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

Abstract

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.

Online Nonlinear Error Compensation Circuit Based on Neural Networks

“…The influence of network parameter scale and temperature on the results is also analyzed. As shown in Figure 4, the experimental device includes the inertial sensor ADIS16475 [29] The key part of a neural network for nonlinear error fitting is the activation function, and the sigmoid activation function is commonly used in related works, which has the following expressions [20][21][22][23][24]:…”

“…This type of error directly affects the stability of the output signals and is difficult to be processed directly through device calibration [8]. Therefore, the modeling and compensation schemes of the nonlinear error components are widely studied and two mainstream research schemes [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] are formed, namely, (1) establishing a statistical model and performing error compensating and (2) error compensation schemes based on machine learning or deep learning.…”

“…The accuracy improvement of statistical methods requires accurate analysis and modeling of error components, while another research idea is to obtain model structure and model parameters with machine learning schemes. The researchers use multilayer perception machines [20,21], recurrent neural networks [22][23][24], mixed deep learning networks [25,26], etc. to establish error models.…”

“…The nonlinear error in the composition of measurement error is discussed. In related research studies [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26], the nonlinear error is modeled as a time series model, in which the error at the current moment is related to the observation values at previous moments. The error compensation scheme discussed in this paper is also based on the analysis of the time series model.…”

“…(a) (b) The key part of a neural network for nonlinear error fitting is the activation function, and the sigmoid activation function is commonly used in related works, which has the following expressions [20][21][22][23][24]:…”