加速度计转台标定

… In traditional calibration methods, although the accelerometer nonlinear scale factor … calibration method for the accelerometer nonlinear scale factor on a low-cost three-axis turntable …

For linear accelerometers, calibration with a precision centrifuge is a key technology, and the input acceleration imposed on the accelerometer should be accurately obtained in the calibration. However, there are often errors in the installation of sample that make the calibration inaccurate. To solve installation errors and obtain the input acceleration in the calibration of the accelerometer, a calibration method based on the rotation principle using a double turntable centrifuge is proposed in this work. The key operation is that the sub-turntable is rotated to make the input axis of the accelerometer perpendicular to the direction of the centripetal acceleration vector. Models of installation errors of angle and radius were built. Based on these models, the static radius and input acceleration can be obtained accurately, and the calibration of the scale factor, nonlinearity and asymmetry can be implemented. Using this method, measurements of the MEMS accelerometer with a range of ±30 g were carried out. The results show that the discrepancy of performance obtained from different installation positions was smaller than 100 ppm after calibrating the input acceleration. Moreover, the results using this method were consistent with those using the back-calculation method. These results demonstrate that the effectiveness of our proposed method was confirmed. This method can measure the static radius directly eliminating the installation errors of angle and radius, and it simplifies the accelerometer calibration procedure.

… squares we can solve scale factor calibration matrix of accelerometers. Step 4:Rotate the outer frame four symmetrical position when the accelerometers are sampling(The experiments …

The paper suggests a new approach to calibration of a micromechanical inertial measurement unit. The data are collected on a simple rotating turntable with horizontal (or close to) rotation axis. For such a turntable, an electric screwdriver with fairly low rotation rate can be used. The algorithm is based on the Fourier transform applied to the rotation experimental data, implemented as FFT. The frequencies and amplitudes of the spectral peaks are calculated and collected in a small set of data, and calibration is done explicitly with these data. Calibration of an accelerometer triad and choosing the IMU coordinate frame are reduced to approximating the collected data with an ellipsoid in three dimensions. With rotation frequency calculated as the peak frequency of accelerometer readings, calibration of the gyros is a straightforward linear least square problem. The algorithm is purely algebraic, requires no iterations and no initial guess on the parameters, and thus encounters no convergence problems. The algorithm was tested both with simulated and experimental data, with some promising results.

… of gyros and accelerometers; in this case, the parameters to be calibrated are determined … calibration, determined from the readings of the turntable angle sensors; for scalar calibration, …

… This paper employs a discrete calibration method for calibrating the accelerometers and gyroscopes of MEMS-IMUs separately. Sensor data from six different positions are collected, …

… Considering the challenges to low-frequency calibration with vibration exciters, we present … -turntable is locked, we can do the centrifuge test of accelerometer on the double turntable …

Aiming at the high requirements of the experimental equipment for the measurement of high precision quartz flexible accelerometer resolution, the gravity measured by high precision tri-axial accelerometers was subdivided by the tri-axial turntable. Tri-axial quartz flexible accelerometers resolution measurement model was established and general mathematical expression for the resolution measurement was derived. Based on the mathematical expression, the effective angle range that satisfied the measurement condition was given out. Besides, the tri-axial quartz flexible accelerometers resolution measurement process was designed. Within the effective angle range, numerical simulations were performed and the simulation results showed that: the proposed method can theoretically measure tri-axial quartz flexible accelerometers of which the resolution was about 10−6g. Then the tri-axial quartz flexible accelerometers resolution repetitive measurement experiments were carried out and the experimental results illustrated that: the difference between the measured value with the theoretical value is within $1~\mu \text{g}$ , which met the requirements for use. In addition, the resolution of tri-axial quartz flexible accelerometers can be measured at one time based on the designed process, demonstrating that the proposed method was valid.

