Homogeneous Sensor Fusion Optimization for Low-Cost Inertial Sensors.

The article deals with sensor fusion and real-time calibration in a homogeneous inertial sensor array. The proposed method allows for both estimating the sensors' calibration constants (i.e., gain and bias) in real-time and automatically suppressing degraded sensors while keeping the overall precision of the estimation. The weight of the sensor is adaptively adjusted according to the RMSE concerning the weighted average of all sensors. The estimated angular velocity was compared with a reference (ground truth) value obtained using a tactical-grade fiber-optic gyroscope. We have experimented with low-cost MEMS gyroscopes, but the proposed method can be applied to basically any sensor array.

An Interface ASIC Design of MEMS Gyroscope with Analog Closed Loop Driving.

This paper introduces a digital interface application-specific integrated circuit (ASIC) for a micro-electromechanical systems (MEMS) vibratory gyroscope. The driving circuit of the interface ASIC uses an automatic gain circuit (AGC) module instead of a phase-locked loop to realize a self-excited vibration, which gives the gyroscope system good robustness. In order to realize the co-simulation of the mechanically sensitive structure and interface circuit of the gyroscope, the equivalent electrical model analysis and modeling of the mechanically sensitive structure of the gyro are carried out by Verilog-A. According to the design scheme of the MEMS gyroscope interface circuit, a system-level simulation model including mechanically sensitive structure and measurement and control circuit is established by SIMULINK. A digital-to-analog converter (ADC) is designed for the digital processing and temperature compensation of the angular velocity in the MEMS gyroscope digital circuit system. Using the positive and negative diode temperature characteristics, the function of the on-chip temperature sensor is realized, and the temperature compensation and zero bias correction are carried out simultaneously. The MEMS interface ASIC is designed using a standard 0.18 µM CMOS BCD process. The experimental results show that the signal-to-noise ratio (SNR) of sigma-delta (ΣΔ) ADC is 111.56 dB. The nonlinearity of the MEMS gyroscope system is 0.03% over the full-scale range.

Automatic Rate and Rate-Integrating Mode-Switchable Axisymmetric Gyroscope.

This paper describes a novel rate and rate-integrating mode-switchable axisymmetric gyroscope. A precession angle tracking algorithm is developed to enable the gyro to switch automatically between rate and rate-integrating modes at preset rate points through a digital control system within the gyro. We also propose a vibrating amplitude control method for the rate-integrating mode that directly extracts the angular rate output to ensure switching stability. In rate mode, the bias instability and angle random walk of the gyro reach 0.106°/h and 0.011°/√h, respectively. Additionally, an input range of over ±5000°/s is measured in rate-integrating mode. The scale factor nonlinearity reaches approximately 116 ppm over the full-scale range. The control system implements effective steering control of the gyroscope, with a switching delay of 10 ms from rate mode to rate-integrating mode and 100 ms from rate-integrating to rate mode. The proposed system actualizes a new type of gyroscope with high accuracy and a wide input range, which combines the benefits of rate and rate-integrating modes.

Research on Nonlinear Compensation of the MEMS Gyroscope under Tiny Angular Velocity.

The Micro-Electro-Mechanical System (MEMS) gyroscope has been widely used in various fields, but the output of the MEMS gyroscope has strong nonlinearity, especially in the range of tiny angular velocity. This paper proposes an adaptive Fourier series compensation method (AFCM) based on the steepest descent method and Fourier series residual correction. The proposed method improves the Fourier series fitting method according to the output characteristics of the MEMS gyroscope under tiny angular velocity. Then, the optimal weights are solved by the steepest descent method, and finally the fitting residuals are corrected by Fourier series to further improve the compensation accuracy. In order to verify the effectiveness of the proposed method, the angle velocity component of the earth's rotation is used as the input of the MEMS gyroscope to obtain the output of the MEMS gyroscope under tiny angular velocities. Experimental characterization resulted in an input angular velocity between -0.0036°/s and 0.0036°/s, compared with the original data, the polynomial compensation method, and the Fourier series compensation method, and the output nonlinearity of the MEMS gyroscope was reduced from 1150.87 ppm, 641.13 ppm, and 250.55 ppm to 68.89 ppm after AFCM compensation, respectively, which verifies the effectiveness and superiority of the proposed method.

Ocean Wind Observation Based on the Mean Square Slope Using a Self-Developed Miniature Wave Buoy.

