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Herein, we investigate the temperature compensation for a dual-mass MEMS gyroscope. After introducing and simulating the dual-mass MEMS gyroscope's working modes, we propose a hybrid algorithm for temperature compensation relying on improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), sample entropy, time–frequency peak filtering, non-dominated sorting genetic algorithm-II (NSGA II) and extreme learning machine. Firstly, we use ICEEMDAN to decompose the gyroscope's output signal, and then we use sample entropy to classify the decomposed signals. For noise segments and mixed segments with different levels of noise, we use time–frequency peak filtering with different window lengths to achieve a trade-off between noise removal and signal retention. For the feature segment with temperature drift, we build a compensation model using extreme learning machine. To improve the compensation accuracy, NSGA II is used to optimize extreme learning machine, with the prediction error and the 2-norm of the output-layer connection weight as the optimization objectives. Enormous simulation experiments prove the excellent performance of our proposed scheme, which can achieve trade-offs in signal decomposition, classification, denoising and compensation. The improvement in the compensated gyroscope's output signal is analyzed based on Allen variance; its angle random walk is decreased from 0.531076°/h/√Hz to 6.65894 × 10−3°/h/√Hz and its bias stability is decreased from 32.7364°/h to 0.259247°/h. [ABSTRACT FROM AUTHOR]

This document is an editorial for a special issue of the journal Micromachines on Micro-Electromechanical System (MEMS) inertial devices. It explains that MEMS are miniature systems that combine micro-mechanical sensors, actuators, and microelectronic circuits. MEMS inertial devices, such as accelerometers and gyroscopes, capture physical motion and convert it into electrical signals. The editorial highlights various applications of MEMS inertial devices, including aerospace, underwater exploration, robotics, and healthcare. It also discusses the challenges faced by these devices and presents 11 papers in the special issue that cover different aspects of MEMS inertial devices, including design, manufacturing, optimization, and maintenance. [Extracted from the article]

This study proposes an improved multi-scale permutation entropy complete ensemble empirical mode decomposition with adaptive noise (MPE-CEEMDAN) method based on adaptive Kalman filter (AKF) and grey wolf optimizer-least squares support vector machine (GWO-LSSVM). By establishing a temperature compensation model, the gyro temperature output signal is optimized and reconstructed, and a gyro output signal is obtained with better accuracy. Firstly, MPE-CEEMDAN is used to decompose the FOG output signal into several intrinsic mode functions (IMFs); then, the IMFs signal is divided into mixed noise, temperature drift, and other noise according to different frequencies. Secondly, the AKF method is used to denoise the mixed noise. Thirdly, in order to denoise the temperature drift, the fiber gyroscope temperature compensation model is established based on GWO-LSSVM, and the signal without temperature drift is obtained. Finally, the processed mixed noise, the processed temperature drift, the processed other noise, and the signal-dominated IMFs are reconstructed to acquire the improved output signal. The experimental results show that, by using the improved method, the output of a fiber optic gyroscope (FOG) ranging from −30 °C to 60 °C decreases, and the temperature drift dramatically declines. The factor of quantization noise (Q) reduces from 6.1269 × 10−3 to 1.0132 × 10−4, the factor of bias instability (B) reduces from 1.53 × 10−2 to 1 × 10−3, and the factor of random walk of angular velocity (N) reduces from 7.8034 × 10−4 to 7.2110 × 10−6. The improved algorithm can be adopted to denoise the output signal of the FOG with higher accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a fault identification algorithm combining a signal processing algorithm and machine learning algorithm is proposed, using a four-mass vibration MEMS gyroscope (FMVMG) for signal acquisition work, constructing a gyroscope fault dataset, and performing the model training task based on this dataset. Combining the improved EWT algorithm with SEResNeXt-50 reduces the impact of white noise in the signal on the identification task and significantly improves the accuracy of fault identification. The EWT algorithm is a wavelet analysis algorithm with adaptive wavelet analysis, which can significantly reduce the impact of boundary effects, and has a good effect on decomposition of signal segments with short length, but a reconstruction method is needed to effectively separate the noise signal and effective signal, and so this paper uses multiscale permutation entropy for calculation. For the reason that the neural network has a better ability to characterize high-dimensional signals, the one-dimensional signal is reconstructed into a two-dimensional image signal and the signal features are extracted. Then, the constructed image signals are fed into the SEResNeXt-50 network, and the characterization ability of the model is further improved in the network with the addition of the Squeeze-and-Excitation module. Finally, the proposed model is applied to the FMVMG fault dataset and compared with other models. In terms of recognition accuracy, the proposed method improves about 30.25% over the BP neural network and about 1.85% over ResNeXt-50, proving the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

