such as physical activity under free-living conditions. An important prerequisite to obtain reliable results is the correct calibration of the sensors. However, accurate calibration is often neglected, leading to potentially biased results. Here, we demonstrate and quantify the effect of accelerometer miscalibration on the estimation of objectively measured physical activity under free-living conditions. The total volume of moderate to vigorous physical activity (MVPA) was significantly reduced after post hoc auto-calibration for uniaxial and triaxial count data, as well as for Euclidean Norm Minus One and mean amplitude deviation raw data. Weekly estimates of MVPA were reduced on average by 5.5, 9.2, 45.8, and 4.8 min, respectively, when compared to the original uncalibrated estimates. Our results indicate a general trend of overestimating physical activity when using factory-calibrated sensors. In particular, the accuracy of estimates derived from the Euclidean Norm Minus One feature suffered from uncalibrated sensors. For all modalities, the more uncalibrated the sensor was, the more MVPA was overestimated. This might especially affect studies with lower sample sizes.

Adults with intellectual disabilities experience numerous health inequalities. Targeting unhealthy lifestyle behaviours, such as high levels of sedentary behaviour and overweight/obesity, is a priority area for improving the health and adults with intellectual disabilities and reducing inequalities. Energy expenditure is a fundamental component of numerous health behaviours and an essential component of various free-living behaviour measurements, e.g. accelerometry. However, little is known about energy expenditure in adults with intellectual disabilities and no population-specific accelerometer data interpretation methods have been calibrated. The limited research in this area suggests that adults with intellectual disabilities have a higher energy expenditure, which requires further exploration, and could have significant impacts of device calibration. However, due to the complex methods required for measuring energy expenditure, it is essential to first evaluate feasibility and develop an effective protocol. This study aims to test the feasibility of a laboratory-based protocol to enable the measurement of energy expenditure and accelerometer calibration in adults with intellectual disabilities. We aimed to recruit ten adults (≥ 18 years) with intellectual disabilities. The protocol involved a total of nine sedentary, stationary, and physical activities, e.g. sitting, lying down, standing, and treadmill walking. Each activity was for 5 min, with one 10 min lying down activity to measure resting energy expenditure. Breath by breath respiratory gas exchange and accelerometry (ActiGraph and ActivPAL) were measured during each activity. Feasibility was assessed descriptively using recruitment and outcome measurement completion rates, and participant/stakeholder feedback. Ten adults (N = 7 female) with intellectual disabilities participated in this study. The recruitment rate was 50% and 90% completed the protocol and all outcome measures. Therefore, the recruitment strategy and protocol are feasible. This study addresses a significant gap in our knowledge relating to exercise laboratory-based research for adults with intellectual disabilities The findings from this study provide essential data that can be used to inform the development of future protocols to measure energy expenditure and for accelerometer calibration in adults with intellectual disabilities.

No abstract available

Inertial navigation technology stands as a prominent and widely adopted solution in the realm of vehicular applications that demand meticulous and reliable navigation. In these applications, accelerometers serve as a vital source of data for inertial navigation system, supplying crucial information in acceleration. However, when the navigation system is used in an outdoor setting over an extended period of time, the complex dynamic environment causes the nonlinear error parameters of the accelerometers to change. This results in erroneous output data, thereby reducing navigation accuracy. The current calibration methods for accelerometers rely heavily on the measurement equipment, such as high-precision tri-axial rotary tables or centrifuges. These results in the existing calibration methods are limited to laboratory settings, with the application to outdoor scenarios being challenging. Swarm intelligent optimization algorithms offer a novel approach to this problem. This paper proposes an accelerometer calibration strategy based on a hybrid boundary dynamics optimization (HBDO) algorithm, with the aim of achieving high-precision calibration of accelerometers in the absence of accurate and expensive measurement equipment. The results of extensive experimentation demonstrate that the accelerometer calibration strategy based on the HBDO algorithm is equivalent to the system-level calibration method using precision measurement equipment in static navigation experiments, which achieve equivalent navigation accuracy.

The use of high-sensitivity (∼100 V (m s−2)−1) piezoelectric accelerometers is becoming increasingly prevalent in microvibration (∼10−2 m s−2) measurement for satellite attitude stabilization and machinery health monitoring. Calibration with microvibration identical to those in real scenarios is needed to ensure the reliability of such accelerometers. We conducted primary calibration at a low vibration level (<10−2 m s−2) from 5 Hz to 6.3 kHz, resulting in a small half-peak-to-peak displacement amplitude of 1.4 pm. The calibration uncertainties of magnitude and phase shift (the median value throughout the frequency range) are 1.9% and 0.76°, respectively. To the best of our knowledge, this study has the lowest vibration level used for primary accelerometer calibration in this frequency range, ensuring the reliability of microvibration measurement.

Micro-Electro Mechanical Systems (MEMS) arrays can reduce outliers in Inertial Measurement Units (IMUs) through data fusion. But there are various errors in low-cost IMUs that can lead to abnormal array fusion. To improve the fusion effect, IMU calibration is crucial. At present, most calibrations only focus on six axis IMU calibration. Considering the need for magnetometers to provide heading angle information in attitude estimation and the ability of array fusion to improve attitude estimation accuracy, we proposes a nine axis MEMS array fusion calibration method. Firstly, collect twenty-four types of static data and attitude change data by manually rotating the IMU. Then, the accelerometer calibration is completed using static data, the gyroscope calibration is completed based on the calibrated accelerometer and attitude changes, and the magnetometer calibration is completed based on the calibrated accelerometer and local magnetic vectors. Finally, array fusion is achieved by updating the calibrated IMU weights in real-time through an adaptive support matrix. The above method completes the calibration and fusion of the nine axis IMU through simplified rotation operations, without relying on precision equipment assistance, making the entire process simple and efficient. The effectiveness and reliability of the method were verified through testing in various environments based on the designed hardware.

