Hybrid Deep Recurrent Neural Networks for Noise Reduction of MEMS-IMU with Static and Dynamic Conditions

Abstract

Micro-electro-mechanical system inertial measurement unit (MEMS-IMU), a core component in many navigation systems, directly determines the accuracy of inertial navigation system; however, MEMS-IMU system is often affected by various factors such as environmental noise, electronic noise, mechanical noise and manufacturing error. These can seriously affect the application of MEMS-IMU used in different fields. Focus has been on MEMS gyro since it is an essential and, yet, complex sensor in MEMS-IMU which is very sensitive to noises and errors from the random sources. In this study, recurrent neural networks are hybridized in four different ways for noise reduction and accuracy improvement in MEMS gyro. These are two-layer homogenous recurrent networks built on long short term memory (LSTM-LSTM) and gated recurrent unit (GRU-GRU), respectively; and another two-layer but heterogeneous deep networks built on long short term memory-gated recurrent unit (LSTM-GRU) and a gated recurrent unit-long short term memory (GRU-LSTM). Practical implementation with static and dynamic experiments was carried out for a custom MEMS-IMU to validate the proposed networks, and the results show that GRU-LSTM seems to be overfitting large amount data testing for three-dimensional axis gyro in the static test. However, for X-axis and Y-axis gyro, LSTM-GRU had the best noise reduction effect with over 90% improvement in the three axes. For Z-axis gyroscope, LSTM-GRU performed better than LSTM-LSTM and GRU-GRU in quantization noise and angular random walk, while LSTM-LSTM shows better improvement than both GRU-GRU and LSTM-GRU networks in terms of zero bias stability. In the dynamic experiments, the Hilbert spectrum carried out revealed that time-frequency energy of the LSTM-LSTM, GRU-GRU, and GRU-LSTM denoising are higher compared to LSTM-GRU in terms of the whole frequency domain. Similarly, Allan variance analysis also shows that LSTM-GRU has a better denoising effect than the other networks in the dynamic experiments. Overall, the experimental results demonstrate the effectiveness of deep learning algorithms in MEMS gyro noise reduction, among which LSTM-GRU network shows the best noise reduction effect and great potential for application in the MEMS gyroscope area.

Online Nonlinear Error Compensation Circuit Based on Neural Networks

“…For real-time online signal processing, the results of the proposed scheme are compared with small-scale networks, and the use of MLP network and leaky ReLU activation function with simple calculations are sufficient to achieve the corresponding error suppression effect. From Table 2, when smallscale recurrent neural networks are used [23,24], the error suppression effect obtained is similar to that of the MLP network used in this article, and with large-scale networks [22,26], the error suppression effect obtained is better than that of the proposed method. The result of the comparison shows that the compensation effect of the adopted scheme at the algorithm level is effective and reasonable.…”

“…The computational complexity of the error compensation scheme based on neural networks is large, which is a challenge for real-time online applications. Compared with related works [22][23][24][25][26], the network model and activation function used in this paper are simpler and less complex. When the number of neurons in the input layer and the number of neurons in the hidden layer are N and H, the shape of the input vector is (1, N), the shape of the hidden layer parameter matrix is (N, H), and the shape of the hidden layer feature matrix is (1, N).…”

“…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.…”