Real-time, continuous, and long-term marine monitoring data benefits ocean research. This study developed a low-cost, multi-parameter, miniature wave buoy. High spatial and temporal resolution of sea surface parameters, including wind, waves, and current, can be obtained at low cost through the deployment of numerous buoys, thus forming an observation array. Tested in the laboratory water tank, the relative error of water surface slope measurement of the buoy was approximately 5.6% when the slope angle was less than 15°. For frequencies between 0.1 and 1.0 Hz, the measurement of slope spectrum was almost identical to that of the wave gauge. The buoy underestimated the slope spectrum between 1.0−1.56 Hz. A good relationship (r2 = 0.75) was obtained between wind speed at 10 m above sea surface (U10) and the low-pass-filtered mean square slope (LPMSS). After incorporating the wave age into the U10 inversion process, the root mean square error (RMSE) and BIAS were reduced to 1.15 m/s and 0.02 m/s, respectively. The 2D distribution of buoy-measured slope components was used to detect the wind direction, with an RMSE of 23.7°. The spectral tail slope steepened with increasing wind speed at low wind speeds (<7 m/s). A technical flow chart of the miniature wave buoy is proposed to observe the sea surface parameters. This miniature buoy will play an essential complementary role in the growing demand for sea state monitoring, especially in nearshore oceans.

Design and Fabrication of a Novel Wheel-Ring Triaxial Gyroscope.

This paper presents a new type of three-axis gyroscope. The gyroscope comprises two independent parts, which are nested to further reduce the structure volume. The capacitive drive was adopted. The motion equation, capacitance design, and spring design of a three-axis gyroscope were introduced, and the corresponding formulas were derived. Furthermore, the X/Y driving frequency of the gyroscope was 5954.8 Hz, the Y-axis detection frequency was 5774.5 Hz, and the X-axis detection frequency was 6030.5 Hz, as determined by the finite element simulation method. The Z-axis driving frequency was 10,728 Hz, and the Z-axis sensing frequency was 10,725 Hz. The MEMS gyroscope's Z-axis driving mode and the sensing mode's frequency were slightly mismatched, so the gyroscope demonstrated a larger bandwidth and higher Z-axis mechanical sensitivity. In addition, the structure also has good Z-axis impact resistance. The transient impact simulation of the gyroscope structure showed that the maximum stress of the sensitive structure under the impact of 10,000 g@5 ms was 300.18 Mpa. The gyroscope was produced by etching silicon wafers in DRIE mode to obtain a high aspect ratio structure, tightly connected to the glass substrate by silicon/glass anode bonding technology.

Optimal Compensation of MEMS Gyroscope Noise Kalman Filter Based on Conv-DAE and MultiTCN-Attention Model in Static Base Environment.

Errors in microelectromechanical systems (MEMS) inertial measurement units (IMUs) are large, complex, nonlinear, and time varying. The traditional noise reduction and compensation methods based on traditional models are not applicable. This paper proposes a noise reduction method based on multi-layer combined deep learning for the MEMS gyroscope in the static base state. In this method, the combined model of MEMS gyroscope is constructed by Convolutional Denoising Auto-Encoder (Conv-DAE) and Multi-layer Temporal Convolutional Neural with the Attention Mechanism (MultiTCN-Attention) model. Based on the robust data processing capability of deep learning, the noise features are obtained from the past gyroscope data, and the parameter optimization of the Kalman filter (KF) by the Particle Swarm Optimization algorithm (PSO) significantly improves the filtering and noise reduction accuracy. The experimental results show that, compared with the original data, the noise standard deviation of the filtering effect of the combined model proposed in this paper decreases by 77.81% and 76.44% on the x and y axes, respectively; compared with the existing MEMS gyroscope noise compensation method based on the Autoregressive Moving Average with Kalman filter (ARMA-KF) model, the noise standard deviation of the filtering effect of the combined model proposed in this paper decreases by 44.00% and 46.66% on the x and y axes, respectively, reducing the noise impact by nearly three times.

Gyroscope-Based Video Stabilization for Electro-Optical Long-Range Surveillance Systems.

Video stabilization is essential for long-range electro-optical systems, especially in situations when the field of view is narrow, since the system shake may produce highly deteriorating effects. It is important that the stabilization works for different camera types, i.e., different parts of the electromagnetic spectrum independently of the weather conditions and any form of image distortion. In this paper, we propose a method for real-time video stabilization that uses only gyroscope measurements, analyze its performance, and implement and validate it on a real-world professional electro-optical system developed at Vlatacom Institute. Camera movements are modeled with 3D rotations obtained by integration of MEMS gyroscope measurements. The 3D orientation estimation quality depends on the gyroscope characteristics; we provide a detailed discussion on the criteria for gyroscope selection in terms of the sensitivity, measurement noise, and drift stability. Furthermore, we propose a method for improving the unwanted motion estimation quality using interpolation in the quaternion domain. We also propose practical solutions for eliminating disturbances originating from gyro bias instability and noise. In order to evaluate the quality of our solution, we compared the performance of our implementation with two feature-based digital stabilization methods. The general advantage of the proposed methods is its drastically lower computational complexity; hence, it can be implemented for a low price independent of the used electro-optical sensor system.