MEMS gyroscopes are one of the core components of inertial navigation systems. The maintenance of high reliability is critical for ensuring the stable operation of the gyroscope. Considering the production cost of gyroscopes and the inconvenience of obtaining a fault dataset, in this study, a self-feedback development framework is proposed, in which a dualmass MEMS gyroscope fault diagnosis platform is designed based on MATLAB/Simulink simulation, data feature extraction, and classification prediction algorithm and real data feedback verification. The platform integrates the dualmass MEMS gyroscope Simulink structure model and the measurement and control system, and reserves various algorithm interfaces for users to independently program, which can effectively identify and classify seven kinds of signals of the gyroscope: normal, bias, blocking, drift, multiplicity, cycle and internal fault. After feature extraction, six algorithms, ELM, SVM, KNN, NB, NN, and DTA, were respectively used for classification prediction. The ELM and SVM algorithms had the best effect, and the accuracy of the test set was up to 92.86%. Finally, the ELM algorithm is used to verify the actual drift fault dataset, and all of them are successfully identified. [ABSTRACT FROM AUTHOR]

This paper presents an improved empirical modal decomposition (EMD) method to eliminate the influence of the external environment, accurately compensate for the temperature drift of MEMS gyroscopes, and improve their accuracy. This new fusion algorithm combines empirical mode decomposition (EMD), a radial basis function neural network (RBF NN), a genetic algorithm (GA), and a Kalman filter (KF). First, the working principle of a newly designed four-mass vibration MEMS gyroscope (FMVMG) structure is given. The specific dimensions of the FMVMG are also given through calculation. Second, finite element analysis is carried out. The simulation results show that the FMVMG has two working modes: a driving mode and a sensing mode. The resonant frequency of the driving mode is 30,740 Hz, and the resonant frequency of the sensing mode is 30,886 Hz. The frequency separation between the two modes is 146 Hz. Moreover, a temperature experiment is performed to record the output value of the FMVMG, and the proposed fusion algorithm is used to analyse and optimise the output value of the FMVMG. The processing results show that the EMD-based RBF NN+GA+KF fusion algorithm can compensate for the temperature drift of the FMVMG effectively. The final result indicates that the random walk is reduced from 99.608°/h/Hz1/2 to 0.967814°/h/Hz1/2, and the bias stability is decreased from 34.66°/h to 3.589°/h. This result shows that the algorithm has strong adaptability to temperature changes, and its performance is significantly better than that of an RBF NN and EMD in compensating for the FMVMG temperature drift and eliminating the effect of temperature changes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The micro-electro-mechanical system (MEMS) gyroscope is a micro-mechanical gyroscope with low cost, small volume, and good reliability. The working principle of the MEMS gyroscope, which is achieved through Coriolis, is different from traditional gyroscopes. The MEMS gyroscope has been widely used in the fields of micro-inertia navigation systems, military, automotive, consumer electronics, mobile applications, robots, industrial, medical, and other fields in micro-inertia navigation systems because of its advantages of small volume, good performance, and low price. The material characteristics of the MEMS gyroscope is very significant for its data output, and the temperature determines its accuracy and limits its further application. In order to eliminate the effect of temperature, the MEMS gyroscope needs to be compensated to improve its accuracy. This study proposed an improved variational modal decomposition—extreme learning machine (VMD-ELM) algorithm based on convolutional neural networks—long short-term memory (CNN-LSTM) and particle swarm optimization—support vector machines (PSO-SVM). By establishing a temperature compensation model, the gyro temperature output signal is optimized and reconstructed, and the gyro output signal with better accuracy is obtained. The VMD algorithm separates the gyro output signal and divides the gyro output signal into low-frequency signals, mid-frequency signals, and high-frequency signals according to the different signal frequencies. Once again, the PSO-SVM model is constructed by the mid-frequency temperature signal to find the temperature error. Finally, the signal is reconstructed through the ELM neural network algorithm, and then, the gyro output signal after noise is obtained. Experimental results show that, by using the improved method, the output of the MEMS gyroscope ranging from −40 to 60 °C reduced, and the temperature drift dramatically declined. For example, the factor of quantization noise (Q) reduced from 1.2419 × 10−4 to 1.0533 × 10−6, the factor of bias instability (B) reduced from 0.0087 to 1.8772 × 10−4, and the factor of random walk of angular velocity (N) reduced from 2.0978 × 10−5 to 1.4985 × 10−6. Furthermore, the output of the MEMS gyroscope ranging from 60 to −40 °C reduced. The factor of Q reduced from 2.9808 × 10−4 to 2.4430 × 10−6, the factor of B reduced from 0.0145 to 7.2426 × 10−4, and the factor of N reduced from 4.5072 × 10−5 to 1.0523 × 10−5. The improved algorithm can be adopted to denoise the output signal of the MEMS gyroscope to improve its accuracy. [ABSTRACT FROM AUTHOR]

