A Random Error Compensation Method for MEMS Gyroscope Based on Improved EMD and ARMA

doi:10.12382/bgxb.2023.0738

Abstract

Abstract:

It is difficult to increase the measurement accuracy of micro-electro-mechanical system (MEMS) gyroscope due to random error. An error compensation method based on improved empirical modal decomposition (EMD) and an optimized autoregressive moving average (ARMA) model is proposed to lessen the random error of MEMS gyroscope. The proposed method is used to extract the noise and trend components from a signal based on Hausdorff distance, the mean of the accumulated standardized modes, and the conventional empirical mode decomposition. Then, ARMA modeling and filtering are applied to the remaining components. The ordering procedure of ARMA model is optimized using the sand cat swarm optimization algorithm.The improved adaptive filter is used to compensate the random error. The experimental results show that, compared to the traditional EMD and traditional ARMA model, the root mean square error obtained by the proposed method in static experiment is decreased by 52.5% and 34.4% and the root mean square error obtained by the proposed method in dynamic experiments is decreased by 50% and 32.35%, respectively. The proposed method might successfully reduce the random error and raise the measurement accuracy of MEMS gyroscope.

Key words: micro-electro-mechanical system, gyroscope, improved empirical mode decomposition, time series modelling, Hausdorff distance, adaptive filter

CLC Number:

V241.5

ZENG Xin, XIAN Sujie, WANG Kang, SI Peng, WU Zhilin. A Random Error Compensation Method for MEMS Gyroscope Based on Improved EMD and ARMA[J]. Acta Armamentarii, 2024, 45(9): 3297-3306.

Figures/Tables 14

Fig.1 Flowchart of the proposed method

Table 1 Parameters of the equation of state

X_k	V_k	A	B
$\left[\begin{array}{ll}\hat{x}_{k} & \hat{x}_{k-1}\end{array}\right]^{\mathrm{T}}$	[a_k a_k_-1]^T	$φ 1 φ 2 10$	$1 θ 1 00$

Table 1 Parameters of the equation of state

X_k	V_k	A	B
$\left[\begin{array}{ll}\hat{x}_{k} & \hat{x}_{k-1}\end{array}\right]^{\mathrm{T}}$	[a_k a_k_-1]^T	$φ 1 φ 2 10$	$1 θ 1 00$

Fig.2 Loop and update process of AKF

Fig.3 MEMS experimental platform

Table 2 Parameters of MEMS gyroscope

参数	数值
量程/(°)	±200
标度因数/(LSB·((°)·s^-1))^-1	210
角增益	0.3208
质量块/mg	0.2315
电容量/pf	0.4377

Fig.4 Static data for the x-axis of gyroscope

Fig.5 Each IMF and residuals obtained by EMD

Fig.6 Hausdorff distance between original signal and each IMF

Fig.7 Extracting trend term based on MASM

Fig.8 Comparison of compensation results in static test

Table 3 Static compensation results of each scheme

原始信号与方法	RMSE/((°)·s^-1)	SD/((°)·s^-1)
原始信号	0.0161	1.6047×10^-2
直接建模方法	0.0050	4.9900×10^-3
传统EMD方法	0.0040	3.6415×10^-3
传统ARMA建模方法	0.0029	2.3747×10^-3
本文方法	0.0019	8.2046×10^-4

Fig.9 Comparison of compensation results in dynamic test

Table 4 Comparison of dynamic compensation results

项目	RMSE/((°)·s^-1)	SNR/dB
原始信号	0.1345	23.4445
直接建模方法	0.0123	45.5609
传统EMD方法	0.0046	52.8295
传统ARMA建模方法	0.0034	55.3855
本文方法	0.0023	58.6109

Fig.10 Experimental results of disk resonant gyroscope and four-mass gyroscope

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