全温域MEMS三轴加速度计传感器校正

Abstract A nonlinear cost function is defined for field calibration of the accelerometer, using the rule that the norm of the measured vector in a static state is equal to the magnitude of the gravity vector. To solve this cost function, various optimization methods like Newton and Levenberg–Marquardt have been presented in different references. However, these methods are complicated, time-consuming, and require an initial value. This study presents a method that simplifies the cost function and obtains the error coefficients, including bias, scale factor, and non-orthogonality using the linear least-squares method which is simpler and faster than other optimization methods and does not need initial values. Also, the output of the low-cost MEMS accelerometer depends on temperature due to its silicon property. Thus, by finding the dependency of the error coefficients on temperature, they can be compensated. This paper models dependency of error coefficients on temperature using cubic spline interpolation and minimizes the temperature effect. Simulation results of MATLAB and the proposed field calibration method and temperature compensation on the low-cost MPU6050 sensor show its good performance.

Structural health monitoring (SHM) is an advancing area in the field of structural engineering. The main objective of SHM is the verification of structural health and status in order to ensure proper performance and cost savings for maintenance using nondestructive tests. It is not limited to diagnosis but is extended to prognosis of what are the standards to implement in order to mitigate such destruction of civil infrastructures. However, there are still implementation issues such as improper calibration of sensors resulting to poor data integrity. This study is concerned in reducing the inconsistency of characteristics of the ADXL345 accelerometer and DS18B20 temperature sensors in laboratory and working conditions. Experimental design was employed in this study. Combined inclination sensing and subwoofer-setup calibration technique was employed to six accelerometers, which yielded 95.796% accuracy. Two-point calibration technique was employed to twelve temperature sensors, which yielded 90.960% accuracy. Less than 10 %, which is considered highly accurate measurement, were yielded from measuring structural vibration and temperature, and environment temperature data from a reinforced concrete bridge test platform. Thus, the proposed experimental study addressed successful enhancement of sensing characteristics of sensors.

Motion sensors as inertial measurement units (IMU) are widely used in robotics, for instance in the navigation and mapping tasks. Nowadays, many low cost micro electro mechanical systems (MEMS) based IMU are available off the shelf, while smartphones and similar devices are almost always equipped with low-cost embedded IMU sensors. Nevertheless, low cost IMUs are affected by systematic error given by imprecise scaling factors and axes misalignments that decrease accuracy in the position and attitudes estimation. In this paper, we propose a robust and easy to implement method to calibrate an IMU without any external equipment. The procedure is based on a multi-position scheme, providing scale and misalignments factors for both the accelerometers and gyroscopes triads, while estimating the sensor biases. Our method only requires the sensor to be moved by hand and placed in a set of different, static positions (attitudes). We describe a robust and quick calibration protocol that exploits an effective parameterless static filter to reliably detect the static intervals in the sensor measurements, where we assume local stability of the gravity's magnitude and stable temperature. We first calibrate the accelerometers triad taking measurement samples in the static intervals. We then exploit these results to calibrate the gyroscopes, employing a robust numerical integration technique. The performances of the proposed calibration technique has been successfully evaluated via extensive simulations and real experiments with a commercial IMU provided with a calibration certificate as reference data.

The errors of low-cost inertial sensors, especially Micro-Electro Mechanical Systems (MEMS) ones, are highly dependent on environmental conditions such as the temperature. Thus, there is a need for the development of accurate and reliable thermal compensation models to reduce the impact of such thermal drift of the sensors. Since the conventional thermal calibration methods are typically time-consuming and costly, an efficient thermal calibration method to investigate the thermal drift of a full set of gyroscope and accelerometer errors (i.e., biases, scale factor errors and non-orthogonalities) over the entire temperature range in a few hours is proposed. The proposed method uses the idea of the Ramp method, which removes the time-consuming process of stabilizing the sensor temperature, and addresses its inherent problems with several improvements. We change the temperature linearly for a complete cycle and take a balanced strategy by making comprehensive use of the sensor measurements during both heating and cooling processes. Besides, an efficient 8-step rotate-and-static scheme is designed to further improve the calibration accuracy and efficiency. Real calibration tests showed that the proposed method is suitable for low-grade IMUs and for both lab and factory calibration due to its efficiency and sufficient accuracy.

An attitude estimation algorithm is developed using an adaptive extended Kalman filter for low-cost microelectromechanical-system (MEMS) triaxial accelerometers and gyroscopes, that is, inertial measurement units (IMUs). Although these MEMS sensors are relatively cheap, they give more inaccurate measurements than conventional high-quality gyroscopes and accelerometers. To be able to use these low-cost MEMS sensors with precision in all situations, a novel attitude estimation algorithm is proposed for fusing triaxial gyroscope and accelerometer measurements. An extended Kalman filter is implemented to estimate attitude in direction cosine matrix (DCM) formation and to calibrate gyroscope biases online. We use a variable measurement covariance for acceleration measurements to ensure robustness against temporary nongravitational accelerations, which usually induce errors when estimating attitude with ordinary algorithms. The proposed algorithm enables accurate gyroscope online calibration by using only a triaxial gyroscope and accelerometer. It outperforms comparable state-of-the-art algorithms in those cases when there are either biases in the gyroscope measurements or large temporary nongravitational accelerations present. A low-cost, temperature-based calibration method is also discussed for initially calibrating gyroscope and acceleration sensors. An open source implementation of the algorithm is also available.

MEMS chips have become ideal candidates for various applications since they are small sized, light weight, have low power consumption and are extremely low cost and reliable. However, the performance of MEMS sensors, especially their biases and scale factors, is highly dependent on environmental conditions such as temperature. Thus a quick and convenient calibration is needed to be conducted by users in field without any external equipment or any expert knowledge of calibration. A novel and efficient in situ hand calibration method is presented to meet these demands in this paper. The algorithm of the proposed calibration method makes use of the navigation algorithm of the loosely-coupled GPS/INS integrated systems, but replaces the GPS observations with a kind of pseudo-observations, which can be stated as follows: if an inertial measurement unit (IMU) was rotating approximately around its measurement center, the range of its position and its linear velocity both would be within a limited scope. Using a Kalman filtering algorithm, the biases and scale factors of both accelerometer triad and gyroscope triad can be calibrated together within a short period (about 30 s), requiring only motions by hands. Real test results show that the proposed method is suitable for most consumer grade MEMS IMUs due to its zero cost, easy operation and sufficient accuracy.

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This paper presents a new calibration method to overcome the challenges of MEMS inertial sensors for underwater navigation. The MEMS inertial sensor module is composed of an accelerometer, a gyroscope and a circuit of signal process. For navigation estimation, it is easy to be influenced by errors which come from MEMS inertial sensors. In general, the sources of error can be categorized into two groups, deterministic type and stochastic type. The former primarily includes bias errors, misalignment and nonlinearity; the latter contains temperature effect and signal drifting. Subsequently, the linearity calibration is used to modify the deterministic error and the wavelet analysis can suppress the stochastic noise. Therefore, the new calibration method integrated of linearity calibration and wavelet signal processing is utilized to enhance the accuracy and performance of MEMS inertial sensor module. The experimental results demonstrate that the output signal can be corrected suitability by means of the proposed method.