In this paper, the structure and working principle of four-mass vibration MEMS gyroscope (FMVMG) are introduced, and the working modes of FMVMG are simulated and analyzed. On the basis of this, an improved noise reduction method based on interval local mean decomposition (ILMD) and parabolic tracking time-frequency peak filtering (PTTFPF) is proposed. PTTFPF can resample the signal along a parabolic path and select the optimal filtering trajectory, but there is still a contradiction, choosing a short window length may lead to good signal amplitude retention, but the random noise reduction effect is not good, while choosing a long window length may lead to serious amplitude attenuation, but the random noise reduction effect is better. In order to achieve a better balance between effective signal amplitude preservation and random noise reduction, the ILMD method was used to improve PTTFPF. First, the original signal was decomposed into product functions (PFs) by local mean decomposition (LMD) method, and the sample entropy (SE) of each PF was calculated. The PFs are divided into three different components. Then, short window PTTFPF is used for useful PF and long window PTTFPF is used for mixed PF, noise PF is directly removed. Then the final signal is reconstructed. Finally, the denoised useful PF and mixed PF are reconstructed to obtain the final signal. The proposed ILMD-PTTFPF algorithm was verified by temperature experiments. The results show that the denoising performance of the ILMD-PTTFPF algorithm is better than that of traditional wavelet threshold denoising and Kalman filtering. [ABSTRACT FROM AUTHOR]

This article investigates a neurodynamic quantized control problem with improved transient performances for microelectromechanical system (MEMS) gyroscopes subject to lumped disturbances induced by parameter uncertainties, dynamic coupling, and external disturbances. First, a modified prescribed performance control mechanism based on a hyperbolic cosecant performance function is proposed to specify the transient behavior of tracking errors with an arbitrarily small overshoot. Then, to eliminate the lumped disturbances with a better identification property, a novel echo state network approximator that uses the estimation error to learn neural weights is designed with the aid of a minimal learning parameter technique, which not only can exclude the poor transient behaviors occurring extensively in the existing neural control with a large adaptive gain, but also dramatically reduce the number of parameters to be updated online. Furthermore, contrasting to the available tracking results assuming a continuous control updating, a hysteresis quantizer is introduced to provide discrete values of control signals, supporting the use of digital devices in MEMS gyroscope implementations to realize a closed-loop error stabilization. Finally, ultimately uniformly bounded stability of closed-loop system is proved with the aid of Lyapunov function and nonsmooth analysis technique, while not only simulations but also experimental results are performed to validate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

A z-axis decoupled multi-frame vibration MEMS gyroscope (DMFVMG) is presented in this paper. Firstly, the decoupled principle is employed and the sense frame, Coriolis frame and drive frame are arranged through inner fame, intermediate frame and outer frame, and the movement characteristic analysis indicates that the structure is fully decoupled. The structure is simulated through mode analysis, harmonic response and drop shock response. The simulation results show that the resonant frequencies of the Sense Mode and Drive Mode are 10094Hz and 10162Hz, and the maximum deformation and stress with the shock analysis is 7.14 $\mu {\mathrm{ m}}$ and 235.19MPa (among three different directions). Then, the structure is fabricated through MEMS processing, and P-type single-crystalline silicon wafer and 7740 glass wafer are used. After that, the structure is packaged in a ceramic vacuum tube shell and the resonant frequencies and quality values of the sense and drive mode are 10354.21Hz and 5364, 10438.23Hz and 5219, the error between fabrication and simulation is 2.58% and 2.72%. And the monitoring system of DMFVMG prototype is established by analog circuit with drive closed-loop and sense open-loop. Then, the DMFVMG prototype is tested through turntable, and the range, scale factor and intercept are ±300°/s, −19.06mV/°/s and 95.43mV respectively. Finally, five repeated bias tests are arranged and the angular random walking values and bias stability are 0.2408°/ $\surd \text{h}$ , 0.2358°/ $\surd \text{h}$ , 0.2413°/ $\surd \text{h}$ , 0.2397°/ $\surd \text{h}$ and 0.2480°/ $\surd \text{h}$ , 2.858°/h, 3.159°/h, 3.428°/h, 1.891°/h and 3.467°/h respectively. [ABSTRACT FROM AUTHOR]

