Adaptive Non-Gaussian Cubature Filter Based on GS-MCC With Correlated Multiplicative Noises

Due to complex environmental factors, the position measurement data of mobile robots are susceptible to pollution from multiplicative noise and non-Gaussian characteristics, which poses a challenge for the existing adaptive filtering methods to obtain high-performance pose estimation. Based on the comprehensive consideration of non-Gaussian multiplicative noise and correlated noise, a non-Gaussian adaptive Cubature Kalman Filter design method based on Gaussian sum and maximum correntropy techniques is proposed. Firstly, an enhanced Gaussian-sum and Cubature Kalman Filter method is designed to re-derive the innovation covariance and cross-variance for the multiplicative noise system. Secondly, under the framework of the maximum correntropy filter, the design strategy of the Gaussian kernel function weight matrix is improved, and a Cubature Kalman Filter method based on the improved maximum correntropy criterion is proposed. Then, based on consideration of the correlation between multiplicative noise and measurement noise, a Gaussian sum maximum correntropy Cubature Kalman Filter method with a known correlation coefficient is established. Finally, an adaptive Gaussian sum maximum correntropy Cubature Kalman Filter method that can dynamically estimate the correlation coefficient of multiplicative noise in real time is proposed, which can perform joint high-performance estimation of mobile robot’s pose and correlation coefficient.
Note to Practitioners
—This paper focuses on nonlinear multiplicative noise systems which are non-Gaussian. On one hand, non-Gaussian multiplication noise is pervasive in all types of systems, seriously affecting signal transmission and data acquisition. On the other hand, the correlation between multiplicative noise and measurement noise will seriously affect filter accuracy and create new challenges. Particularly, as it is difficult to obtain the correlation coefficient in the current system, the method to estimate the correlation coefficient between non-Gaussian noise is a challenging problem. To address these issues. Firstly, the Gaussian sum technique is used to approximate the non-Gaussian noise. Secondly, the correntropy technique is used to further reduce the influence of non-Gaussian noise on the filter accuracy. Then, the problem of correlated noises is solved by improving the cost function. Finally, the problem of inaccurate noise correlation coefficient in the real system is solved by the principle of covariance correspondence. This method is suitable for systems with correlated multiplicative noise. If the accuracy of sensor measurement data is too low, it will affect estimation performance. In future research, we will address the issue of reduced filtering accuracy in various correlated noise environments.