Inertial Measurement Unit (IMU) calibration accuracy is easily affected by turntable errors, so the primary aim of this study is to reduce the dependence on the turntable’s precision during the calibration process. Firstly, the indicated-output of the IMU considering turntable errors is constructed and with the introduction of turntable errors, the functional relationship between turntable errors and the indicated-output was derived. Then, based on a D-suboptimal design, a calibration method for simultaneously identifying the IMU error model parameters and the turntable errors was proposed. Simulation results showed that some turntable errors could thus be effectively calibrated and automatically compensated. Finally, the theoretical validity was verified through experiments. Compared with the traditional method, the method proposed in this paper can significantly reduce the influence of the turntable errors on the IMU calibration accuracy.

… The TS algorithm is based on an estimation of linear minimum mean square error, which is applied in accelerometer calibration. More details of this algorithm are described in Šipoš et …

… , it is essential to design different attitudes for accelerometers and … the calibration problem when a turntable cannot provide continuous rotation, this paper presents a new calibration …

This paper presents a calibration method for Micro-Electro-Mechanical Systems Inertial Measurement Unit (MEMSIMU) based on a three-axis turntable, utilizing the turntable to perform offline calibration of error parameters for MEMS accelerometers and MEMS gyroscopes. The sources of error in MEMS-IMU were analyzed, and error models for accelerometers and gyroscopes were established based on zero bias error, scale factor error, and cross-axis coupling error. This paper designed multi-position static calibration experiments and positive-negative angular position calibration experiments to calibrate the accelerometers and gyroscopes. The error parameter matrices for the accelerometers and gyroscopes were determined using the least squares method to compensate for the sensor data. To verify the calibration effectiveness, experiments comparing the original sensor data with the compensated data were conducted. The results demonstrate that this method has improved the consistency of the three axes of the MEMS-IMU, reduced the zero bias error, and enhanced the positioning accuracy.

Received: 19 March 2019 Accepted: 10 July 2019 To optimize the systematic calibration of strapdown inertial navigation system (SINS), this paper derives a systematic calibration model according to the relationship between IMU’s errors and velocity errors output by navigation algorithm of IMU. Then, the advantages of horizontal three-axis turntable (3AT) where IMU errors are calibrated were utilized to decouple the mounting misalignments of the IMU, and an equal interval rotation test plan was designed to provide 16 rotation stimuli for the IMU. On the basis of it, the three sets of coupling relations of IMU’s mounting misalignments were decoupled, and the systematic calibration model was applied successfully in identifying 21 errors, including scale factor errors, biases and mounting misalignment. The simulation results show that, when the accelerometers and gyros in the IMU were at the accuracies of 10μg and 0.01/h, respectively, the uncertainty of the accelerometer biases was 3.6g and of the gyro’s biases was 0.004/h. Finally, a 24h pure inertial navigation simulation was conducted in static positions. The attitude errors of systematic calibration are 6 in the xand y-directions, and 2.2 in the z-direction, respectively, the maximum velocity error of systematic calibration was smaller than 0.3m/s. These results fully demonstrate the effectiveness of the systematic calibration method for the IMU calibrated on horizontal 3AT. This method suppresses the effects of turntable errors, and enhances the calibration accuracies of IMU.

… The error model of MEMS accelerometers is similar to that of gyroscopes, and since this … on a three-axis turntable under a gravitational field of 1g, only the accelerometers are varied in …

Rectification error is a critical characteristic of inertial accelerometers. Accelerometers working in operational situations are stimulated by composite inputs, including constant acceleration and vibration, from multiple directions. However, traditional methods for evaluating rectification error only use one-dimensional vibration. In this paper, a double turntable centrifuge (DTC) was utilized to produce the constant acceleration and vibration simultaneously and we tested the rectification error due to the composite accelerations. At first, we deduced the expression of the rectification error with the output of the DTC and a static model of the single-axis pendulous accelerometer under test. Theoretical investigation and analysis were carried out in accordance with the rectification error model. Then a detailed experimental procedure and testing results were described. We measured the rectification error with various constant accelerations at different frequencies and amplitudes of the vibration. The experimental results showed the distinguished characteristics of the rectification error caused by the composite accelerations. The linear relation between the constant acceleration and the rectification error was proved. The experimental procedure and results presented in this context can be referenced for the investigation of the characteristics of accelerometer with multiple inputs.

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%.

