An Efficient Gauss-Seidel Cubature Kalman Filter

Abstract

The Cubature Kalman filter (CKF) is a widely used filter with excellent performance, particularly on large non-linear systems. However, the CKF is computationally challenging to implement. The matrix inversion operation increases the computational burden if exact inversion methods, such as the Cholesky decomposition, are used. To reduce the CKF computational cost without losing accuracy in non-linear systems, in this study, we propose an efficient CKF, called the Gauss-Seidel Cubature Kalman filter (GSCKF), where the traditional Kalman gain calculating operation is replaced with the Gauss-Seidel (GS) method. The GS method is exploited to calculate the Kalman gain without complicated matrix inversion. To choose the optimal number of iterations adaptively, the Euclidean norm is considered as the evaluation criterion, which helps the GSCKF achieve the accuracy similar to CKF with less complexity. The computational complexity analysis and execution time results reveal that the GSCKF computational cost is significantly reduced. Numerical simulation results on different large non-linear systems show that the GSCKF, with only a few iterations and outstanding time efficiency, can provide a performance that is indistinguishable with respect to the performance of the CKF. The proposed algorithm will be useful in a variety of engineering areas, specifically in signal processing issues involving large non-linear systems.