To solve the problem of micro-electro-mechanical system (MEMS) gyroscope noise, this paper presents a variational mode decomposition (VMD) method based on crow search algorithm. First, the signal was decomposed by variational mode decomposition for optimization of crow search algorithm (CSA-VMD) method. The parameters required by the VMD method (penalty parameter α and decomposition number K) are given by the crow search algorithm, and then the signal is decomposed into the superposition of multiple subsignals, called intrinsic mode functions (IMFs). The sample entropy (SE) corresponding to each IMF is then obtained. By calculating the sample entropy, the noise signal can be divided into pure noise part, mixing part, and temperature drift part. Second, Savitzky–Golay smoothing denoising (SG) is used to filter the mixed noise signal to eliminate the influence of noise. Third, for the filtering of the drift part, the least square support vector machine optimized by the crow search algorithm (CSA-LSSVM) was used to filter, so as to reduce the effect of temperature drift. Finally, the processed signal is reconstructed to achieve the goal of denoising. Through the results, it can be found that the optimized VMD and LSSVM using CSA algorithm can achieve more effective denoising. After using the method proposed in this paper, the angular random walk value is 1.1175 ∗ 10−4°/h/√Hz, and the bias stability is 0.0017°/h. Compared with the original signal, the two signals are optimized by 98.1% and 98.2%, respectively. It can be seen from the experimental results that the proposed CSA-VMD method, SG method, and CSA-LSSVM method can effectively eliminate noise effects. [ABSTRACT FROM AUTHOR]

Purpose: To reduce the influence of temperature on MEMS gyroscope, this paper aims to propose a temperature drift compensation method based on variational modal decomposition (VMD), time-frequency peak filter (TFPF), mind evolutionary algorithm (MEA) and BP neural network. Design/methodology/approach: First, VMD decomposes gyro's temperature drift sequence to obtain multiple intrinsic mode functions (IMF) with different center frequencies and then Sample entropy calculates, according to the complexity of the signals, they are divided into three categories, namely, noise signals, mixed signals and temperature drift signals. Then, TFPF denoises the mixed-signal, the noise signal is directly removed and the denoised sub-sequence is reconstructed, which is used as training data to train the MEA optimized BP to obtain a temperature drift compensation model. Finally, the gyro's temperature characteristic sequence is processed by the trained model. Findings: The experimental result proved the superiority of this method, the bias stability value of the compensation signal is 1.279 × 10–3°/h and the angular velocity random walk value is 2.132 × 10–5°/h/vHz, which is improved compared to the 3.361°/h and 1.673 × 10–2°/h/vHz of the original output signal of the gyro. Originality/value: This study proposes a multi-dimensional processing method, which treats different noises separately, effectively protects the low-frequency characteristics and provides a high-precision training set for drift modeling. TFPF can be optimized by SEVMD parallel processing in reducing noise and retaining static characteristics, MEA algorithm can search for better threshold and connection weight of BP network and improve the model's compensation effect. [ABSTRACT FROM AUTHOR]

The noise signal in the gyroscope is divided into four levels: sampling frequency level, device bandwidth frequency level, resonant frequency level, and carrier frequency level. In this paper, the signal in the dual-mass MEMS gyroscope is analyzed. Based on the variational mode decomposition (VMD) algorithm, a novel dual-mass MEMS gyroscope noise reduction method is proposed. The VMD method with different four-level center frequencies is used to process the original output signal of the MEMS gyroscope, and the results are analyzed by the Allan analysis of variance, which shows that the ARW of the gyroscope is increased from 1.998*10−1°/√h to 1.552*10−4°/√h, BS increased from 2.5261°/h to 0.0093°/h. [ABSTRACT FROM AUTHOR]

This article suggested two methods to compensate for the temperature drift of the micro-electro-mechanical system gyroscopes, which are support vector machine method and C-means support vector machine. The output of X axis which was ranged from −40°C to 60°C based on the micro-electro-mechanical system gyroscope is reduced and analyzed in this article. The results showed the correctness of the two methods. The final results indicate that when the temperature is ranged from −40°C to 60°C, the factor of B is reduced from 0.424 (° h) to 0.02194 (° h) , and when the temperature is ranged from 60°C to −40°C, the factor of B is reduced from 0.1056 (° h) to 0.0329 (° h) , and the temperature drift trend and noise characteristics are improved clearly. [ABSTRACT FROM AUTHOR]