… output value contains variety of errors and the test turntable includes positioning error which is caused by measured angle error, control system positioning accuracy, verticality and …

… covariances of the estimated parameters k are known, we can construct an n-… twoaxes turntable is to be fixed on the test region of a centrifuge. The outer axis (tilt axis) of the turntable is …

The attitude accuracy of the existing rotational inertial navigation system (RINS) is affected by oscillatory attitude errors caused by the installation errors of rotation axes or inertial sensors. Additional equipment is required to estimate installation errors under dynamic conditions. Methods that use the output of a single RINS to estimate installation errors under dynamic conditions are currently lacking. To address this challenge, this study proposes an installation error estimation method that combines a correlation method, an averaging method, and the Kalman filter. The proposed method adopts a correlation method to increase the signal-to-noise ratio, an averaging method to block certain sine signals, and the Kalman filter to identify installation errors in real time. Simulation, turntable, and sea tests were conducted to verify the proposed algorithm. Results show that the estimation accuracy of installation errors is at 10 arcsec levels, which indicates that said errors are estimated accurately using the RINS output initially obtained under dynamic conditions.

… Adjust the turntable so that the accelerometer inputs are [−1, 0, 0]T , [0, 0, 1]T , [0, 1, 0]T , [0, 0… Select 279 s of output data for error parameter identification in the experiment. The signal is …

… It is necessary to re-calibrate the inertial measurement unit (IMU) parameters for … and move back to the indoor laboratory with high precision turntable, which is costly and has a heavy …

High precision calibration of Micro inertial measurement unit (MIMU) for large installation misalignment can improve the instrument and the practical use of the system precision. It can use high precision turntable to get the coarse value of installation misalignment angle as the optimization initial value, and take the standard deviation of turntable angular rate and the acceleration of gravity as the optimum index to find MIMU misalignment parameters using artificial fish swarm algorithm. Simulation and analysis are carried out based on the position and rate experiment. In addition, static navigation test is taken by using self-developed MEMS heading and attitude measurement system. Both the simulation and experimental results show that this method can improve the calibration accuracy of MIMU effectively with reduced of heading and attitude error.

Artificial fish swarm algorithm (AFSA) is one of the state-of-the-art swarm intelligence techniques, which is widely utilized for optimization purposes. Triaxial accelerometer error coefficients are relatively unstable with the environmental disturbances and aging of the instrument. Therefore, identifying triaxial accelerometer error coefficients accurately and being with lower costs are of great importance to improve the overall performance of triaxial accelerometer-based strapdown inertial navigation system (SINS). In this study, a novel artificial fish swarm algorithm (NAFSA) that eliminated the demerits (lack of using artificial fishes’ previous experiences, lack of existing balance between exploration and exploitation, and high computational cost) of AFSA is introduced at first. In NAFSA, functional behaviors and overall procedure of AFSA have been improved with some parameters variations. Second, a hybrid accelerometer error coefficients identification algorithm has been proposed based on NAFSA and Monte Carlo simulation (MCS) approaches. This combination leads to maximum utilization of the involved approaches for triaxial accelerometer error coefficients identification. Furthermore, the NAFSA-identified coefficients are testified with 24-position verification experiment and triaxial accelerometer-based SINS navigation experiment. The priorities of MCS-NAFSA are compared with that of conventional calibration method and optimal AFSA. Finally, both experiments results demonstrate high efficiency of MCS-NAFSA on triaxial accelerometer error coefficients identification.

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.

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.

Inertial measurement unit (IMU) comprising of the accelerometer and gyroscope is prone to various deterministic errors like bias, scale factor, and nonorthogonality, which need to be calibrated carefully. In this paper, a survey has been carried out over different calibration techniques that try to estimate these error parameters. These calibration schemes are discussed under two broad categories, that is, calibration with high-end equipment and without any equipment. Traditional calibration techniques use high-precision equipment to generate references for calibrating inertial sensors and are generally laboratory-based setup. Inertial sensor calibration without the use of any costly equipment is further studied under two subcategories: ones based on multiposition method and others with Kalman filtering framework. Later, a brief review of vision-based inertial sensor calibration schemes is also provided in this work followed by a discussion which indicates different shortcomings and future scopes in the area of inertial sensor calibration.