A Combined Method for MEMS Gyroscope Error Compensation Using a Long Short-Term Memory Network and Kalman Filter in Random Vibration Environments.

In applications such as carrier attitude control and mobile device navigation, a micro-electro-mechanical-system (MEMS) gyroscope will inevitably be affected by random vibration, which significantly affects the performance of the MEMS gyroscope. In order to solve the degradation of MEMS gyroscope performance in random vibration environments, in this paper, a combined method of a long short-term memory (LSTM) network and Kalman filter (KF) is proposed for error compensation, where Kalman filter parameters are iteratively optimized using the Kalman smoother and expectation-maximization (EM) algorithm. In order to verify the effectiveness of the proposed method, we performed a linear random vibration test to acquire MEMS gyroscope data. Subsequently, an analysis of the effects of input data step size and network topology on gyroscope error compensation performance is presented. Furthermore, the autoregressive moving average-Kalman filter (ARMA-KF) model, which is commonly used in gyroscope error compensation, was also combined with the LSTM network as a comparison method. The results show that, for the x-axis data, the proposed combined method reduces the standard deviation (STD) by 51.58% and 31.92% compared to the bidirectional LSTM (BiLSTM) network, and EM-KF method, respectively. For the z-axis data, the proposed combined method reduces the standard deviation by 29.19% and 12.75% compared to the BiLSTM network and EM-KF method, respectively. Furthermore, for x-axis data and z-axis data, the proposed combined method reduces the standard deviation by 46.54% and 22.30% compared to the BiLSTM-ARMA-KF method, respectively, and the output is smoother, proving the effectiveness of the proposed method.

A Filtering Algorithm of MEMS Gyroscope to Resist Acoustic Interference.

To reduce the impact of acoustic interference in a microelectromechanical system (MEMS) gyroscope and to improve the reliability of output data, a filtering algorithm based on orthogonal demodulation is proposed. According to the working principle and failure mechanism of a MEMS gyroscope, the sound and angular velocity frequencies are not identical, which lead to a different frequency signal output of the original single-channel demodulation scheme. Therefore, a Q channel demodulation filtering process was added to the origin single-channel demodulation scheme. For the Q channel demodulated signal, a Hilbert transform was used to compensate for the 90 degree phase shift. The IQ dual-channel difference can remove the acoustic interference signal. The simulation results indicate that the scheme can effectively suppress the acoustic interference signal and it can eliminate more than 95% of the impact of sound waves. We assembled the acoustic interference experimental platform, collected the driving and sensing data, and verified the denoising performance with our algorithm, which eliminated more than 70% of the noise signal. The simulation and experimental results demonstrate that the scheme can eliminate acoustic interference signal without destroying angular velocity signal.

Design, Analysis and Simulation of a MEMS-Based Gyroscope with Differential Tunneling Magnetoresistance Sensing Structure.

The design, analysis, and simulation of a new Micro-electromechanical System (MEMS) gyroscope based on differential tunneling magnetoresistance sensing are presented in this paper. The device is driven by electrostatic force, whereas the Coriolis displacements are transferred to intensity variations of magnetic fields, further detected by the Tunneling Magnetoresistance units. The magnetic fields are generated by a pair of two-layer planar multi-turn copper coils that are coated on the backs of the inner masses. Together with the dual-mass structure of proposed tuning fork gyroscope, a two-stage differential detection is formed, thereby enabling rejection of mechanical and magnetic common-mode errors concurrently. The overall conception is described followed by detailed analyses of proposed micro-gyroscope and rectangle coil. Subsequently, the FEM simulations are implemented to determine the mechanical and magnetic characteristics of the device separately. The results demonstrate that the micro-gyroscope has a mechanical sensitivity of 1.754 nm/°/s, and the micro-coil has a maximum sensitivity of 41.38 mOe/µm. When the detection height of Tunneling Magnetoresistance unit is set as 60 µm, the proposed device exhibits a voltage-angular velocity sensitivity of 0.131 mV/°/s with a noise floor of 7.713 × 10-6°/s/Hz in the absence of any external amplification.

Twist-n-Sync: Software Clock Synchronization with Microseconds Accuracy Using MEMS-Gyroscopes.