This paper presents a delay-free tracking differentiator based on variational mode decomposition (VMD) for extracting the useful signal from a noisy measurement of gyroscope. Sigmoid function-based tracking differentiator (STD) is a novel tracking differentiator with the advantages of noise-attenuation ability and dynamical performance. However, there is a contradiction in STD; i.e., selecting a larger acceleration factor may cause faster convergence but bad random noise reduction whereas selecting a smaller acceleration factor may lead to signal delay but effective random noise reduction. Here, multiscale transformation is introduced to overcome the contradiction of STD. VMD is selected to decompose the noisy signal into multiscale components, and the correlation coefficients between each component and original signal are calculated, then the component with biggest correlation coefficient is reserved and other components are filtered by the proposed adaptive STD algorithm based on the correlation coefficient of each component, and finally the denoising result is obtained after reconstruction. The prominent advantages of the proposed algorithm are as follows: (i) compared to traditional tracking differentiators, better noise suppression ability can be achieved with suppression of time delay; (ii) compared to other widely used denoising methods, a simpler structure but better denoising ability can be obtained. [ABSTRACT FROM AUTHOR]

This paper presents a bandwidth expansion method for dual-mass microelectromechanical system (MEMS) gyroscopes based on the pole–zero temperature compensation method. When the sense loop operates under open conditions, the mechanical sensitivity of the gyroscope structure conflicts with the bandwidth and is governed by the frequency difference between the drive and the sense modes (min {Δω1, Δω2}), which is proven to change with temperature during the experiment. The pole–zero temperature compensation proportional controller (PZTCPC) is proposed to expand the bandwidth under different temperatures based on the pole–zero compensation method. The force rebalancing combs stimulation method (FRCSM) is used to achieve accurate gyroscope bandwidth characteristics. The mechanical bandwidth of the gyroscope is proven to be approximately 13 Hz when the sense-mode loop is open, and the simulation results show that the PZTCPC method expands the bandwidth to greater than 91.7 Hz after the sense-mode loop is closed. The FRCSM experiments indicate that gyroscope bandwidth is expanded to 95 Hz at –40 °C, 94 Hz at 20 °C and 92 Hz at 60 °C, while the bandwidths at –40, 20, and 60 °C are all 93 Hz with the turntable method. The experimental curves match the simulation curves well and verify the simulation results. The new limiting condition of the closed-loop bandwidth is the trough generated by conjugate zeros, formed by superposition of in-phase and anti-phase sense modes. [ABSTRACT FROM AUTHOR]

This paper proposed three methods to compensate the temperature energy influence drift of the MEMS vibration gyroscope, including radial basis function neural network (RBF NN), RBF NN based on genetic algorithm (GA), and RBF NN based on GA with Kalman filter (KF). Three-axis MEMS vibration gyroscope (Gyro X, Gyro Y, and Gyro Z) output data are compensated and analyzed in this paper. The experimental results proved the correctness of these three methods, and MEMS vibration gyroscope temperature energy influence drift is compensated effectively. The results indicate that, after RBF NN-GA-KF method compensation, the bias instability of Gyros X, Y, and Z improves from 139°/h, 154°/h, and 178°/h to 2.9°/h, 3.9°/h, and 1.6°/h, respectively. And the angle random walk of Gyros X, Y, and Z was improved from 3.03°/h1/2, 4.55°/h1/2, and 5.89°/h1/2 to 1.58°/h1/2, 2.58°/h1/2, and 0.71°/h1/2, respectively, and the drift trend and noise characteristic are optimized obviously. [ABSTRACT FROM AUTHOR]

This paper presents the bandwidth expanding method with wide-temperature range for sense mode coupling dual-mass MEMS gyro. The real sensing mode of the gyroscope is analyzed to be the superposition of in-phase and anti-phase sensing modes. The mechanical sensitivity and bandwidth of the gyroscope structure are conflicted with each other and both governed by the frequency difference between sensing and drive modes (min {Δω1, Δω2}). The sensing mode force rebalancing combs stimulation method (FRCSM) is presented to simulate the Coriolis force, and based on this method, the gyro’s dynamic characteristics are tested. The sensing closed- loop controller is achieved by operational amplifier based on phase lead method, which enable the magnitude margin and phase margin of the system to reach 7.21 dB and 34.6° respectively, and the closed-loop system also expands gyro bandwidth from 13 Hz (sensing open-loop) to 102 Hz (sensing closed-loop). What’s more, the turntable test results show that the sensing closed-loop works stably in wide-temperature range (from −40 °C to 60 °C) and the bandwidth values are 107 Hz @−40 °C and 97 Hz @60 °C. The results indicate that the higher temperature causes lower bandwidth, and verify the simulation results are 103 Hz @−40 °C and 98.2 Hz @60 °C. The new bottleneck of the closed loop bandwidth is the valley generated by conjugate zeros, which is formed by superposition of sensing modes. [ABSTRACT FROM AUTHOR]

