### Post by kellyyu on Mar 29, 2024 2:51:18 GMT -5

The random drift error of MEMS gyroscope is slow time varying and has no linear rule, so it is difficult to establish an accurate mathematical model to describe it. In inertial navigation system, when the accuracy of MEMS gyro sensor is low, the output signal contains a large random drift error, which will have a great impact on the accuracy of the navigation system. How to effectively identify and compensate the random drift error of MEMS gyroscope is of great significance. This paper introduces several methods of MEMS gyro random error modeling.

At present, the following three methods are often used to improve the accuracy of MEMS gyroscopes: First, starting from the structure of the gyroscope itself, the use of new production processes and materials to weaken the impact of the gyroscope's own structure on its accuracy, but this method has a high development cost and a long time, and it is difficult to improve the production process; The second is to use the temperature control device to compensate the error of MEMS gyro sensor caused by temperature change, and reduce the influence of temperature on the accuracy of MEMS gyros; The third is to use the software method to establish the corresponding mathematical model and compensation for the error of MEMS gyro sensor, so as to improve the accuracy of MEMS gyroscope, this method is low cost, good effect and short time, usually there are the following methods:

1. Time series analysis method

The time series analysis method is based on probability statistics, and the random signal is modeled according to its statistical characteristics. After stabilizing, normalizing and zero-mean processing the random signal, the random signal is transformed into a time-dependent sequence. It usually includes AR, MA and ARMA three model structures. The random error model of MEMS gyroscope can be easily obtained by using this method, and the model structure is simple and can be directly applied to Kalman and other filtering algorithms. The disadvantage is that the gyroscope output data needs to be stabilized, normalized, zero-mean processing, etc., which will affect the gyroscope modeling accuracy, so it is only suitable for modeling stable random sequences, and the modeling accuracy is high.

2. Allan Variance method

The Allan variance method was proposed by D.W. Allen in 1966. It is a method to analyze the signal in time domain. According to the relationship between the power spectral density function and Allan variance function of the signal, each error term is identified by Allan variance curve. This method is simple to calculate and can easily characterize and identify the various error sources contained in the error signal and the degree of influence on the statistical characteristics of the whole noise. Accurate analysis results can be obtained for the ideal signal, but the actual MEMS gyroscope signal is unstable with the change of environment and temperature. Allan variance method is difficult to accurately analyze the random error of MEMS gyroscope, and it requires the output of gyroscope to have a large sample.

3. Wavelet Neural Network (WNN)

Wavelet neural network is a combination of neural network and wavelet analysis, it inherits the advantages of wavelet transform and neural network, has the advantages of self-learning, self-adaptation, good time-frequency characteristics, strong modeling ability, and has the ability of optimal approximation and global approximation to nonlinear functions, and has been successfully applied in nonlinear modeling. According to the characteristics of the output signal of the gyroscope, the corresponding WNN model is established, and the output data of the gyroscope is used to train the network. The accurate error model can be obtained, and the structure of the model is very simple and the interference suppression ability is strong.

In addition, power spectral density analysis, wavelet analysis and other methods can be used to model the random error of the gyroscope. Power spectral density analysis (PSD) is a frequency-domain analysis method, which uses different random errors with different power spectral densities to identify each error term. Wavelet transform is a signal analysis and processing method developed on the basis of Fourier transform, which can characterize the signal in time domain and frequency domain at the same time. At present, the researchers use the method of wavelet denoising to process the random error signal of the gyroscope, which greatly reduces the influence of random error on the precision of the gyroscope.

In order to improve the accuracy of MEMS gyroscope and effectively compensate the random error, Ericco has taken measures from many aspects, such as upgrading the materials of MEMS gyroscope and implementing strict calibration; The MEMS gyro will also be fully temperature compensated and multi-directional test; At the same time, Allan variance analysis is used to identify the performance indicators of MEMS gyro. Nowadays, navigation, tactical and consumer MEMS gyroscopes are widely available on the market, and Ericco mainly develops navigation and tactical MEMS gyroscopes. Navigation-grade MEMS gyro has a higher level of accuracy and better performance, for example, ER-MG2-50/100 is an excellent north-finding MEMS gyro, while ER-MG2-300/400 is a high-performance navigational MEMS gyro. However, MEMS gyros are not only single-axis chip forms, there are also two - and three-axis MEMS gyros, two-axis MEMS gyros can measure attitude (roll and pitch), and three-axis gyros can conduct system development research.