Sensor networks require a high degree of synchronization in order to produce a stream of data useful for further purposes. Examples of time misalignment manifest as undesired artifacts when doing multi-camera bundle-adjustment or global positioning system (GPS) geo-localization for mapping. Network Time Protocol (NTP) variants of clock synchronization can provide accurate results, though present high variance conditioned by the environment and the channel load. We propose a new precise technique for software clock synchronization over a network of rigidly attached devices using gyroscope data. Gyroscope sensors, or IMU, provide a high-rate measurements that can be processed efficiently. We use optimization tools over the correlation signal of IMU data from a network of gyroscope sensors. Our method provides stable microseconds accuracy, regardless of the number of sensors and the conditions of the network. In this paper, we show the performance of the gyroscope software synchronization in a controlled environment, and we evaluate the performance in a sensor network of smartphones by our open-source Android App, Twist-n-Sync, that is publicly available.

Research on Filtering Algorithm of MEMS Gyroscope Based on Information Fusion.

As an important inertial sensor, the gyroscope is mainly used to measure angular velocity in inertial space. However, due to the influence of semiconductor thermal noise and electromagnetic interference, the output of the gyroscope has a certain random noise and drift, which affects the accuracy of the detected angular velocity signal, thus interfering with the accuracy of the stability of the whole system. In order to reduce the noise and compensate for the drift of the MEMS (Micro Electromechanical System) gyroscope during usage, this paper proposes a Kalman filtering method based on information fusion, which uses the MEMS gyroscope and line accelerometer signals to implement the filtering function under the Kalman algorithm. The experimental results show that compared with the commonly used filtering methods, this method allows significant reduction of the noise of the gyroscope signal and accurate estimation of the drift of the gyroscope signal, and thus improves the control performance of the system and the stability accuracy.

Design of a 1-Bit MEMS Gyroscope Using the Model Predictive Control Approach.

In this paper, a bi-level Delta-Sigma modulator-based MEMS gyroscope design is presented based on a Model Predictive Control (MPC) approach. The MPC is popular because of its capability of handling hard constraints. In this work, we propose to combine the 1-bit nature of the bi-level Delta-Sigma modulator output with the MPC to develop a 1-bit processing-based MPC (OBMPC). This paper will focus on the affine relationship between the 1-bit feedback and the in-loop MPC controller, as this can potentially remove the multipliers from the controller. In doing so, the computational requirement of the MPC control is significantly alleviated, which makes the 1-bit MEMS Gyroscope feasible for implementation. In addition, a stable constrained MPC is designed, so that the input will not overload the quantizer while maintaining a higher Signal-to-Noise Ratio (SNR).

Oscillation Suppression in the Sense Mode of a High-Q MEMS Gyroscope Using a Simplified Closed-Loop Control Method.

The oscillation of the sense mode of the micro-machined Coriolis vibratory gyroscope (MCVG) with high quality factor (Q) is analyzed in this study and the corresponding force feedback control scheme is presented to suppress this oscillation. The controller consists of integrator and some filters, instead of the common but complicated demodulation and remodulation modules. Compared with using no oscillation suppression scheme, the proposed simplified oscillation suppression control scheme can achieve an improvement of the sense mode of the MCVG. The inband spectrum ripple of the angular rate output are improved from 51.4 dB to 4.23 × 10-4 dB. Correspondingly, these two performance parameters are improved by 370.4 and 186.2 times, which are higher than two orders of magnitude, respectively. Bias stability is improved from 9.72 deg/h to 2.5 deg/h. Test results prove that the proposed control scheme is effective in suppressing the oscillation.

A Novel Tri-Axial MEMS Gyroscope Calibration Method over a Full Temperature Range.

The micro-electro-mechanical inertial measurement unit (MEMS-IMU) has gradually become a research hotspot in the field of mid-low navigation, because of its advantages of low cost, small size, light weight, and low power consumption (CSWap). However, the performance of MEMS-IMUs can be severely degraded when subjected to temperature changes, especially gyroscopes. In order to make full use of the navigation accuracy, this paper proposes an optimized error calibration method for a tri-axial MEMS gyroscope across a full temperature range. First of all, a calibration error model is established which includes package misalignment error, sensor-to-sensor non-orthogonality error, scale factor, and bias. Then, a simple three-position positive/reversed test is undertaken by carrying out a single-axis temperature-controlled turntable at different reference temperature points. Lastly, the error compensation vector is obtained using the least squares method to establish an error matrix. It is worth mentioning that the error compensation vector at a known temperature point can be calculated through Lagrange interpolation; then, the outputs of the tri-axial MEMS gyroscope can be well compensated, eliminating the need for a recalibration step. The experimental results confirm the effectiveness of the proposed method, which is feasible and operational in engineering applications, and has a certain reference value.