This paper analyzes different noise components in MEMS gyroscope silicon structure, including mechanical–thermal noise (MTN), electronic-thermal noise (ETN), flicker noise (FN) and Coriolis signal in-phase noise (IPN). The structure equivalent electronic model is established, and the improved differential interface is proposed based on weak signal detection technology, after that, the noise components in silicon structure are introduced and analyzed in sense open loop. The quadrature error (QE) signal automatically cancellation loop is proposed, and the results of the experiment indicate that the equivalent angular rates of QE and IPN are 46°/s and 4.55°/s respectively. The interfaces contrast experiments show that the DC noise and the useful signal amplitudes of differential and single-side detection interfaces are −49.8 dBmV, −16.8 dBmV and −39.8 dBmV (−42.1 dBmV), −22.1 dBmV (−22.2 dBmV), which confirms the differential interface has better SNR. The carrier experiments also illustrate that higher carrier frequency (from 500 kHz to 10 MHz) can restrain DC noise (from −19.8 dBmV to −54.2 dBmV) better, which demonstrate the FN is the dominant noise component of the silicon structure under normal temperature. The temperature experiments show the DC noise enhances from −48.5 dBmV to −14.6 dBmV over the range 20 °C to 60°C while the useful signal amplitude remains around -16.6dBmV, and this phenomenon indicates the MTN and ETN become the dominant structure noise components gradually with temperature rising. [ABSTRACT FROM AUTHOR]

The traditional processing model of the temperature error for a gyroscope is serial, meaning that de-noising and temperature drift compensation are implemented in a two-step procedure. Hence, the result of the latter depends on the performance of the former; in particular, negative de-noising produces a negative compensation result. To reduce this dependence, we propose a parallel processing algorithm of the temperature error based on variational mode decomposition (VMD) and an augmented nonlinear differentiator (AND). An application to a micro-electro-mechanical system gyroscope is described to demonstrate the effectiveness and applicability of the proposed algorithm. Its major advantages are (i) a combination of VMD, extreme learning machines, and AND is proposed, and an adaptive accelerometer factor determination method for AND is given based on the VMD, both of which improve the effectiveness of the de-noising process; (ii) temperature drift and noise in the temperature error can be extracted and processed synchronously, thereby reducing the dependency of drift compensation on the de-noising result and making the temperature error process more efficient. [ABSTRACT FROM AUTHOR]

A novel method is investigated in this paper to estimate the temperature's influence upon the resonant frequency (RESF) and quality factor (Q) of a vacuum packaged Micro-Electro-Mechanical-System (MEMS) gyroscope, which can give suggestions to improve the architecture's temperature robustness. The dual-mass decoupled gyroscope's architecture is introduced, and the drive and sense modes' mechanical character are analyzed. The models of RESF and damping are established, and the influence factors are investigated. Four samples are tested and the results indicate that the models can estimate and evaluate the tendency of the RESF and Q in different temperature. The investigation also considers the Young Modulus is the dominate element influencing RESF and increasing the thickness and width of the U-shaped spring can decrease this influence; Q is impacted mainly by the air viscosity coefficient and ambient pressure. The errors of the models are caused by manufacture error and the air getter's influence. [ABSTRACT FROM AUTHOR]

To eliminate the noise and temperature drift in an Micro-Electro-Mechanical Systems (MEMS) gyroscope's output signal for improving measurement accuracy, a parallel processing model based on Multi-objective particle swarm optimization based on variational modal decomposition-time-frequency peak filter (MOVMD–TFPF) and Beetle antennae search algorithm- Elman neural network (BAS–Elman NN) is established. Firstly, variational mode decomposition (VMD) is optimized by multi-objective particle swarm optimization (MOPSO); then, the best decomposition parameters [kbest,abest] can be obtained. Secondly, the gyroscope output signals are decomposed by VMD optimized by MOPSO (MOVMD); then, the intrinsic mode functions (IMFs) obtained after decomposition are classified into a noise segment, mixed segment, and drift segment by sample entropy (SE). According to the idea of a parallel model, the noise segment can be discarded directly, the mixed segment is denoised by time-frequency peak filtering (TFPF), and the drift segment is compensated at the same time. In the compensation part, the beetle antennae search algorithm (BAS) is adopted to optimize the network parameters of the Elman neural network (Elman NN). Subsequently, the double-input/single-output temperature compensation model based on the BAS-Elman NN is established to compensate the drift segment, and these processed segments are reconstructed to form the final gyroscope output signal. Experimental results demonstrate the superiority of this parallel processing model; the angle random walk of the compensated gyroscope output is decreased from 0.531076 to 5.22502 × 10−3°/h/√Hz, and its bias stability is decreased from 32.7364°/h to 0.140403°/h, respectively. [ABSTRACT FROM AUTHOR]