Over the past decade and a half, the combination of low-cost, lightweight micro-electro-mechanical sensors (MEMS) technology and multisensor integration has enabled inertial sensors to be deployed over a much wider range of navigation applications [1]. Examples include pedestrian dead-reckoning using step detection technology [2, 3], aiding of GNSS signal tracking during jamming [4, 5], and simultaneous localisation and mapping (SLAM) using radio signals [6]. However, for best performance, a MEMS inertial measurement unit (IMU) must be calibrated in the laboratory prior to use, which increases the cost by more than $1000 per unit. In this paper, we examine and present a range of techniques which use an array of inexpensive MEMS sensors to improve the performance of a MEMS IMU without requiring a full calibration prior to use. As the cost of calibration of a high-performance MEMS IMU far outweighs the cost of the hardware, there is considerable scope to improve the performance by adding additional sensors, before the cost of the IMU reaches that of a laboratory calibrated equivalent. Combining MEMS IMUs in an array has been studied before. However, the most common approach was simply to take an average of the input of several identical sensors [7]. If the sensor errors were independent, this could be expected to improve performance by a factor of root-n where, n is the number of IMUs combined. In this paper more sophisticated techniques are investigated that use knowledge of the sensor characteristics to obtain better performance. Three different properties of MEMS sensors may potentially be exploited: 1) The common-mode errors of different sensors of the same design; 2) The different characteristics of in-plane and out-of-plane sensors; and 3) The complementary properties of MEMS sensors with different dynamic ranges. In [8], it is shown that different individual sensors of the same design exhibit similar bias variation with temperature and that improved accuracy may be obtained by differencing the outputs of two gyroscopes mounted with their sensitive axes in opposing directions. Here, this approach will be independently verified and the performance benefits assessed with a range of different MEMS accelerometers and gyros, including Bosch BMA180 accelerometers, Analogue Devices ADXL345 accelerometers, ST Microtronics L3G4200D gyroscopes. Preliminary indications are that there is considerable common bias variation with temperature for the in-plane sensors of L3G4200D gyroscopes, and some common mode behaviour for the low-cost accelerometers. The second idea presented is exploiting the differences between the in-plane and out-of-plane axis outputs of single-chip inertial sensor triads, to improve the performance of an array-based IMU. Early experiment s point to considerable differences between the two which could markedly affect navigation performance. Both accelerometer and gyro triads can exhibit smaller errors from the in-plane sensors than from the out-of-plane sensors. Therefore, experiments were conducted using mutually-perpendicular arrays of accelerometer and gyro triads to determine whether better performance could be obtained using only the in-plane sensors. The third idea is to combine the outputs of MEMS sensors with different dynamic ranges to exploit the lower noise exhibited by some lower-dynamic-range sensors compared to their higher-dynamic-range counterparts. The sensor outputs are thus weighted according to the platform dynamics. That is, predominantly using the high-precision sensor when dynamics are low and using the full-range sensor when the dynamics are high. Several versions of this weighted signal combination will be presented and compared. Early indications are that there can be a significant benefit in this approach for some sensor designs, but not others. Finally, this paper will also examine the efficacy of a once-only static calibration on purchase, performed by the user instead of the supplier, for improving navigation performance. It is essential for a user-performed calibration that the physical movements required of the sensor are very simple and easily understood and completed, even if the underlying method is complex. To this end data, recorded on different days from an array of MEMS sensors within a precisely manufactured rapid prototyped ‘calibration cube’, will be analysed. These measurements are taken at precisely orthogonal angles of the cubes six faces, and allow the scale factor errors, biases and axes alignments of the accelerometers to be determined. The computed calibration corrections over several days will be compared to enable the efficacy of the one-time calibration technique to be assessed. The development of a full calibration routine will be the subject of future research. In summary, this paper will present several new methods for utilising the output of an array of low-cost sensors to improve the performance of a MEMS IMU, and also expands on methods proposed in existing research. As uncalibrated MEMS IMUs are of low performance there is a great potential for new applications if the performance can be improved closer to the level of those which are factory calibrated. / References [1] Groves, P. D., Principles of GNSS, inertial, and multi-sensor integrated navigation systems, Second Edition, Artech House, 2013. [2] Gustafson, D., J. Dowdle, and K. Flueckiger, “A Deeply Integrated Adaptive GPS-Based Navigator with Extended Range Code Tracking,” Proc. IEEE PLANS 2000. [3] Groves, P. D., C. J. Mather and A. A. Macaulay, “Demonstration of Non-Coherent Deep INS/GPS Integration for Optimized Signal to Noise Performance,” Proc. ION GNSS 2007. [4] Ma, Y., W. Soehren, W. Hawkinson, and J. Syrstad, "An Enhanced Prototype Personal Inertial Navigation System," Proc. ION GNSS 2012. [5] Groves, P. D., et al., “Inertial Navigation Versus Pedestrian Dead Reckoning: Optimizing the Integration,” Proc. ION GNSS 2007. [6] Faragher, R. M., C. Sarno, and M. Newman, “Opportunistic Radio SLAM for Indoor Navigation using Smartphone Sensors,” Proc. IEEE/ION PLANS 2012. [7] Bancroft, J. B., and G. Lachapelle, “Data fusion algorithms for multiple inertial measurement units,” Sensors, Vol. 11, No. 7, 2011, pp. 6771-6798. [8] Yuksel, Y., N. El-Sheimy, N., and A. Noureldin, “Error modelling and characterization of environmental effects for low cost inertial MEMS units,” Proc. IEEE/ION PLANS 2010.

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 application of MEMS capacitive accelerometers isimited by its thermal dependence, and each accelerometer must be individually calibrated to improve its performance. In this work, aight 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 requiresess 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, modelIS3DSH, 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 theatter in the first hours after power-up of the sensor by 43%.

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%.

MEMS inertial sensors (gyroscope and accelerometer) are widely used in many areas from automotive to space applications. Inertial sensors are critical components in navigation applications as they provide valuable measurements such as acceleration and rotation. The structure and material used in MEMS inertial sensors are affected from some environmental factors such as vibration, mechanical shock, humidity, electromagnetism, and temperature. The most restrictive environmental factor for MEMS inertial sensors is temperature. The characteristics of noise and deterministic errors change under different temperature conditions. Therefore, these drawbacks of temperature have to be degraded before using inertial sensors in navigation applications. Generally, calibration tests are performed under different temperature conditions to identify the behavior of deterministic errors in the operating temperature range. This process is time-consuming; hence, many IMU producers try to determine the minimum sufficient number of temperature conditions, which are used in the calibration tests. In this study, deterministic error parameters are estimated for two different temperature conditions in separate calibration processes. One of the calibration processes is performed at eleven different temperature points to determine temperature dependent behavior of the deterministic errors in the operating temperature range. Then, second calibration process is carried out at five different temperature points in the operating temperature. Moreover, calibration verification tests have been performed under three different temperature conditions to examine how deterministic error parameters are affected by decreasing temperature points from 11 to 5 points. 8 uncalibrated IMUs from same batch are taken into consideration and their deterministic error characteristics are investigated.

Abstract This paper reports an approach of in-operation temperature bias drift compensation based on phase-based calibration for a stiffness-tunable MEMS accelerometer with double-sided parallel plate (DSPP) capacitors. The temperature drifts of the components of the accelerometer are characterized, and analytical models are built on the basis of the measured drift results. Results reveal that the temperature drift of the acceleration output bias is dominated by the sensitive mechanical stiffness. An out-of-bandwidth AC stimulus signal is introduced to excite the accelerometer, and the interference with the acceleration measurement is minimized. The demodulated phase of the excited response exhibits a monotonic relationship with the effective stiffness of the accelerometer. Through the proposed online compensation approach, the temperature drift of the effective stiffness can be detected by the demodulated phase and compensated in real time by adjusting the stiffness-tuning voltage of DSPP capacitors. The temperature drift coefficient (TDC) of the accelerometer is reduced from 0.54 to 0.29 mg/°C, and the Allan variance bias instability of about 2.8 μg is not adversely affected. Meanwhile, the pull-in resulting from the temperature drift of the effective stiffness can be prevented. TDC can be further reduced to 0.04 mg/°C through an additional offline calibration based on the demodulated carrier phase representing the temperature drift of the readout circuit.

We propose a new fusing method to estimate the vertical velocity and the height of barometer-IMU systems. The method removed initialization processes of the system by calibrating accelerometer errors on-line. An EKF tracks the bias and scale error of each accelerometer, while estimating vertical velocity and height simultaneously. The method is tested on simulation and on an actual low-cost barometer-IMU sensor platform. The errors are successfully modeled before 30 to 60 seconds of system startup. Proposed method may be extensively used for low-cost, chip-scale barometer/IMU integrated devices, since on-line calibration not only removes initialization processes but also enables tracking of time/temperature dependent varying IMU errors from which MEMS based IMUs suffer.

Pavement vibration monitoring under vehicle loads can be used to acquire traffic information and assess the health of pavement structures, which contributes to smart road construction. However, the effectiveness of monitoring is closely related to sensor performance. In order to select the suitable acceleration sensor for pavement vibration monitoring, a printed circuit board (PCB) with three MEMS (micro-electromechanical) accelerometer chips (VS1002, MS9001, and ADXL355) is developed in this paper, and the circuit design and software development of the PCB are completed. The experimental design and comparative testing of the sensing performance of the three MEMS accelerometer chips, in terms of sensitivity, linearity, noise, resolution, frequency response, and temperature drift, were conducted. The results show that the dynamic and static calibration methods of the sensitivity test had similar results. The influence of gravitational acceleration should be considered when selecting the range of the accelerometer to avoid the phenomenon of over-range. The VS1002 has the highest sensitivity and resolution under 3.3 V standard voltage supply, as well as the best overall performance. The ADXL355 is virtually temperature-independent in the temperature range from -20 °C to 60 °C, while the voltage reference values output by the VS1002 and MS9001 vary linearly with temperature. This research contributes to the development of acceleration sensors with high precision and long life for pavement vibration monitoring.

This paper presents a new calibration method to overcome the challenges of MEMS inertial sensors for underwater navigation. The MEMS inertial sensor module is composed of an accelerometer, gyroscope and circuit of signal process. For navigation estimation, it is easy to be influenced by errors which come from MEMS inertial sensors. In general, the sources of error can be categorized into two groups, deterministic and stochastic. The former are mainly including bias error, misalignment and nonlinearity; the latter contain temperature effect and signal drifting. Subsequently, the linearity calibration is used to modify the deterministic error and the wavelet analysis can suppress the stochastic noise. Therefore, the new calibration method integrated of linearity calibration and wavelet signal processing is utilized to enhance the accuracy and performance of MEMS inertial sensor module. The experimental results demonstrate that the output signal can be corrected suitability by means of proposed method.