An Adaptive Filtering Approach Based on the Dynamic Variance Model for Reducing MEMS Gyroscope Random Error.

To improve the dynamic random error compensation accuracy of the Micro Electro Mechanical System (MEMS) gyroscope at different angular rates, an adaptive filtering approach based on the dynamic variance model was proposed. In this paper, experimental data were utilized to fit the dynamic variance model which describes the nonlinear mapping relations between the MEMS gyroscope output data variance and the input angular rate. After that, the dynamic variance model was applied to online adjustment of the Kalman Filter measurement noise coefficients. The proposed approach suppressed the interference from the angular rate in the filtering results. Dynamic random errors were better estimated and reduced. Turntable experiment results indicated that the adaptive filtering approach compensated for the MEMS gyroscope dynamic random error effectively both in the constant angular rate condition and the continuous changing angular rate condition, thus achieving adaptive dynamic random error compensation.

A Multi-Model Combined Filter with Dual Uncertainties for Data Fusion of MEMS Gyro Array.

The gyro array is a useful technique in improving the accuracy of a micro-electro-mechanical system (MEMS) gyroscope, but the traditional estimate algorithm that plays an important role in this technique has two problems restricting its performance: The limitation of the stochastic assumption and the influence of the dynamic condition. To resolve these problems, a multi-model combined filter with dual uncertainties is proposed to integrate the outputs from numerous gyroscopes. First, to avoid the limitations of the stochastic and set-membership approaches and to better utilize the potentials of both concepts, a dual-noise acceleration model was proposed to describe the angular rate. On this basis, a dual uncertainties model of gyro array was established. Then the multiple model theory was used to improve dynamic performance, and a multi-model combined filter with dual uncertainties was designed. This algorithm could simultaneously deal with stochastic uncertainties and set-membership uncertainties by calculating the Minkowski sum of multiple ellipsoidal sets. The experimental results proved the effectiveness of the proposed filter in improving gyroscope accuracy and adaptability to different kinds of uncertainties and different dynamic characteristics. Most of all, the method gave the boundary surrounding the true value, which is of great significance in attitude control and guidance applications.

Signal Quality Improvement Algorithms for MEMS Gyroscope-Based Human Motion Analysis Systems: A Systematic Review.

Motion sensors such as MEMS gyroscopes and accelerometers are characterized by a small size, light weight, high sensitivity, and low cost. They are used in an increasing number of applications. However, they are easily influenced by environmental effects such as temperature change, shock, and vibration. Thus, signal processing is essential for minimizing errors and improving signal quality and system stability. The aim of this work is to investigate and present a systematic review of different signal error reduction algorithms that are used for MEMS gyroscope-based motion analysis systems for human motion analysis or have the potential to be used in this area. A systematic search was performed with the search engines/databases of the ACM Digital Library, IEEE Xplore, PubMed, and Scopus. Sixteen papers that focus on MEMS gyroscope-related signal processing and were published in journals or conference proceedings in the past 10 years were found and fully reviewed. Seventeen algorithms were categorized into four main groups: Kalman-filter-based algorithms, adaptive-based algorithms, simple filter algorithms, and compensation-based algorithms. The algorithms were analyzed and presented along with their characteristics such as advantages, disadvantages, and time limitations. A user guide to the most suitable signal processing algorithms within this area is presented.

Motion Blurred Star Image Restoration Based on MEMS Gyroscope Aid and Blur Kernel Correction.

Under dynamic conditions, motion blur is introduced to star images obtained by a star sensor. Motion blur affects the accuracy of the star centroid extraction and the identification of stars, further reducing the performance of the star sensor. In this paper, a star image restoration algorithm is investigated to reduce the effect of motion blur on the star image. The algorithm includes a blur kernel calculation aided by a MEMS gyroscope, blur kernel correction based on the structure of the star strip, and a star image reconstruction method based on scaled gradient projection (SGP). Firstly, the motion trajectory of the star spot is deduced, aided by a MEMS gyroscope. Moreover, the initial blur kernel is calculated by using the motion trajectory. Then, the structure information star strip is extracted by Delaunay triangulation. Based on the structure information, a blur kernel correction method is presented by utilizing the preconditioned conjugate gradient interior point algorithm to reduce the influence of bias and installation deviation of the gyroscope on the blur kernel. Furthermore, a speed-up image reconstruction method based on SGP is presented for time-saving. Simulated experiment results demonstrate that both the blur kernel determination and star image reconstruction methods are effective. A real star image experiment shows that the accuracy of the star centroid extraction and the number of identified stars increase after restoration by the proposed algorithm.