Adaptive high-degree cubature Kalman filter in the presence of unknown measurement noise covariance matrix

Abstract

Here, the authors address the state estimation problem of non-linear systems in the presence of unknown measurement noise (MN) covariance matrix. Recently, a high-degree cubature Kalman filter (HCKF) has been successfully used in the non-linear-state estimation problem with arbitrary degrees of accuracy in computing the spherical and radial integrals. However, the efficiency of the HCKF depends on a priori knowledge of the MN. To improve the performance of HCKF for non-linear systems with unknown MN covariance matrix, the authors proposed an adaptive HCKF, which combines the high-degree cubature rule with the variational Bayesian (VB) method to jointly estimate the system state and the unknown covariance matrix online. Experimental results demonstrate the effectiveness of the proposed filter.

Keywords

• Kalman filters
• state estimation
• covariance matrices
• Bayes methods
• nonlinear filters
• variational techniques
• variational Bayesian method
• system state estimation
• nonlinear-state estimation problem
• unknown measurement noise covariance matrix
• adaptive high-degree cubature Kalman filter
• unknown covariance matrix online
• high-degree cubature rule
• adaptive HCKF
• unknown MN covariance matrix
• nonlinear systems
• radial integrals
• spherical integrals