No abstract available

The rotational inertial navigation system (RINS) modulates horizontal sensor errors by rotating the inertial measurement unit (IMU) around the vertical axis. In applications demanding high azimuth accuracy, it is essential to mitigate azimuth errors caused by vertical sensor inaccuracies through horizontal rotational modulation. Therefore, this paper proposes a novel rotational strategy that rotates the IMU around the horizontal east axis. A challenge with this approach is that constant biases of the eastward-facing inertial measurement sensors cannot be modulated. This issue is particularly pronounced during long-duration navigation, where accelerometer bias varies with temperature, leading to significant velocity oscillation error and positioning error. To address this problem, this paper primarily investigates methods for the online calibration and compensation of temperature-related errors of eastward accelerometer bias under this new rotational strategy. Simulation and experimental results demonstrate that using the proposed method significantly reduces the velocity oscillations and improves the navigation accuracy of the RINS.

This paper calibrates deterministic errors in accelerometer data from 20 commercial Movella DOT IMUs across four institutions. Applying Jeff Ferguson’s calibration of deterministic errors through a six-point tumble test, we assess accuracy and precision. The results show fixed bias/offset as the dominant error, with larger errors in the z axis. Calibration significantly improves precision and accuracy for gravity-aligned measurements, regardless of institution or axis. Although less effective near-zero values due to sensor sensitivity, this research confirms the method’s effectiveness for enhancing IMU data reliability.

This paper proposes a method of accurately calibrating the second-order coefficient of accelerometer in platform inertial navigation system(PINS) being calibrated by double turntable centrifuge. Firstly, the errors of specific force caused by the angular rate error about spindle system of the centrifuge are derived, and the relationship between the PINS’s output displacements and the centrifuge errors, the accelerometer errors is developed. By way of this, a test plan of calibrating the second-order coefficient of accelerometer by the identification with twice least squares method is drawn up. Secondly, the test plan can separate the angular rate error and the second-order coefficient of accelerometer from the output displacement errors of the PINS’s, and eliminate the effect of the angular rate error on the calibration accuracy of the second-order coefficient, so the calibrating accuracy of the second-order coefficient is greatly raised. Finally, simulation results verified that the calibration accuracy of the second-order coefficient of the accelerometer can be raised to an order of 10-7g/g2. 

In order to achieve calibration of the performance indicators of FBG accelerometers, this study proposes a vibration table calibration method. By establishing the relationship between displacement and acceleration, a method for setting the vibration table output frequency and output acceleration is obtained. Taking a three-axis FBG accelerometer as an example, the study investigates its time-domain and frequency-domain waveforms after calibration on the vibration table, obtaining empirical representations of its resonance frequency and operating frequency band. Finally, an empirical calculation formula representing its sensitivity is derived, providing important reference for parameter calibration of FBG accelerometers and similar vibration sensors.

The electro-optical pod is an important optical payload of the drone, provides the operators with the required visual images, serves as a crucial basis for command decisions. The Strapdown Inertial Navigation System (SINS) in the electro-optical pod utilizes signals collected by the Inertial Measurement Unit (IMU) to provide the drone with precise positioning and navigation capabilities. The FOG (Fiber Optic Gyroscope)–MEMS (Micro-Electro-Mechanical Systems) accelerometer SINS combines the advantages of optical gyroscopes and MEMS accelerometers, with high performance, small size, and low power consumption characteristics. It has gradually become a optional choice for unmanned aerial vehicle electro-optical pod. As an important feedback component in the control loop of electro-optical pod, SINS needs to be periodically calibrated and compensated for its errors in order to ensure the stability of the electro-optical gimbals during actual stabilization processes. Taking into account the measurement and error characteristics of the SINS, a mathematical error model is established considering the asynchronous time between the gyroscope and accelerometer, inner lever arm error, outer lever arm error, and quadratic error of the FOG-MEMS accelerometer SINS. A 40-D Kalman filter is formed based on the velocity error observation and position error observation, and a reasonable calibration path is used to estimate the system error parameters. The effectiveness of the system-level calibration method is verified through semi-physical simulation experiment and real experiments.

Optical sensors are a promising technology in structural and health monitoring due to their high sensitivity and immunity to electromagnetic interference. Because of their high sensitivity, they can register the responses of buildings to a wide range of motions, including those induced by ambient noise, or detect small structural changes caused by aging or environmental factors. In previous work, an FBG-based accelerometer was introduced that is suitable for use as an autonomous unit since it does not make use of any interrogator equipment. In this paper, we present the results of the characterization of this device, which yielded the best precision and accuracy. The results show the following: (i) improvements in the orthogonality of the sensor axes, which impact their cross-axis sensitivity; (ii) reductions in the electronic noise, which increase the signal-to-noise ratio. The results of our static characterization show that, in the worst case, we can obtain a correlation coefficient R2 of 0.9999 when comparing the output voltage with the input acceleration for the X- and Y-axes of the sensor. We developed an analytical, non-iterative, 12-parameter matrix calibration approach based on the least-squares method, which allows compensation for different gains in its axes, offset, and cross-axis. To improve the accuracy of our sensor, we propose a table with correction terms that can be subtracted from the estimated acceleration. The mean error of each estimated acceleration component of the sensor is zero, with a maximum standard deviation of 0.018 m/s2. The maximum RMSE for all tested positions is 6.7 × 10−3 m/s2.