基于改进EMD和ARMA的MEMS陀螺仪随机误差补偿方法

doi:10.12382/bgxb.2023.0738

摘要/Abstract

摘要：

微机电系统(Micro-Electro-Mechanical System,MEMS)陀螺仪的随机误差限制了其测量精度。为了降低MEMS陀螺仪的随机误差,提出一种基于改进的经验模态分解(Empirical Mode Decomposition,EMD)和优化的自回归滑动平均(Autoregressive Moving Average,ARMA)模型的方法。该方法在传统EMD的基础上,结合Hausdorff距离和累积标准化模态均值以提取信号中的噪声和趋势项,对剩余信号进行ARMA建模和滤波。采用沙猫群优化算法优化建模的定阶过程,采用改进的自适应滤波补偿随机误差。试验结果表明:相较于传统EMD和传统ARMA方法,新方法在静态试验中得到的均方根误差分别降低52.5%和34.4%,在动态试验中得到的均方根误差分别降低50%和32.35%;新方法有效抑制了随机误差,提升了MEMS陀螺仪的使用精度。

关键词: 微机电系统, 陀螺仪, 改进经验模态分解, 时间序列建模, Hausdorff距离, 自适应滤波

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

中图分类号:

V241.5

曾鑫, 先苏杰, 王康, 司鹏, 吴志林. 基于改进EMD和ARMA的MEMS陀螺仪随机误差补偿方法[J]. 兵工学报, 2024, 45(9): 3297-3306.

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.

图/表 14

图1 本文方法总体框图

Fig.1 Flowchart of the proposed method

表1 状态方程的参数

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	$φ 1 φ 2 10$	$1 θ 1 00$

表1 状态方程的参数

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	$φ 1 φ 2 10$	$1 θ 1 00$

图2 AKF的循环和更新过程

Fig.2 Loop and update process of AKF

图3 MEMS试验平台

Fig.3 MEMS experimental platform

表2 陀螺仪的性能参数

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

图4 陀螺仪轴的静态数据

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

图5 EMD分解后的各阶IMF和残差

Fig.5 Each IMF and residuals obtained by EMD

图6 原始数据与各阶IMF间的Hausdorff距离

Fig.6 Hausdorff distance between original signal and each IMF

图7 基于MASM提取趋势项

Fig.7 Extracting trend term based on MASM

图8 静态试验补偿结果对比

Fig.8 Comparison of compensation results in static test

表3 各方法的静态补偿结果对比

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

图9 动态试验补偿结果对比

Fig.9 Comparison of compensation results in dynamic test

表4 动态补偿结果对比

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

图10 多环谐振陀螺和四质量陀螺的试验结果

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

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