A review of various calibration techniques of MEMS inertial sensors is presented in this paper. MEMS inertial sensors are subject to various sources of error, so it is essential to correct these errors through calibration techniques to improve the accuracy and reliability of these sensors. In this paper, we first briefly describe the main characteristics of MEMS inertial sensors and then discuss some common error sources and the establishment of error models. A systematic review of calibration methods for inertial sensors, including gyroscopes and accelerometers, is conducted. We summarize the calibration schemes into two general categories: autonomous and nonautonomous calibration. A comprehensive overview of the latest progress made in MEMS inertial sensor calibration technology is presented, and the current state of the art and development prospects of MEMS inertial sensor calibration are analyzed with the aim of providing a reference for the future development of calibration technology.

Inertial measurement unit (IMU) calibration is essential to ensure the successful operation of various navigation systems. This article describes a novel method for self-calibration of IMU with distributed sensor architectures. The IMU is composed of modules that are distributed along the measurement axes. Each module is equipped with a single-axis gyroscope and three-axis accelerometer sensors. The modules have also their own signal-conditioning circuits and processors. This enables single-axis calibration of the module with a servo system based on a piezoelectric actuator (PEA). The proposed IMU and calibration method are capable of on-site self-calibration. The calibration is performed with the sinusoidal movements generated by the servo system. Despite the limited displacement of the PEA, high angular velocity and tangential acceleration can be achieved with the servo system. Thus, the gyroscope sensor can be directly calibrated with the angular velocity produced by the servo system. On the other hand, the calibration parameters of the accelerometer are determined by using the tangential and centripetal acceleration produced by the servo system. With the proposed method, the bias, scale factor, and installation errors of accelerometer and gyroscope sensors can be determined. The method has been analyzed by conducting experiments with a prototype IMU. In addition, experiments on 3-DoF turntables have been conducted to confirm the effectiveness of the proposed self-calibration method.

… calibration uses precise alignment of a multi-axis turntable to the local level frame (LLF). The IMU is mounted on the aligned turntable … position calibration to calibrate the inertial sensors. …

… In order to obtain the proper sensor outputs for calibration, a 2 or 3-axis turntable was used … assumed that the inertial sensors used in the RIMU are low-grade MEMS sensors. Therefore, …

… The turntable was designed to be rigid to provide a solid base for the moving platform. The calibration data collection board is mounted on top of the turntable and is directly connected …

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.

… , the deterministic error sources have been estimated and used for calibration. Both of … the error characterization of MEMS-based accelerometer and suggested a stochastic model to …

Accelerometers are used in a wide variety of applications including inertial navigation systems and activity monitors. In order to reduce systematic and random errors and improve accuracy and precision, this paper proposes a differential accelerometer system where two triaxial accelerometers are combined in opposite directions. The differential system allows to create additional constraints that can be used for improving calibration and estimation. Calibration methods based on nonlinear optimization are suggested to determine the offset and the scaling vectors. The differential system also permits to determine and update the offset and the scaling factors dynamically based on the system’s constraints. Sensor fusion is accomplished using a weighted least squares method. Experiments are carried out to evaluate and validate the system and the proposed methods including comparison with a single accelerometer system. It is shown that the differential system facilitates and improves acceleration estimation in terms of accuracy and precision.

… error model is first introduced and thereafter the calibration models are constructed for gyroscopes, accelerometers, … In the models, all the reference signals are presented in the same …

… accurately calibrate nonlinear error coefficients of accelerometer … Centrifuge calibration method can continuously provide a … excite the nonlinear errors of accelerometer components and …