This paper presents a new calibration method to overcome the challenges of MEMS inertial sensors for underwater navigation. The MEMS inertial sensor module is composed of an accelerometer, gyroscope and circuit of signal process. For navigation estimation, it is easy to be influenced by errors which come from MEMS inertial sensors. In general, the sources of error can be categorized into two groups, deterministic and stochastic. The former are mainly including bias error, misalignment and nonlinearity; the latter contain temperature effect and signal drifting. Subsequently, the linearity calibration is used to modify the deterministic error and the wavelet analysis can suppress the stochastic noise. Therefore, the new calibration method integrated of linearity calibration and wavelet signal processing is utilized to enhance the accuracy and performance of MEMS inertial sensor module. The experimental results demonstrate that the output signal can be corrected suitability by means of proposed method.

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 T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> . 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 x- and y-axes are reduced from -19.2 and 11.6 mg to -0.7 and -0.6 mg, respectively. The Z-axis drift is reduced from -23.9 to 3.5 mg. This proves the feasibility of the method and scheme proposed in this article.

This paper presents a fast and low cost way to calibrate different inertial measurement sensors. In particular the calibration of an accelerometer and a gyroscope using nonlinear least squares is presented. A model of the sensors which includes the main errors that MEMS devices present is used. A calibration method is proposed for estimating the static parameters of the model and a temperature adjustment is proposed and implemented.

Given the growing development and production of low-cost digital MEMS sensors, e.g. accelerometers, gyroscopes, microphones, humidity, pressure and temperature sensors, large-scale measurements are nowadays a possible reality in many different fields, from industry 4.0 to environmental monitoring and smart cities. However, in most of cases, digital MEMS sensors still lack the required metrological traceability needed to provide traceable measurements. As a matter of fact, at present, a preliminary sensitivity value of these sensors is provided by the manufacturers by performing a simple adjustment, without a proper traceable calibration. This is basically due to the impossibility, nowadays, to guarantee large-scale calibration procedures at costs comparable to those of the sensors. For this purpose, it is first of all necessary to know their current technical performances, in terms of sensitivity and associated uncertainties, and then to define possible large-scale calibration methods. In this work, 100 nominally equal 3-axis MEMS digital accelerometers are calibrated with a recently-developed calibration setup at INRiM. Sensitivity values, together with their calibration expanded uncertainties, are compared to statistically analyze their dispersion and distribution within the considered sample. This is the first necessary step towards the development of large-scale calibration methods.

MEMS inertial sensors have become more and more popular in recent years due to their low-cost, small size and low power consumption, and have been widely used in various fields, but they have the disadvantage of being very sensitive to temperature changes (thermal drift). We propose a real-time thermal compensation method for a MEMS accelerometer to provide an online compensation strategy to mitigate temperature effects in this paper. First, this study uses an in-house-designed Guidance Navigation and Control Module (GNC Module) for temperature effect testing, and the output of the accelerometer is collected during the test. Second, the real-time compensation model based on the accelerometer output at the previous moment is proposed. And then, the false nearest neighbor algorithm is introduced to determine the number of neurons in the hidden layer of the neural network. At last, a recently popular Recurrent Neural Network (RNN) variant, the Simple Recurrent Unit (SRU-RNN), is used to process the MEMS accelerometer raw outputs. With temperature calibration, the thermal drift of the MEMS accelerometer is significantly improved, which undoubtedly proves the effectiveness of the employed method in this paper.

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We propose calibration methods for microelectromechanical system (MEMS) 3D accelerometers and gyroscopes that are efficient in terms of time and computational complexity. The calibration process for both sensors is simple, does not require additional expensive equipment, and can be performed in the field before or between motion measurements. The methods rely on a small number of defined calibration measurements that are used to obtain the values of 12 calibration parameters. This process enables the static compensation of sensor inaccuracies. The values detected by the 3D sensor are interpreted using a generalized 3D sensor model. The model assumes that the values detected by the sensor are equal to the projections of the measured value on the sensor sensitivity axes. Although this finding is trivial for 3D accelerometers, its validity for 3D gyroscopes is not immediately apparent; thus, this paper elaborates on this latter topic. For an example sensor device, calibration parameters were established using calibration measurements of approximately 1.5 min in duration for the 3D accelerometer and 2.5 min in duration for the 3D gyroscope. Correction of each detected 3D value using the established calibration parameters in further measurements requires only nine addition and nine multiplication operations.

In order to build a tilt sensor having a desired sensitivity and measuring range, one should select an appropriate type, orientation, and initial position of an accelerometer. Various cases of tilt measurements are considered: determining exclusively pitch, axial tilt, or both pitch and roll, where Cartesian components of the gravity acceleration are measured by means of low-g uni-, bi-, tri-, or multiaxial micromachined accelerometers. 15 different orientations of such accelerometers are distinguished (each illustrated with respective graphics) and related to the relevant mathematical formulas. Results of the performed experimental study revealed inherent misalignments of the sensitive axes of micromachined accelerometers as large as 1°. Some of the proposed orientations make it possible to avoid a necessity of using the most misaligned pairs of the sensitive axes; some increase the accuracy of tilt measurements by activating all the sensitive axes or reducing the effects of anisotropic properties of micromachined triaxial accelerometers; other orientations make it possible to reduce a necessary number of the sensitive axes at full measurement range. An increase of accuracy while using multiaxial accelerometers is discussed. Practical guidelines for an optimal selection of a particular micromachined accelerometer for a specific case of tilt measurement are provided.

Accelerometers in animal-attached tags are powerful tools in behavioural ecology, they can be used to determine behaviour and provide proxies for movement-based energy expenditure. Researchers are collecting and archiving data across systems, seasons and device types. However, using data repositories to draw ecological inference requires a good understanding of the error introduced according to sensor type and position on the study animal and protocols for error assessment and minimisation.Using laboratory trials, we examine the absolute accuracy of tri-axial accelerometers and determine how inaccuracies impact measurements of dynamic body acceleration (DBA), a proxy for energy expenditure, in human participants. We then examine how tag type and placement affect the acceleration signal in birds, using pigeons <i>Columba livia</i> flying in a wind tunnel, with tags mounted simultaneously in two positions, and back- and tail-mounted tags deployed on wild kittiwakes <i>Rissa tridactyla</i>. Finally, we present a case study where two generations of tag were deployed using different attachment procedures on red-tailed tropicbirds <i>Phaethon rubricauda</i> foraging in different seasons.Bench tests showed that individual acceleration axes required a two-level correction to eliminate measurement error. This resulted in DBA differences of up to 5% between calibrated and uncalibrated tags for humans walking at a range of speeds. Device position was associated with greater variation in DBA, with upper and lower back-mounted tags varying by 9% in pigeons, and tail- and back-mounted tags varying by 13% in kittiwakes. The tropicbird study highlighted the difficulties of attributing changes in signal amplitude to a single factor when confounding influences tend to covary, as DBA varied by 25% between seasons.Accelerometer accuracy, tag placement and attachment critically affect the signal amplitude and thereby the ability of the system to detect biologically meaningful phenomena. We propose a simple method to calibrate accelerometers that can be executed under field conditions. This should be used prior to deployments and archived with resulting data. We also suggest a way that researchers can assess accuracy in previously collected data, and caution that variable tag placement and attachment can increase sensor noise and even generate trends that have no biological meaning.

This paper presents an innovative model for integrating thermal compensation of gyro bias error into an augmented state Kalman filter. The developed model is applied in the Zero Velocity Update filter for inertial units manufactured by exploiting Micro Electro-Mechanical System (MEMS) gyros. It is used to remove residual bias at startup. It is a more effective alternative to traditional approach that is realized by cascading bias thermal correction by calibration and traditional Kalman filtering for bias tracking. This function is very useful when adopted gyros are manufactured using MEMS technology. These systems have significant limitations in terms of sensitivity to environmental conditions. They are characterized by a strong correlation of the systematic error with temperature variations. The traditional process is divided into two separated algorithms, i.e., calibration and filtering, and this aspect reduces system accuracy, reliability, and maintainability. This paper proposes an innovative Zero Velocity Update filter that just requires raw uncalibrated gyro data as input. It unifies in a single algorithm the two steps from the traditional approach. Therefore, it saves time and economic resources, simplifying the management of thermal correction process. In the paper, traditional and innovative Zero Velocity Update filters are described in detail, as well as the experimental data set used to test both methods. The performance of the two filters is compared both in nominal conditions and in the typical case of a residual initial alignment bias. In this last condition, the innovative solution shows significant improvements with respect to the traditional approach. This is the typical case of an aircraft or a car in parking conditions under solar input.

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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 <i>T</i> and its square <i>T</i>², ambient temperature variation ∆<i>T</i> and its square ∆<i>T</i>², 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.