If you are interested in other knowledge of MEMS gyro, please contact us.

At present, the following three methods are often used to improve the accuracy of MEMS gyroscopes: First, starting from the structure of the gyroscope itself, the use of new production processes and materials to weaken the impact of the gyroscope's own structure on its accuracy, but this method has a high development cost and a long time, and it is difficult to improve the production process; The second is to use the temperature control device to compensate the error of MEMS gyro sensor caused by temperature change, and reduce the influence of temperature on the accuracy of MEMS gyros; The third is to use the software method to establish the corresponding mathematical model and compensation for the error of MEMS gyro sensor, so as to improve the accuracy of MEMS gyroscope, this method is low cost, good effect and short time, usually there are the following methods:

1. Time series analysis method

The time series analysis method is based on probability statistics, and the random signal is modeled according to its statistical characteristics. After stabilizing, normalizing and zero-mean processing the random signal, the random signal is transformed into a time-dependent sequence. It usually includes AR, MA and ARMA three model structures. The random error model of MEMS gyroscope can be easily obtained by using this method, and the model structure is simple and can be directly applied to Kalman and other filtering algorithms. The disadvantage is that the gyroscope output data needs to be stabilized, normalized, zero-mean processing, etc., which will affect the gyroscope modeling accuracy, so it is only suitable for modeling stable random sequences, and the modeling accuracy is high.

2. Allan Variance method

The Allan variance method was proposed by D.W. Allen in 1966. It is a method to analyze the signal in time domain. According to the relationship between the power spectral density function and Allan variance function of the signal, each error term is identified by Allan variance curve. This method is simple to calculate and can easily characterize and identify the various error sources contained in the error signal and the degree of influence on the statistical characteristics of the whole noise. Accurate analysis results can be obtained for the ideal signal, but the actual MEMS gyroscope signal is unstable with the change of environment and temperature. Allan variance method is difficult to accurately analyze the random error of MEMS gyroscope, and it requires the output of gyroscope to have a large sample.

3. Wavelet Neural Network (WNN)

Wavelet neural network is a combination of neural network and wavelet analysis, it inherits the advantages of wavelet transform and neural network, has the advantages of self-learning, self-adaptation, good time-frequency characteristics, strong modeling ability, and has the ability of optimal approximation and global approximation to nonlinear functions, and has been successfully applied in nonlinear modeling. According to the characteristics of the output signal of the gyroscope, the corresponding WNN model is established, and the output data of the gyroscope is used to train the network. The accurate error model can be obtained, and the structure of the model is very simple and the interference suppression ability is strong.

In addition, power spectral density analysis, wavelet analysis and other methods can be used to model the random error of the gyroscope. Power spectral density analysis (PSD) is a frequency-domain analysis method, which uses different random errors with different power spectral densities to identify each error term. Wavelet transform is a signal analysis and processing method developed on the basis of Fourier transform, which can characterize the signal in time domain and frequency domain at the same time. At present, the researchers use the method of wavelet denoising to process the random error signal of the gyroscope, which greatly reduces the influence of random error on the precision of the gyroscope.

**Conclusion**

In order to improve the accuracy of MEMS gyroscope and effectively compensate the random error, Ericco has taken measures from many aspects, such as upgrading the materials of MEMS gyroscope and implementing strict calibration; The MEMS gyro will also be fully temperature compensated and multi-directional test; At the same time, Allan variance analysis is used to identify the performance indicators of MEMS gyro. Nowadays, navigation, tactical and consumer MEMS gyroscopes are widely available on the market, and Ericco mainly develops navigation and tactical MEMS gyroscopes. Navigation-grade MEMS gyro has a higher level of accuracy and better performance, for example, ER-MG2-50/100 is an excellent north-finding MEMS gyro, while ER-MG2-300/400 is a high-performance navigational MEMS gyro. However, MEMS gyros are not only single-axis chip forms, there are also two - and three-axis MEMS gyros, two-axis MEMS gyros can measure attitude (roll and pitch), and three-axis gyros can conduct system development research.

If you are interested in other knowledge of MEMS gyro, please contact us.