Measurement is a process to find out the object quantity in a certain unit. Accelerometer sensor is an inertial measurement unit that can be used to measure the motion states of certain objects either static or dynamic. The accelerometer as a measurement tool must be reliable and valid in expressing the value. So, the accelerometer must be calibrated first before being used to measure the motion state of the object. In this paper, we propose the polynomial curve fitting method for calibrating the accelerometer sensor. Basically, this accelerometer sensor works based on the Analog to Digital Converter (ADC) principle where it converts the tilt of the sensor to the corresponding voltage. It should be noted that this accelerometer consists of a triple-axis where all of the axes have the same input-output value. Hence, by collecting the data that contains a number of the tilts of the sensor and the corresponding voltages, it is possible to generate the mathematical model that maps the tilts of the accelerometer sensor to the corresponding voltages. From the experiment, we can generate the five-order polynomials model that can be used to predict the new value that approximates the ground-truth value. It can be proved by measuring the Mean Absolute Error (MAE) score of the polynomial curve fitting between the ground-truth value and the prediction value. As a result, the Mean Absolute Error (MAE) score for each of the axes is 0.57. It indicates that our proposed method based on the polynomial curve fitting has been successfully applied for calibrating the accelerometer sensor.

The application of MEMS accelerometers used to measure inclination is constrained by their temperature dependence, and each accelerometer needs to be calibrated individually to increase stability and accuracy. This paper presents a calibration and thermal compensation method for triaxial accelerometers that aims to minimize cost and processing time while maintaining high accuracy. First, the number of positions to perform the calibration procedure is optimized based on the Levenberg-Marquardt algorithm, and then, based on this optimized calibration number, thermal compensation is performed based on the least squares method, which is necessary for environments with large temperature variations, since calibration parameters change at different temperatures. The calibration procedures and algorithms were experimentally validated on marketed accelerometers. Based on the optimized calibration method, the calibrated results achieved nearly 100 times improvement. Thermal drift calibration experiments on the triaxial accelerometer show that the thermal compensation scheme in this paper can effectively reduce drift in the temperature range of −40 °C to 60 °C. The temperature drifts of x- and y-axes are reduced from −13.2 and 11.8 mg to −0.9 and −1.1 mg, respectively. The z-axis temperature drift is reduced from −17.9 to 1.8 mg. We have conducted various experiments on the proposed calibration method and demonstrated its capacity to calibrate the sensor frame error model (SFEM) parameters. This research proposes a new low-cost and efficient strategy for increasing the practical applicability of triaxial accelerometers.

… the accelerometer random bias: the variance of the bias errors … factor errors are both as large as the ratio of the accelerometer … the magnitude of the scale factor error is almost half of the …

… In this paper, to obtain the error coefficients of the accelerometer include bias, scale factor, and nonorthogonality, the measurement vector norm law is used with a proper variable …

… effectively calibrate the deterministic error of the accelerometers… the turntable rotation scheme in the lever arm error calibration … , that is a kind of consumer-grade MEMS accelerometer. …

MEMS-IMUs have an extensive application in multifarious studies, as well as industrial and commercial areas. It is crucial to diminish their intrinsic errors in a suitable calibration procedure. In this paper, a novel calibration procedure was proposed for Inertial Measurement Units (IMUs) on a turntable. A general nonlinear model of the IMU output including the effects of bias, scale factor, misalignment, and lever arm was derived. Transformed Unscented Kalman Filter (TUKF) was utilized to perform the estimation of error parameters for gyroscopes and accelerometers. The calibration maneuvers were applied using a tri-axis turntable to create input signals. In addition, assuming the sensors not placing in the center of the table makes angular acceleration become another variable which affects the estimation of the error parameters. Therefore, a suitable angular acceleration estimator was designed utilizing the angular velocity output. According to experimental results, applying the proposed method caused 66% and 63% increase in the accuracy of gyroscopes and accelerometers outputs, respectively, compared with the calibrated signals based on the least square method.

… , the MEMS accelerometer sensitive … turntable to make the accelerometer sensitive axis aligned with the acceleration of gravity, and then estimate the scale factor of MEMS accelerometer…

… for calibration of microelectromechanical system accelerometers. A … For collecting data sets, the accelerometer is moved … the second section shows the turntable experiment results. In …

… This error is because of the distance of the accelerometers from the center of the turntable, which is … However, since in this study an angle turntable is utilized for applying the calibration …