The traditional temperature modeling method is based on the full heating of the accelerometer to achieve thermal balance, which is not suitable for the cold start-up phase of the micro-accelerometer. For decreasing the complex temperature drift of the cold start-up phase, a new temperature compensation method based on a high-order Fourier transform combined model is proposed. The system structure and repeatability test of the micro digital quartz flexible accelerometer are provided at first. Additionally, we analyzed where the complex temperature drift of the cold start-up phase comes from based on the system structure and repeatability test. Secondly, a high-order temperature compensation model combined with K-means clustering and the symbiotic organisms search (SOS) algorithm is established with repeatability test data as training data. To verify the proposed temperature compensation model, a test platform was built to transmit the measured values before and after compensation with the proposed Fourier-related model and the other time-related model, which is also a model aiming at temperature compensation in the cold start-up phase. The experimental results indicate that the proposed method achieves better compensation accuracy compared with the traditional temperature compensation methods and the time-related compensation model. Furthermore, the compensation for the cold start-up phase has no effect on the original accuracy over the whole temperature range. The stability of the accelerometer can be significantly improved to about 30 μg in the start-up phase of different temperatures after compensation.

Vibration correction by using an accelerometer to measure vibration is one of the critical technologies for field measurement of atom gravimeters. However, the accelerometer is often affected by temperature and other environmental factors, resulting in a drift of vibration signal. Temperature drift of accelerometer modeling and compensation is one of the main methods to restrain the drift. Considering different effects on the drift of various temperatures, temperature change rates, and temperature rise and drop processes, taking temperature and temperature change rate as inputs, we establish the temperature drift model of the accelerometer and use the positive and negative signs of temperature change rate to indicate the rise and drop of temperature. The model is described by support vector regression (SVR), and the particle swarm optimization (PSO) algorithm is utilized for tuning the model parameters. We carried out the heating and cooling experiments with temperature change rates of ±2, ±1, and ±0.5 °C/min, respectively. Instead of modeling separately for various temperature change rates, we trained the same PSO-SVR model with the accelerometer drift data obtained under various temperature conditions to improve accuracy and adaptability. By comparing its accuracy with the PSO-tuned back-propagation neural network (PSO-BP) and polynomial least squares (PLS) models and their performance on non-training data, we verified that the PSO-SVR model has a good compensation effect and excellent generalization performance, and the atom gravimeter interferometric phase noise induced by vibration is significantly reduced after compensation. The method proposed in this article is of reference significance for improving the field measurement accuracy of the atom gravimeter.

In order to enhance the temperature independence of MEMS capacitive accelerometer (MCA), a novel temperature drift error (TDE) model is proposed. On the basis of the principle of MCA, the primary cause for TDE is analyzed, and TDE model is established based on temperature variation and its square. A temperature experiment is made to test MCA, and TDE model is implemented with the test data and Back-propagation artificial neural network (BP-ANN). Then, its performance is evaluated by Mean Square Deviation (MSD), which is compared with a model based on Third-Order Least Square Method (LSM-3 model). The results show MSD compensated by TDE model is reduced more efficiently, which means TDE model can reduce TDE of MCA more accurately. It enhances the temperature independence of MCA greatly, and ensures MCA to perform stably in a long run.

Downhole instrumentation requires more and more accuracy of MEMS inertial sensors. However, in measurement while drilling, temperature drift phenomenon of the sensor will have a cumulative impact on the drill pipe attitude solution. After experimental testing, the output response of the accelerometer had strong local linear and global nonlinear characteristics. In this paper, we proposed a temperature compensation model based on tent chaotic mapping and sparrow search algorithm optimized back propagation (BP) neural network (Tent-SSA-BPNN). Sparrow search algorithm (SSA) was optimized by tent chaotic mapping, which was utilized to improve the uniformity and search ability of SSA populations. Then, the improved SSA was used to optimize the weight and bias parameters of the BP neural network for constructing the temperature compensation model. Finally, the trained compensation model is integrated into the microprogram control unit for real-time compensation testing. The experimental results show that after sacrificing a small amount of sampling frequency, the compensation model proposed in this article has good global compensation performance, and the mean absolute percentage error is reduced from 2% to 0.2% compared to the original output. The mean absolute error and root mean square error of the improved compensation model are all reduced compared to the pre-improved BP compensation model. This temperature-compensated modeling method has a reference value for low-cost and high-precision modeling in high temperature environments, while greatly saving time cost and measurement costs.

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A novel parasitic resistance-based high precision capacitive MEMS accelerometer temperature compensation method is proposed. The performance of MEMS accelerometer is severely affected by temperature drift. After a careful modeling analysis of the MEMS sensor, it is found that phase shift of the system is majorly affected by the parasitic resistor of the sensor cap. Thus, it can be used for sensor temperature compensation. Detailed analytic models and simulations are provided. Experimental results show that the bias stability is reduced from 0.26 to 0.18 mg after real-time temperature compensation. The temperature drift is reduced.

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In this paper, the method for compensating the temperature drift of high-G MEMS accelerometer (HGMA) is proposed, including radial basis function neural network (RBF NN), RBF NN based on genetic algorithm (GA), RBF NN based on GA with Kalman filter (KF), and the RBF NN + GA + KF method compensated by the temperature drift model. First, this paper introduces an HGMA structure working principle, conducts a finite element analysis, and produces the results. The simulation results show that the HGMA working mode is the 1st order mode, and its resonant frequency is 408 kHz. The 2nd order mode resonant frequency is 667 kHz, and the gap with the first mode is 260 kHz, indicating that the coupling movement between the two modes is tiny, so the HGMA has good linearity. Then, a temperature experiment is performed to obtain the output value of HGMA. The output values of HGMA are analyzed and optimized by using the algorithms proposed in this paper. The processing results show that the RBF NN + GA + KF method compensated by the temperature drift model achieves the best denoing consequent. The processing results show that the temperature drift of the HGMA is effectively compensated. The final results show that acceleration random walking improved from 17130 g/h/Hz0.5 to 765.3 g/h/Hz0.5, and bias stability improved from 4720 g/h to 57.27 g/h, respectively. The results show that after using the RBF NN + GA + KF method, combined with the temperature drift model, the temperature drift trend and noise characteristics of HGMA are well optimized.

In order to improve the performance of a micro-electro-mechanical system (MEMS) accelerometer, three algorithms for compensating its temperature drift are proposed in this paper, including deep long short-term memory recurrent neural network (DLSTM-RNN, short DLSTM), DLSTM based on sparrow search algorithm (SSA), and DLSTM based on improved SSA (ISSA). Moreover, the piecewise linear approximation (PLA) method is employed in this paper as a comparison to evaluate the impact of the proposed algorithm. First, a temperature experiment is performed to obtain the MEMS accelerometer's temperature drift output (TDO). Then, we propose a real-time compensation model and a linear approximation model for neural network methods compensation and PLA method compensation, respectively. The real-time compensation model is a recursive method based on the TDO at the last moment. The linear approximation model considers the MEMS accelerometer's temperature and TDO as input and output, respectively. Next, the TDO is analyzed and optimized by the real-time compensation model and the three algorithms mentioned before. Moreover, the TDO is also compensated by the linear approximation model and PLA method as a comparison. The compensation results show that the three neural network methods and the PLA method effectively compensate for the temperature drift of the MEMS accelerometer, and the DLSTM + ISSA method achieves the best compensation effect. After compensation by DLSTM + ISSA, the three Allen variance coefficients of the MEMS accelerometer that bias instability, rate random walk, and rate ramp are improved from 5.43×10-4mg, 4.33×10-5mg/s12, 1.18×10-6mg/s to 2.77×10-5mg, 1.14×10-6mg/s12, 2.63×10-8mg/s, respectively, with an increase of 96.68% on average.

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Hierarchical thermal models of strapdown inertial navigation system with fiber-optic gyros and accelerometers are constructed and studied. Thermal drift models of gyros and accelerometers are constructed and identified using experimental output data, and methods to minimize and algorithmically compensate the thermal drift are developed. Temperature calibration of sensors is performed using the thermal sensors’ data based on the constructed mathematical thermal compensation models, and the gyro drift is minimized.

Abstract Temperature-dominated drift is generally the main error source for high-performance micromachined resonant accelerometers (MRAs) due to inherent thermal stress effect of resonator structure and die-attach process. This paper describes the design and experimental evaluation of a temperature compensation scheme for MEMS resonant accelerometers that demonstrates excellent bias and scale factor stability against temperature variation. An on-chip temperature sensor fabricated by sputtering platinum film on glass substrate is proposed to accurately sense the temperature-induced frequency change of the resonator. A polynomial fitting-based post-compensation model is firstly used to suppress the temperature sensitivity of the MRA over dynamic temperature environment. The temperature drift test and compensation of four accelerometer prototypes in a range from −40 ∘ C to 60 ∘ C show that the stability of bias and scale factor has been improved greatly with navigation-grade performance. Temperature compensation results with three improved drift models based on polynomial fitting, convolutional neural network and support vector regression respectively are presented and compared to suppress the temperature drift hysteresis in consecutive temperature-varying tests. These experimental results indicate that this resonant accelerometer exhibits excellent temperature stability after compensation, which offers the promise for high-performance inertial navigation applications.