For the sake of decreasing the effects of noise and temperature error on the measurement accuracy of micro-electro-mechanical system (MEMS) gyroscopes, a denoising and temperature drift compensation parallel model method based on wavelet transform and forward linear prediction (WFLP) and support vector regression based on the cuckoo search algorithm (CS-SVR) is proposed in this paper. First, variational mode decomposition (VMD) is proposed in this paper, which is aimed at dividing the output signal of the gyroscope into intrinsic mode functions (IMFs); then, the IMFs are classified into three features—drift, mixed, and pure noise features—by the sample entropy (SE) value. Second, a wavelet transform and forward linear prediction (WFLP) are combined to remove the noise from the mixed features. Meanwhile, the drift feature is compensated by support vector regression based on the cuckoo search algorithm (CS-SVR). Finally, through reconstruction, the final signal is obtained. Experimental results demonstrate that the VMD-SE-WFLP-CS-SVR method proposed in this paper can decrease noise and compensate the temperature error effectively (angular random walking value is optimized from 1.667°/√h to 0.0667°/√h and the bias stability is reduced from 30°/h to 4°/h). In terms of denoising, the performance of the WFLP algorithm is superior to the wavelet threshold and FLP, as it combines their advantages; furthermore, in terms of temperature compensation, the proposed CS-SVR algorithm uses the cuckoo search algorithm to find the optimal parameters of SVR, improving the accuracy of the model. [ABSTRACT FROM AUTHOR]

To deal with the influence of temperature drift for a Micro-Electro-Mechanical System (MEMS) gyroscope, this paper proposes a new temperature error parallel processing method based on a novel fusion algorithm. Firstly, immune based particle swarm optimization (IPSO) is employed for optimal parameters search for Variational Modal Decomposition (VMD). Then, we can get the optimal decomposition parameters, wherein permutation entropy (PE) is employed as the fitness function of the particles. Then, the improved VMD is performed on the output signal of the gyro to obtain intrinsic mode functions (IMFs). After judging by sample entropy (SE), the IMFs are divided into three categories: noise term, mixed term and feature term, which are processed differently. Filter the mixed term and compensate the feature term at the same time. Finally, reconstruct them and get the result. Compared with other optimization algorithms, IPSO has a stronger global search ability and faster convergence speed. After Back propagation neural network (BP) is enhanced by Adaptive boosting (Adaboost), it becomes a strong learner and a better model, which can approach the real value with higher precision. The experimental result shows that the novel parallel method proposed in this paper can effectively solve the problem of temperature errors. [ABSTRACT FROM AUTHOR]

In this paper, a novel temperature compensation method for a dual-mass MEMS gyroscope is proposed based on drive mode vibration characteristic compensation using a temperature variable resistor. Firstly, the drive and sense modes of the gyroscope re analyzed and investigated, and it is found that the scale factor is proportional to the drive mode amplitude controlling reference voltage. Then, the scale factor temperature compensation method is proposed, and a temperature variable resistor is utilized to compensate the drive amplitude working point and make it change with temperature. In addition, the temperature compensation circuit is designed and simulated. After that, the temperature bias drift is compensated in a modular output. The experimental results show that scale factor and bias variation during the temperature range from −40 °C to 60 °C decrease from 3.680% to 1.577% and 3.880% to 1.913%, respectively. In addition, the bias value improves from 103.395 °/s to 22.478 °/s (optimized 78.26%). The bias stability and angular rate walking parameter are also optimized to 45.97% and 16.08%, respectively, which verify the method proposed in this paper. [ABSTRACT FROM AUTHOR]

This study presents a new microelectromechanical system, a vibration ring gyroscope with a double U-beam (DUVRG), which was designed using a combination of mathematical analysis and the finite element method. First, a ring vibration resonator with eight double U-beam structures was developed, and 24 capacitive electrodes were designed for drive and sense according to the advantageous characteristics of a thin-shell vibrating gyroscope. Then, based on the elastic mechanics and thin-shell theory, a mathematical stiffness model of the double U-beam was established. The maximum mode resonant frequency error calculated by the DUVRG stiffness model, finite element analysis (FEA) and experiments was 0.04%. DUVRG structures were manufactured by an efficient fabrication process using silicon-on-glass (SOG) and deep reactive ion etching (DRIE), and the FEA value and theoretical calculation had differences of 5.33% and 5.36% with the measured resonant frequency value, respectively. Finally, the static and dynamic performance of the fabricated DUVRG was tested, and the bias instability and angular random walk were less than 8.86 (°)/h and 0.776 (°)/√h, respectively. [ABSTRACT FROM AUTHOR]