In the strapdown inertial navigation system (SINS), which is based on a high-precision rotary table for system-level calibration, the complexity of the transposition scheme and the long calibration time will inevitably lead to low calibration accuracy of the error parameters. These calibration results will seriously affect the navigation accuracy of SINS. In addition, the small observability of the error parameters often leads to unreliable results of system-level calibration, thus affecting the navigation accuracy of SINS. Here, we propose an improved observability calculation method and design a system-level calibration scheme with four-position continuous rotation. First, we establish a calibration error model containing 24 error parameters and a 30-D Kalman filter model. Then, based on the observability analysis method, we innovatively demonstrate the feasibility of the three-axis rotation scheme. Finally, an efficient system-level calibration scheme for four-position continuous transposition is designed, which can calibrate all the state variables. At the same time, compared with the popular 19-position calibration method, the calibration scheme in this article improves the positioning accuracy by 20.49% and the velocity accuracy by 13.77%.

… The work reported in this paper was motivated by a specific calibration task, namely, the accurate estimation of pendulous integrating gyroscopic accelerometer (PIGA) cross-axis g2 …

… is observable only in two conditions: the system measurement models are built up with platform angles and accelerometer … are built up only with accelerometers triad outputs, the system …

… and accelerometer triads and (2) the optimal calibration scheme design. A new approach to … , the separate multi-position calibrations for the gyroscope triad and the accelerometer triad …

… accelerometers. Based on the fact that the norm of measurement outputs of the accelerometer triad ideally equals to the gravity value in constant thermal conditions, a multiposition least …

… When the calibration is conducted outside the laboratory, it is … traditional multi-position method, which affects the calibration … new multi-position calibration method for the accelerometers …

… calibration of accelerometers, the majority of the proposed methods are based on the basic idea of the multi-position calibration … that is based on multi-position calibration generalized to …

… of rotational inertial navigation system, self-calibration is utilized as an effective way to reduce … Since the accuracy of the self-calibration method is susceptible to the positioning error of …

… multi-position calibration algorithm that takes the Earth’s rotation rate and gravity as inputs, and calculates calibration … In summary, the proposed algorithm can achieve accelerometer …

… multi-position calibration method for the low cost MEMS IMUs was presented. The error parameters of accelerometers … of accelerometer calibration results, while the gyroscopes were …

Navigation grade inertial measurement units (IMUs) should be calibrated after Inertial Navigation Systems (INSs) are assembled and be re-calibrated after certain periods of time. The multi-position calibration methods with advantage of not requiring high-precision equipment are widely discussed. However, the existing multi-position calibration methods for IMU are based on the model of linear scale factors. To improve the precision of INS, the nonlinear scale factors should be calibrated accurately. This paper proposes an optimized multi-position calibration method with nonlinear scale factor for IMU, and the optimal calibration motion of IMU has been designed based on the analysis of sensitivity of the cost function to the calibration parameters. Besides, in order to improve the accuracy and robustness of the optimization, an estimation method on initial values is presented to solve the problem of setting initial values for iterative methods. Simulations and experiments show that the proposed method outperforms the calibration method without nonlinear scale factors. The navigation accuracy of INS can be improved by up to 17% in lab conditions and 12% in the moving vehicle experiment, respectively.

Inertial Navigation System (INS) is used in a variety of applications such as missile and marine navigation. INS is comprised of an inertial measuring unit (IMU) and a processor unit that performs the navigation mathematics calculations. In order to get accurate navigation data via INS, calibration of IMU sensors are necessary. Mechanical sensors are used in high-precision navigation, such as strategic missiles and are characterized by their low random noise. However, deterministic errors can cause very significant errors in positioning such as biases, scale factors, non-orthogonality errors, and g-sensitive and non-g-sensitive drifts. Therefore, determining an effective and accurate method of calibration is necessary to estimate and compensate for these errors. The suggested methodology accurately calculates the calibration parameters to minimize those errors. The traditional calibration techniques of the accelerometer are restricted in precision, since the estimation of scale factor and bias obtained from a limited number of positions depending on the gravity direction. These calibration techniques are also limited in the estimation of g-sensitive and non-g-sensitive drifts impacting gyro performance. This paper presents a new technique of calibration that overcomes these drawbacks, based on an enhancement of multi-position technique. Experimental results for the proposed technique was carried out to confirm its efficiency.