The output of the micromachined silicon resonant accelerometer (MSRA) is prone to drift in a temperature-changing environment. Therefore, it is crucial to adopt an appropriate suppression method for temperature error to improve the performance of the accelerometer. In this study, an improved firefly algorithm-backpropagation (IFA-BP) neural network is proposed in order to realize temperature compensation. IFA can improve a BP neural network's convergence accuracy and robustness in the training process by optimizing the initial weights and thresholds of the BP neural network. Additionally, zero-bias experiments at room temperature and full-temperature experiments were conducted on the MSRA, and the reproducible experimental data were used to train and evaluate the temperature compensation model. Compared with the firefly algorithm-backpropagation (FA-BP) neural network, it was proven that the IFA-BP neural network model has a better temperature compensation performance. The experimental results of the zero-bias experiment at room temperature indicated that the stability of the zero-bias was improved by more than an order of magnitude after compensation by the IFA-BP neural network temperature compensation model. The results of the full-temperature experiment indicated that in the temperature range of -40 °C~60 °C, the variation of the scale factor at full temperature improved by more than 70 times, and the variation of the bias at full temperature improved by around three orders of magnitude.

In recent years, High‐G MEMS accelerometers have been widely used in aviation, medicine, and other fields. So it is extremely important to improve the accuracy and performance of High‐G MEMS accelerometers. For this purpose, we propose a fusion algorithm that combines EMD, wavelet thresholding, and temperature compensation to process measurement data from a High‐G MEMS accelerometer. In the fusion algorithm, the original accelerometer signal is first decomposed by EMD to obtain the intrinsic mode function (IMF). Then, sample entropy (SE) is used to divide the IMF components into three segments. The noise segment is directly omitted, wavelet thresholding is performed on the mixing segment, and a GA‐BP performs temperature compensation on the drift segment. Finally, signal reconstruction is implemented. Later, a comparative analysis is carried out on the results from four models: EMD, wavelet thresholding, EMD + wavelet thresholding, and EMD + wavelet thresholding + temperature compensation. The experimental data show that the acceleration random walk change from 1712.66 g/h/Hz 0.5 to 79.15 g/h/Hz 0.5 and the zero‐deviation stability change from 49275 g/h to 774.7 g/h. This indicates that the fusion algorithm (EMD + wavelet thresholding + temperature compensation) not only effectively suppresses the noise of high‐frequency components but also compensates for temperature drift in the accelerometer.

This paper presents a modular and generic micromachined oven-control system for use with miniature micro-electro-mechanical system (MEMS) transducers. The micro-oven-controlled off-the-shelf commercial six-axis MEMS inertial measurement unit (IMU), Invensense MPU-6050, provides the lowest reported temperature-induced root of sum of squares bias errors of 62.71°/h and 1.920 mg from -40°C to 85°C for three-axis gyroscopes and three-axis accelerometers, respectively. The micro-oven control system provides thermal isolation from the surrounding environment using a micro-machined isolation platform, vacuum-sealing, and a metal package. In addition, a CMOS temperature sensor, a proportional-integral-derivative-based temperature control scheme, and least mean square and random forest compensation algorithms are utilized to reduce temperature-induced bias drifts of IMUs. The most stable axes achieve peak-to-peak bias drifts of 12.78°/h and 665.2 ug during a thermal-cycle test for gyroscopes and accelerometers, respectively. The oven's heater power consumption is <;125mW at the lowest temperature, -40°C. This oven-control system can be applied to a wide range of MEMS sensors to reduce performance degradation due to temperature variation.

Purpose Three-axis accelerometers play a vital role in monitoring the vibrations in aircraft machinery, especially in variable flight temperature environments. The sensitivity of a three-axis accelerometer under different temperature conditions needs to be calibrated before the flight test. Hence, the authors investigated the efficiency and sensitivity calibration of three-axis accelerometers under different conditions. This paper aims to propose the novel calibration algorithm for the three-axis accelerometers or the similar accelerometers. Design/methodology/approach The authors propose a hybrid genetic algorithm–particle swarm optimisation–back-propagation neural network (GA–PSO–BPNN) algorithm. This method has high global search ability, fast convergence speed and strong non-linear fitting capability; it follows the rules of natural selection and survival of the fittest. The authors describe the experimental setup for the calibration of the three-axis accelerometer using a three-comprehensive electrodynamic vibration test box, which provides different temperatures. Furthermore, to evaluate the performance of the hybrid GA–PSO–BPNN algorithm for sensitivity calibration, the authors performed a detailed comparative experimental analysis of the BPNN, GA–BPNN, PSO–BPNN and GA–PSO–BPNN algorithms under different temperatures (−55, 0 , 25 and 70 °C). Findings It has been showed that the prediction error of three-axis accelerometer under the hybrid GA–PSO–BPNN algorithm is the least (approximately ±0.1), which proved that the proposed GA–PSO–BPNN algorithm performed well on the sensitivity calibration of the three-axis accelerometer under different temperatures conditions. Originality/value The designed GA–PSO–BPNN algorithm with high global search ability, fast convergence speed and strong non-linear fitting capability has been proposed to decrease the sensitivity calibration error of three-axis accelerometer, and the hybrid algorithm could reach the global optimal solution rapidly and accurately.

Earth coordinate determination of current requires measurement of heading and tilt of the sensor to rotate the instrument frame measurement of velocity into Earth frame coordinates. Gimbaled magnetometer coils allow the magnetic heading to be determined but solid state three-axis magnetometers require tilt in addition to the Earth's magnetic vector to resolve heading. A measure of tilt is also desirable if the current meter cannot be assured of a vertical orientation. Two-axis MEMS accelerometers by Analog Devices, Inc. are capable of providing this tilt measurement but require temperature correction to remove a significant error at zero tilt. The determination and application of this temperature coefficient to correct the error has enabled a versatile attitude sensor to be incorporated in the modular acoustic velocity sensor (MAVS) for conversion of flow measurements by the sensor into Earth-coordinate currents. Residual tilt error is less than 0.3 degrees from 5degC to 28degC. Absolute accuracy of the sensor is better than 1deg between -50deg and +50deg and is better than 3deg between -70deg and +70deg. Because the accelerometer works equally well inverted, the current meter can be mounted upside down to place the velocity sensor above instead of below the housing without opening the case. A second socket for the accelerometer at right angles to the first permits a horizontal mounting of the current meter with only minor internal rearrangement of a part

The paper presents a way to obtain an intelligent miniaturized three-axial accelerometric sensor, based on the on-line estimation and compensation of the sensor errors generated by the environmental temperature variation. Taking into account that this error’s value is a strongly nonlinear complex function of the values of environmental temperature and of the acceleration exciting the sensor, its correction may not be done off-line and it requires the presence of an additional temperature sensor. The proposed identification methodology for the error model is based on the least square method which process off-line the numerical values obtained from the accelerometer experimental testing for different values of acceleration applied to its axes of sensitivity and for different values of operating temperature. A final analysis of the error level after the compensation highlights the best variant for the matrix in the error model. In the sections of the paper are shown the results of the experimental testing of the accelerometer on all the three sensitivity axes, the identification of the error models on each axis by using the least square method, and the validation of the obtained models with experimental values. For all of the three detection channels was obtained a reduction by almost two orders of magnitude of the acceleration absolute maximum error due to environmental temperature variation.

In order to meet the requirements of the small guided ammunition aerodynamic layout and the internal small space assembly requirements, this paper designs a hollow and non-centroid configurations Micro-Inertial Measurement Unit. The installation position of MEMS gyros and MEMS accelerometers are given in MIMU PCB. The error characteristics of the inertial sensor are analyzed and the error model of the sensor is constructed. With high-precision three-axis turret and centrifuge equipment, applying discrete calibration algorithm to calibrate the various coefficients of the error model. The performance of the MIMU is considerably improved by detailed calibration, including temperature compensation, nonlinear error compensation, cross-coupling error compensation and so on. Focus on the analysis of the influences of center distance error for the sensors output. Finally, MIMU is equipped with a small rocket for flight test, the test results show that the MIMU designed has a certain anti-overload capability, and meet the flight environment measurement requirements.

Multi-axis magnetic and accelerometer sensor are widely used in consumer product such as smart phones. The vector output of multi-axis sensors have errors on each axis such as offset error, scale error, non-orthogonality. These errors cause many problems on the performance of the applications. In this paper, we designed the effective inline compensation algorithm for calibrating of 3 axis sensors using ellipsoid for mass production of multi-axis sensors. The outputs with those kinds of errors can be modeled by ellipsoid, and the proposed algorithm makes sequential mappings of the virtual ellipsoid to perfect sphere which is calibrated function of the sensor on three-dimensional space. The proposed calibrating process composed of four main stages and is very straightforward and effective. In addition, another imperfection of the sensor such as the drift from temperature can be easily inserted in each mapping stage. Numerical simulation and experimental results shows great performance of the proposed compensation algorithm.