This paper proposes an effective method to calibrate the microelectromechanical systems (MEMS) vibratory gyroscope based on the virtual Coriolis force. This method utilizes a series of voltage signals to simulate the Coriolis force input, and the gyroscope output is monitored to obtain the scale factor characteristics of the gyroscopes. The scale factor and bias parameters of the gyroscope can be calibrated conveniently and efficiently in the sense-mode open loop. The calibration error of the scale factor based on the turntable and the virtual Coriolis force method is only 1.515%, which proves the correction of the method proposed in this paper. Meanwhile, the non-linearity and bias value of the turntable and the virtual Coriolis force method are 742 ppm and 42.04 mV and 3389 ppm and 0.66 mV, respectively. [ABSTRACT FROM AUTHOR]

An adaptive multi-scale method based on the combination generalized morphological filter (CGMF) is presented for de-noising of the output signal from a MEMS gyroscope. A variational mode decomposition is employed to decompose the original signal into multi-scale modes. After choosing a length selection for the structure element (SE), the adaptive multi-scale CGMF method reduces the noise corresponding to the different modes, after which a reconstruction of the de-noised signal is obtained. From an analysis of the effect of de-noising, the main advantages of the present method are that it: (i) effectively overcomes deficiencies arising from data deviation compared with conventional morphological filters (MFs); (ii) effectively targets the different components of noise and provides efficacy in de-noising, not only primarily eliminating noise but also smoothing the waveform; and (iii) solves the problem of SE-length selection for a MF and produces feasible formulae of indicators such as the power spectral entropy and root mean square error for mode evaluations. Compared with the other current signal processing methods, the method proposed owns a simpler construction with a reasonable complexity, and it can offer better noise suppression effect. Experiments demonstrate the applicability and feasibility of the de-noising algorithm. [ABSTRACT FROM AUTHOR]

To address the effect of temperature, we establish a temperature compensation model for gyroscope output signal using long short-term memory network (LSTM), support vector machine (SVM), and depth belief network (DBN). We develop a denoising algorithm using variational mode decomposition (VMD), and sampling entropy (SE) to eliminate the influence of factors other than temperature on the MEMS gyroscope. First, the signal is decomposed into several intrinsic mode functions (IMF) using VMD. Then, the decomposed IMFs are classified into three categories: feature terms, mixture terms, and noise terms using SE. These three categories of signals are processed separately, preserving the useful signal of the original signal while precisely removing the noise. Subsequently, the processed signals are reconstructed to obtain the reconstructed signals. Finally, we perform temperature experiments and find that the rate random wander and bias instability of the gyroscope compensated output signal are reduced by 84.35% and 95.57%, respectively. [Display omitted] • Parallel processing effectively protects the static drift model. • The proposed LSTM-SVM-DBN model, is particularly well-suited for effectively analyzing MEMS gyroscope signals. • The rate random wander and bias instability of the gyroscope output signal were reduced by 84.35% and 95.57%. [ABSTRACT FROM AUTHOR]

A temperature error processing method for a dual-mass micro-electromechanical system (MEMS) gyroscope based on multi-scale parallel model is proposed. At first, a sample entropy based bounded ensemble empirical mode decomposition (SE-BEEMD) is proposed to decompose the original signal into different scales, include noise-only scale, mixed scale and drift scale; then forward linear prediction (FLP) is employed to eliminate the noise at mixed scale and extreme learning machine (ELM) based model is employed to compensate the drift at drift scale, the two steps are carried out paralleled; at last the final results can be obtained after reconstruction. Experimental results show that: (1) compared to tradition serial model, the proposed parallel model can eliminate the temperature errors more effectively, and each parameter of Allan analysis is improved. Specially, the quantification noise reduced from 0.035 μrad to 9.93e4 μrad, angle random walk reduced from 2.13e-5/s 1/2 to 7.94e-6/s 1/2 , bias instability reduced from 5.28e-4/s to 4.79e-4/s, rate random walk from 0.012/s 3/2 to 0.092/s 3/2 and angular rate ramp reduced from 0.013/s 2 to 0.011/s 2 ; (2) compared to traditional time consuming neural networks, the ELM has the best modeling accurate and shortest training time, which would be valuable for online temperature drift modeling and compensation. [ABSTRACT FROM AUTHOR]