Abstract The temperature cycling test is always carried out in thermal calibration scheme of the inertial navigation systems, in which the temperature-stabilization chamber is quite needed. The temperature cycling test can provide full temperature parameters of the accelerometer and gyro triads, but it also requires complex operation procedures and expensive test instruments. A fast estimation method using multi-position continuous rotate-stop data is proposed here to estimate temperature parameters of the accelerometers. The calibration off-line data can be obtained from the systematic calibration experiment, which means no additional temperature experiment is needed. The method can be easily extended to apply in full temperature range through interpolation of the temperature parameters. At last, the systematic calibration tests verified that the repeatability of the estimation result of error parameters of the inertial sensors can be greatly improved, and land vehicular tests verified that the horizontal positioning precision can be greatly improved.

… Multi-position calibration and continuous calibration methods are adopted to deal with the calibration for gyros and accelerometers … calibration schemes in the multi-position calibration …

… 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 …

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.

The European Space Agency Gravity field and steady-state Ocean Circular Explorer (GOCE) carries a gradiometer consisting of three pairs of accelerometers in an orthogonal triad. Precise GOCE science orbit solutions (PSO), which are based on satellite-to-satellite tracking observations by the Global Positioning System and which are claimed to be at the few cm precision level, can be used to calibrate and validate the observations taken by the accelerometers. This has been done for each individual accelerometer by a dynamic orbit fit of the time series of position co-ordinates from the PSOs, where the accelerometer observations represent the non-gravitational accelerations. Since the accelerometers do not coincide with the center of mass of the GOCE satellite, the observations have to be corrected for rotational and gravity gradient terms. This is not required when using the so-called common-mode accelerometer observations, provided the center of the gradiometer coincides with the GOCE center of mass. Dynamic orbit fits based on these common-mode accelerations therefore served as reference. It is shown that for all individual accelerometers, similar dynamic orbit fits can be obtained provided the above-mentioned corrections are made. In addition, accelerometer bias estimates are obtained that are consistent with offsets in the gravity gradients that are derived from the GOCE gradiometer observations.

… drifts, such as scale factor and zero bias, thereby affecting … is necessary throughout the accelerometer's lifecycle to … method through gap identification experiments and scale factor self-…

Abstract For more than 14 years, the Gravity Recovery and Climate Experiment (GRACE) mission has provided information about Earth’s gravity field with unprecedented accuracy. The twin satellites GRACE-A and GRACE-B are both equipped with a three-axis electrostatic accelerometer, measuring the non-gravitational forces acting on the spacecraft. In order to make use of the uncalibrated Level-1B accelerometer (ACC1B) data during gravity field recovery, bias and scale parameters have to be estimated. The proposed calibration method is a two-step approach and makes use of modeled non-conservative accelerations. The simulated non-conservative accelerations serve as reference for the a priori accelerometer calibration, i.e. for the ACC1B data. During gravity field recovery the calibration parameters are re-estimated. Several calibration parameters for the GRACE accelerometers using different methods have already been published. The aim of our study was primarily to analyze the temperature-dependent behavior of the accelerometer scale factors and biases, and the impact of the parametrization of scale factors and biases on the recovered gravity field solutions; but not to obtain calibrated accelerometer data. Within the ITSG-Grace2016 release, the accelerometer biases are estimated daily using uniform cubic basis splines (UCBS), the scale factors are also estimated daily using a fully-populated scale factor matrix. Therefore, not only the scale factors in along-track, cross-track, and radial direction are estimated, but also the non-orthogonality of the accelerometer axes (cross-talk) and the misalignment between the Accelerometer Frame (AF) and Science Reference Frame (SRF) are taken into account. The time evolution of the estimated calibration parameters over the whole GRACE period (2002-04 to 2016-01) shows a clear temperature-dependency for both scale factors and biases. Using this new approach, the estimates of the C20 coefficient significantly improve, with results now comparable to Satellite Laser Ranging (SLR) solutions. Based on the achieved results, we suggest the presence of a clear temperature-dependent behavior and the presence of off-diagonal elements in the accelerometer scale factor matrix.

… To avoid this, we solve the system identification problem using the … bias of the i-th accelerometer output and [⋅]T denotes the transpose operation. The accelerometer scale factor …