Measurement of temperature errors of fiber optic gyro (FOG) scale factor is important in FOG technology. In traditional methods, the measurement errors of FOG scale factors are greatly affected by the turntable’s orientation control errors. This article proposes a systematic method to measure the positive and negative FOG scale factor errors using a low-precision turntable. The relationship between the inertial navigation errors and the complete inertial measurement unit (IMU) errors is revealed. A simplified tracking algorithm is devised to obtain the change rates of the velocity errors with lower computation. A measurement procedure is designed, with three groups of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi $ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$- \pi $ </tex-math></inline-formula> rotations around the east axis of the turntable at each temperature. Observation equations are derived to estimate the positive and negative FOG scale factor errors. Simulation and experimental results show that a low-precision turntable can accurately measure the FOG scale factor errors at each temperature. Furthermore, temperature errors of accelerometer biases, scale factors, and nonlinear scale factors can also be measured at the same time using the rotation sequences and formulas in this article without additional rotations.

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We report a new silicon Microelectromechanical systems (MEMS) accelerometer based on differential frequency modulation (FM) with experimentally demonstrated thermal compensation over a dynamic temperature environment and μg-level Allan deviation of bias. The sensor architecture is based on resonant frequency tracking in a vacuum packaged siliconon-insulator (SOI) tuning fork oscillator. To address drift over temperature, the MEMS sensor die incorporates two identical tuning forks with opposing axes of sensitivity. Demodulation of the differential FM output from the two simultaneously operated oscillators eliminates common mode errors and provides an FM output with continuous thermal compensation. The first SOI prototype with quality factor of 350000 was built and characterized over a temperature range between 30 °C and 75 °C. Temperature characterization of the FM accelerometer showed less than a 0.5% scale-factor change throughout a temperature range from 30 °C to 75 °C, without any external compensation. This is enabled by an inherently differential frequency output, which cancels common-mode influences, such as those due to temperature. Allan deviation of the differential FM accelerometer revealed a bias instability of 6 μg at 20 s, along with an elimination of any temperature drift due to increases in averaging time. After comparing the measured bias instability with the designed linear range of 20 g, the sensor demonstrates a wide dynamic range of 130 dB. A second design iteration of the FM accelerometer, vacuum-sealed with getter material, was created to maximize Q-factor, and thereby frequency resolution. A Q-factor of 2.4 million was experimentally demonstrated, with a time constant of >20 min.

The micromechanical silicon resonant accelerometer has attracted considerable attention in the research and development of high-precision MEMS accelerometers because of its output of quasi-digital signals, high sensitivity, high resolution, wide dynamic range, anti-interference capacity and good stability. Because of the mismatching thermal expansion coefficients of silicon and glass, the micromechanical silicon resonant accelerometer based on the Silicon on Glass (SOG) technique is deeply affected by the temperature during the fabrication, packaging and use processes. The thermal stress caused by temperature changes directly affects the frequency output of the accelerometer. Based on the working principle of the micromechanical resonant accelerometer, a special accelerometer structure that reduces the temperature influence on the accelerometer is designed. The accelerometer can greatly reduce the thermal stress caused by high temperatures in the process of fabrication and packaging. Currently, the closed-loop drive circuit is devised based on a phase-locked loop. The unloaded resonant frequencies of the prototype of the micromechanical silicon resonant accelerometer are approximately 31.4 kHz and 31.5 kHz. The scale factor is 66.24003 Hz/g. The scale factor stability is 14.886 ppm, the scale factor repeatability is 23 ppm, the bias stability is 23 μg, the bias repeatability is 170 μg, and the bias temperature coefficient is 0.0734 Hz/°C.

Northrop Grumman, LITEF is developing MEMS (micro-electro-mechanical systems) based Inertial Measurement Units (IMU) for future attitude and heading reference systems (AHRS) with a target accuracy of 5 deg/h for the gyroscopes and 2.5 mg for the accelerometers. Within the technology development phase, prototype single axis gyroscopes have been realized and extensively tested for effects including temperature, acoustic and vibration sensitivities. These devices employ micro-machined all-silicon gyroscope sensor chips processed with deep reactive ion etching (DRIE). Silicon fusion bonding ensures pressures smaller than 3middot10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> mbar. Sophisticated analog electronics and digital signal processing condition the capacitive pick-off signals and realize full closed loop operation. The current results with overall bias error smaller than 2 deg/h to 5 deg/h, scale factor error <1200 ppm, measurement range >1000 deg/s and angular random walk <0.4 radic/vh indicate that stable production of 5 deg/h gyroscopes is realistic. The fabrication technology for capacitive, pendulous accelerometer chips is based on that used for the gyros with only an increase in the enclosed pressure to obtain overcritical damping. Pulse width modulation (PWM) within a digital control loop is used to realize closed loop operation. Accelerometer chips have been tested over temperature with a residual bias error <2.0 mg and a scale factor error <1400 ppm. These sensor chips have been integrated into an IMU whereby the power budget and size of the sensor electronics have been optimized. In this paper the salient features of the gyro and accelerometer designs are presented together with an overview of the IMU system architecture. Measurement results, with a focus on environmental characteristics and robustness, are included.

This paper develops a physical model of a MEMS capacitive accelerometer in order to use the accelerometer effectively in low-g motion tracking applications. The proposed physical model includes common physical parameters used to rate an accelerometer: scale factor, bias, and misalignment. Simple experiments used to reveal the behavior and characteristics of these parameters are described. A phenomenological modeling method is used to establish mathematical representations of these parameters in relation to errors such as nonlinearity, hysteresis, cross-axis effect, and temperature effect, without requiring a complete understanding of the underlying physics. Experimental results are presented, in which the physical model reduces RMSE by 93.1% in comparison with the manufacturer's recommended method.

This article describes a closed-loop detection MEMS accelerometer for acceleration measurement. This paper analyzes the working principle of MEMS accelerometers in detail and explains the relationship between the accelerometer zero bias, scale factor and voltage reference. Therefore, a combined compensation method is designed via reference voltage source compensation and terminal temperature compensation of the accelerometer, which comprehensively improves the performance over a wide temperature range of the accelerometer. The experiment results show that the initial range is reduced from 3679 ppm to 221 ppm with reference voltage source compensation, zero-bias stability of the accelerometer over temperature is increased by 14.3% on average and the scale factor stability over temperature is increased by 88.2% on average. After combined compensation, one accelerometer zero-bias stability over temperature was reduced to 40 μg and the scale factor stability over temperature was reduced to 16 ppm, the average value of the zero-bias stability over temperature was reduced from 1764 μg to 36 μg, the average value of the scale factor stability over temperature was reduced from 2270 ppm to 25 ppm, the average stability of the zero bias was increased by 97.96% and the average stability of the scale factor was increased by 98.90%.

MEMS based Inertial Measurement Units, which include MEMS accelerometers and gyroscopes, have a wide range of applications due to their low cost, small size and low power consumption. IMU error should be reduced to the lowest level so as to minimize errors of navigation systems which use MEMS IMU. MEMS sensors have bias, scale factor as well as temperature change of these errors. In the error compensation algorithm, polynomials are used to compensate temperature dependent change of errors. The degree of polynomials, which are determined according to sensor characteristics, affect IMU performance. Therefore, optimum degree must be determined by various methods and studies. In this paper, temperature dependent errors of MEMS inertial sensors will be defined and how to determine degree of polynomial will be explained so as to compensate errors by the optimum way. Several simulation studies are supported with real sensor data.

This paper reports results of a high-performance navigation-grade resonant microelectromechanical systems (MEMS) accelerometer with a ±25g dynamic range demonstrating a bias and scale factor (SF) repeatability of 30 μg and 2 ppm respectively over an operational temperature range of -40° to 80°C. The output Allan deviation for measurements conducted at 30°C reveals an in-run bias instability of 35 ng and a velocity random walk of 0.34 μg/✓IIz.

Temperature is one of the most important factors affecting the accuracy of micromechanical silicon resonant accelerometer (SRA). In order to reduce the temperature sensitivity and improve the sensor performance, a new method of temperature self-compensation for SRA is presented in this paper. Utilizing the differential structure of SRA, the temperature compensation for bias and scale factor can be realized simultaneously in this method. Moreover, because no temperature sensor is needed in this method, the error in temperature measurement due to the temperature gradient between the mechanical sensitive structure and temperature sensor is avoided, and the precision of temperature compensation for SRA can be further improved. The test results obtained on SRA prototype which is developed by MEMS Inertial Technology Research Center show that, by employing the method of temperature self-compensation, the temperature coefficients of bias and scale factor are reduced from 3.1 mg/°C and 778 ppm/°C to 0.05 mg/°C and -9.4 ppm/°C, respectively.

This paper reports results obtained from two high-performance navigation grade resonant microelectromechanical systems (MEMS) accelerometer: one with a ±25g dynamic range ("RXL25") and the other with a ±100g dynamic range ("RXL100") demonstrating bias errors of 4 μg and 25 μg respectively over an operational temperature range of -40° to 80°C. The total scale factor (SF) residual errors for both accelerometers over temperature are reported to be less than 2 ppm. The bias instability (BI) and velocity random walk (VRW) of RXL25 are measured to be 0.086 μg and 0.40 $\mu {\text{g}}/\sqrt {{\text{Hz}}} $ respectively. The RXL100 accelerometer yields a BI and VRW of 0.34 μg and 0.91 $\mu {\text{g}}/\sqrt {{\text{Hz}}} $ respectively. The vibration rectification coefficient (VRC) for RXL25 is reported to be less than 10 μg/g <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> .

High-precision, low-temperature-sensitive microelectromechanical system (MEMS) capacitive accelerometers are widely used in aerospace, automotive, and navigation systems. An analytical study of the temperature drift of bias (TDB) and temperature drift of scale factor (TDSF) for an asymmetric comb capacitive accelerometer is presented in this paper. A five-layer model is established for the equivalent expansion ratio in the TDB and TDSF formulas, and the results calculated by the weighted average of thickness and elasticity modulus method are closest to the results of the numerical simulation. The analytical formulas of TDB and TDSF for an asymmetric structure are obtained. For an asymmetric structure, TDB is only related to thermal deformation and fabrication error. Additionally, half of the fixed electrode distance is not included in the expressions of Δ d and Δ D for asymmetric structures, thus resulting in the TDSF of the asymmetric structure being smaller compared to a symmetric structure with the same structural parameters. The TDSF of the symmetric structure is [-200.2 ppm/°C, -261.6 ppm/°C], while the results of the asymmetric structure are [-11.004 ppm/°C, -72.404 ppm/°C] under the same set of parameters. The parameters of the optimal asymmetric structure are obtained for fabrication guidance using numerical methods. In the experiment, the TDSF and TDB of the packaged structure and the non-packaged structure are compared, and a significant effect of the package on the signal output is found. The TDB is reduced from 3000 to 60 μg/°C, while the TDSF is reduced from 3000 to 140 ppm/°C.

EMCORE has demonstrated high-end tactical grade and navigation grade performance of a compact inertial measurement unit (IMU) based on quartz MEMS inertial sensor technology, originally developed by Systron Donner Inertial. Experimental results for the gyroscope reveal angle random walk lower than 0.001 °/$\surd$hr, and bias instability of 0.005 °/hr; bias over a dynamic temperature environment (−55 °C to +90 °C) is <0.2 °/hr and scale factor error is < 50 ppm. Experimental results for the accelerometer have demonstrated a velocity random walk of 0.3 $\mu$g/$\surd$Hz, with bias instability of $0.1 \mu \mathrm{g}$; accelerometer bias and scale factor drift over a full temperature range (−55 °C to +90 °C) were 20 mg and 25 ppm, respectively. This performance was achieved within the form factor of the SDI500 IMU (19 cubic inches, coffee mug size).

Accelerometer metrics of performance include higher dynamic range, lower noise, lower bias instability and lower power. As with all systems, these trade-offs compete. Achieving large dynamic range in accelerometers drives design trade-offs of sensitivity and survivability at the high end and low noise and drift at the low end of the range. CMOS-MEMS technology enables deployment of system-on-chip designs comprising an array of hundreds of individual accelerometer cells integrated with low-noise readout circuits and on-chip temperature, stress, and scale-factor sensors to compensate drift. These systems range to 50 kg shock measurement with 3 mg bias instability and a path toward micro-g bias instability.

This study proposed an all-quartz integrated resonant accelerometer, composed of a quartz pendulum as mass-spring system and quartz double-ended tuning forks (DETFs) as resonators. The detection principle is based on force-frequency characteristic, which the vibration frequency of DETF would change once the z-axis acceleration provokes axial stress variation of vibrating beam. In order to achieve high sensitivity, critical dimensions were analyzed, selected, and simulated. Homogeneous material, integration arrangement, and isolation structure were utilized to eliminate internal mismatch, ensure high-quality resonator, and suppress external disturbance to stabilize the output of sensor. Then, the components of the sensitive structure, the pendulum and DETF, were fabricated through compatible MEMS technology separately, and the prototype was finished by microassembly and package. Experimental platform was built up and the fundamental performances were obtained, such as full-scale range (FSR) of 70 g, bandwidth of more than 150 Hz, scale factor (SF), rotary output, and nonlinearity, which implies high sensitivity as 75.346 Hz/g. Besides, short-time stability of zero bias and SF and full-temperature stability were measured. The 0 g stability for 3 h, bias instability of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.85 ~\mu \text{g}$ </tex-math></inline-formula> , and resolution were measured, calculated, and analyzed as well. All performances verified the high stability of proposed accelerometer, which is comparable or better compared with state-of-the-art counterparts. The experiment results complied with theoretical analysis and suggested its feasibility in the realm of high-precise field.

Inertial measurement units and navigation systems range from low-end tactical to strategic grade, spanning a very large spectrum of sensor performance. EMCORE makes use of its own quartz MEMS gyros for tactical grade systems, while for higher-end systems we use in-house optical gyroscopes (fiber optic and ring laser gyros). These gyroscopes and systems range from 10 °/hr down to 0.0001 °/hr performance over dynamic environment. These systems require accelerometers with suitable levels of performance for each IMU/INS grade. In a previous DGON ISS 2021 paper we described the quartz-MEMS IMU progress toward navigation grade performance [1]. This improvement was based on use of a modified conventional calibration method over a dynamic thermal environment. Here we report the latest experimental results (consistent with a high-end tactical grade accelerometer) which are much-improved due to a method of self-calibration incorporating multiple resonant modes of the accelerometer structure. The results we present are for the quartz MEMS accelerometer, which demonstrate a velocity random walk of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0.1\ \mu \mathrm{g}/\surd{\text{Hz}}$</tex> , and bias instability of 30 ng. The accelerometer bias and scale factor drift over a full temperature range (-55 °C to +90 °C) were <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$25\ \mu \mathrm{g}$</tex> and 25 ppm, respectively, after we improved the conventional calibration. Using an innovative advanced operational regime, called multiple-mode operation, a new self-calibration algorithm was developed demonstrating accelerometer bias over a dynamic thermal profile of less than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2\ \mu \mathrm{g}$</tex> , thus, making the accelerometer suitable for high-end navigation grade systems.

HP is developing a MEMS accelerometer that offers high sensitivity and low noise level for seismic application. During the packaging process, it was found that the thermal mechanical stress resulted from the CTE mismatch between the silicon and the substrate can distort the MEMS structure and alter the device performance. A finite element model was established to understand the effect of substrate material, die attach material and package geometry on the scale factor and bias offset of the MEMS. The model predicted that ceramic substrate introduced less variation of the sensor performance over the operating temperature range (-40 to 70°C) than the FR4 substrate. In order to use the low cost FR4 substrate, one can use die attach adhesive with low modulus and/or small die attach area to minimize the gap and displacement. Ceramic packages and Chip on Board (COB) packages on FR4 substrate were built using various die attach adhesives to validate the model. The performance of the MEMS was measured from -40 to 70°C. Results showed that using a low modulus adhesive with full coverage and moderate thickness provides minimum temperature distortion. On the other hand, a high modulus adhesive can be employed if the die attach area is reduced. The model also indicated that by modifying the structure of the substrate, the stress on MEMS can be reduced. MEMS on pillar packages were built and evaluated to confirm the modeling result.

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.

Abstract In recent years, the analysis and improvement of temperature characteristics of Si-based capacitive accelerometers has received considerable research attention in the field of Microelectromechanical system (MEMS) sensors. Generally, the influence of temperature on the accelerometers can be mitigated by optimizing the structural design and compensating the output signal. Herein, the output characteristics of an accelerometer designed with asymmetrically arranged combs were analyzed under various temperatures. The purpose of this paper is to improve the temperature drift of scale factor (TDSF) of MEMS capacitive accelerometer, using the asymmetric layout structure to improve the TDSF fundamentally, and the least square method to achieve temperature compensation efficiently. The variations in the TDSF were compared for the symmetric and asymmetric structures. In addition, we modeled the accelerometer with an asymmetric structure for simulations to analyze the errors resulting from the electrostatic torsion phenomenon induced by the asymmetric structure. Moreover, a temperature compensation model was developed for the scale factor of the accelerometer, which was validated and verified with the data obtained from simulations and experiment. Furthermore, an accelerometer based on silicon on insulator was fabricated and tested to verify the simulation results and the compensation effects. According to the results, the scale factor of the studied accelerometer was 171.83 mV g −1 and the average value of the TDSF was 83.56 ppm °C −1 Overall, the experimental results were almost consistent with the simulation results. Under the asymmetric layout, the scale-factor stability improvement of the accelerometer could reach up to 86.96%, and the error caused by electrostatic torsion was ∼2.93%, which is relatively negligible. After compensation, the range and standard deviation of the scale factor of the accelerometer with respect to temperature were reduced by 94.46% and 95.69%, respectively, and the average value of TDSF was reduced by 95.90%, which verified the effectiveness of the compensation model.

Zero bias is an important performance index of MEMS accelerometerscope. Based on the large amount of given accelerometer experiments, we study zero bias of random error properties, temperature characteristic, large overload environment variation, and then calculate MEMS accelerometer bias, bias stability, zero bias repeatability. Through least-square method,we fit temperature scale factor and temperature bias of MEMS accelerometer. The experimental results show that the compensation method has the advantages of simple operation, effectively compensation for measuring error of MEMS accelerometer which is induced by temperature, and has strong engineering using value.

Scherzinger's lectures and comments on aided inertial naviga-

MEMS being the most crucial part in advancement of today's technology plays as the backbone for decrement in size of new electronic devices. They are widely used in pedometry, quad-copters, stabilizing platforms, Inertial Measurement Units (IMUs), Inertial Navigation Systems(INS), robotics and medical field etc. In this research paper we have focused on; bias offset, scale factor error, non-orthogonality, drift due to temperature. Because these errors are the major error sources in MEMS sensors. Different techniques like two position method, six position direct method and six position weighted least square method are used to calibrate MEMS sensors for these errors. Calibration data was collected by the help of CNC machines and a platform made of aluminum to mount the sensors easily. Calibration techniques are implemented on ADXRS649z (single axis gyroscope), MPU-3050 (Three axis digital gyroscope) and ADXL377 (single axis accelerometer) sensors. Temperature compensation is also done to compensate the temperature effects on sensors using controlled temperature chamber and finally, a comparison is made between calibration techniques.

Magnetic and inertial measurement units are an emerging technology to obtain 3D orientation of body segments in human movement analysis. In this respect, sensor fusion is used to limit the drift errors resulting from the gyroscope data integration by exploiting accelerometer and magnetic aiding sensors. The present study aims at investigating the effectiveness of sensor fusion methods under different experimental conditions. Manual and locomotion tasks, differing in time duration, measurement volume, presence/absence of static phases, and out-of-plane movements, were performed by six subjects, and recorded by one unit located on the forearm or the lower trunk, respectively. Two sensor fusion methods, representative of the stochastic (Extended Kalman Filter) and complementary (Non-linear observer) filtering, were selected, and their accuracy was assessed in terms of attitude (pitch and roll angles) and heading (yaw angle) errors using stereophotogrammetric data as a reference. The sensor fusion approaches provided significantly more accurate results than gyroscope data integration. Accuracy improved mostly for heading and when the movement exhibited stationary phases, evenly distributed 3D rotations, it occurred in a small volume, and its duration was greater than approximately 20 s. These results were independent from the specific sensor fusion method used. Practice guidelines for improving the outcome accuracy are provided.

Visual–inertial odometry (VIO) is known to suffer from drifting, especially over long-term runs. In this article, we present GVINS, a nonlinear optimization-based system that tightly fuses global navigation satellite system (GNSS) raw measurements with visual and inertial information for real-time and drift-free stateestimation. Our system aims to provide accurate global six-degree-of-freedom estimation under complex indoor–outdoor environments, where GNSS signals may be intermittent or even inaccessible. To establish the connection between global measurements and local states, a coarse-to-fine initialization procedure is proposed to efficiently calibrate the transformation online and initialize GNSS states from only a short window of measurements. The GNSS code pseudorange and Doppler shift measurements, along with visual and inertial information, are then modeled and used to constrain the system states in a factor graph framework. For complex and GNSS-unfriendly areas, the degenerate cases are discussed and carefully handled to ensure robustness. Thanks to the tightly coupled multisensor approach and system design, our system fully exploits the merits of three types of sensors and is able to seamlessly cope with the transition between indoor and outdoor environments, where satellites are lost and reacquired. We extensively evaluate the proposed system by both simulation and real-world experiments, and the results demonstrate that our system substantially suppresses the drift of the VIO and preserves the local accuracy in spite of noisy GNSS measurements. The versatility and robustness of the system are verified on large-scale data collected in challenging environments. In addition, experiments show that our system can still benefit from the presence of only one satellite, whereas at least four satellites are required for its conventional GNSS counterparts.

One of the general trends of the MEMS sensors business is the utilization of the technology to satisfy harsh environment requirements (temperature, shock, vibration, environment security). The conjunction of material (standard silicon, SiC or SOI), with complex micromachining techniques and advanced assembly techniques are the key to provide robust sensors with a minimum concession on specification. The goal of this paper is to present progress on gun hard (>20,000 g) and wide temperature range MEMS accelerometers (-120degC to +180degC). Concrete solutions and results (out of more than 500 tested products) will be presented and discussed in detail

Micro-electromechanical Systems (MEMS) inertial sensors are lightweight, small size and low-cost sensors that consume less power energy compared to their high-precision bulky counterparts. However, this miniaturization is a double-edged sword and MEMS-based inertial sensors suffer from various error sources, noises and instabilities. Indeed, inertial sensor errors vary with time, temperature and from turn on to turn on. In order to exploit the full potential of a MEMS-based inertial navigation system (INS), and to enhance its accuracy, it is indispensable to develop a temperature-dependent model that compensates these errors. Traditional temperature compensation methods rely on polynomial regression method, which fails to take into account the nonlinearities inherent in the sensor errors. This paper proposes a new temperature compensation model for a full inertial measurement unit (IMU), based on a radial basis function neural network (RBFNN) that compensates the significant deterministic errors of both accelerometer and gyroscope triads in a wide temperature range. A high precision rate table and a thermal chamber are used for accurate testing. The effectiveness of the method is investigated with various static and dynamics tests in the laboratory and with a car, and results are compared with the traditional polynomial fitting method.

Nowadays, the Micro Electro-Mechanical Systems (MEMS) are widely employed in both consumer and industrial applications. One of the most important fields adopting MEMS device is the inertial measurement sector where this kind of technology is employed to produce Inertial Measurement Unit (IMU) that are typically composed by a triaxial accelerometer, a triaxial gyroscope, and a triaxial magnetometer. The growth of the MEMS is due to their small dimension and cost, challenges that enable their use in several applications belonging from Industry 4.0 to automotive and aerospace. However, all these sectors have in common operating conditions characterized by wide temperatures range and vibrations of different nature. In this framework, both the scientific and technical literature seems lacks suitable measurement procedures to be applied for testing the reliability of such kind of devices under environmental stress. So, this paper proposes a test procedure for Environmental Stress Screening (ESS) to determine any mechanical and electrical weakness or early degradation in a MEMS-based inertial measurement unit, when subjected to mechanical vibration and thermal cycling temperature tests

This paper presents an application of the ISIF chip (intelligent sensor interface), for conditioning a dual-axis low-g accelerometer in MEMS technology. MEMS are nowadays the standard in automotive applications (and not only), as they feature a drastic reduction in cost, area and power, while they require a more complex electronic interface with respect to traditional discrete devices. ISIF is a platform on chip implementation, aiming to fast prototype a wide range of automotive sensors thanks to its high configuration resources, achieved both by full analog / digital IPs trimming options and by flexible routing structures. This accelerometer implementation exploits a relevant part of ISIF hardware resources, but also requires signal processing add-ins (software emulation of digital DSP blocks) for the closed loop conditioning architecture and for performance improvement (for example temperature drift compensation). In spite the short prototyping time, the resulting system achieves good performances with respect to commercial devices, featuring a 0.9 mg/radicHz noise density with 1024 LSB/g sensitivity on the digital output over a +/- 2g FS, and an offset drift over 100degC range within 30 mg, with 2% of FS sensitivity drift. Miniboards have been developed as product prototypes, consisting of a small PCB with ISIF and accelerometer dies bonded together, firmware embedded in EEPROM and communication transceivers

This paper describes an integrated CMOS-MEMS inertial sensor microsystem, consisting of a 3-axis accelerometer sensor device and its complementary readout circuit, which is designed to operate over a wide temperature range from - 55&deg;C to 175&deg;C. The accelerometer device is based on capacitive transduction and is fabricated using PolyMUMPS, which is a commercial process available from MEMSCAP. The fabricated accelerometer device is then post-processed by depositing a layer of amorphous silicon carbide to form a composite sensor structure to improve its performance over an extended wide temperature range. We designed and fabricated a CMOS readout circuit in IBM 0.13&mu;m process that interfaces with the accelerometer device to serve as a capacitance to voltage converter. The accelerometer device is designed to operate over a measurement range of &plusmn;20g. The described sensor system allows low power, low cost and mass-producible implementation well suited for a variety of applications with harsh or wide temperature operating conditions.