Nonlinear state estimation using neural-cubature Kalman filter

Abstract

The cubature Kalman filter (CKF) has been widely used in solving nonlinear state estimation problems because of many advantages such as satisfactory filtering accuracy and easy implementation compared to extended Kalman filter and unscented Kalman filter. However, the performance of CKF may degrade due to the uncertainty of the nonlinear dynamic system model. To solve this problem, a neural-cubature Kalman filter (NCKF) algorithm containing a multilayer feed-forward neural network (MFNN) in CKF is proposed to further improve the estimation accuracy and enhance the robustness of CKF. In the proposed NCKF algorithm, the MFNN was used to modify the nonlinear state estimation of CKF as the measurements were processed, and the CKF was used as both a state estimator and an online training paradigm simultaneously. The experimental results show that the estimation accuracy and robustness of the proposed method are better than those of the CKF, square-root CKF and particle filter.

Extended Kalman filters for fractional‐order nonlinear continuous‐time systems containing unknown parameters with correlated colored noises

“…The Kalman filter is a very famous robust state observer, which can effectively realize state estimation in the presence of noises. For integer‐order systems, Kalman filers have been explored to obtain the state information in other works . Certainly, the Kalman filter is also extended to the state estimation of fractional‐order systems.…”

“…For integer-order systems, Kalman filers have been explored to obtain the state information in other works. [9][10][11][12][13] Certainly, the Kalman filter is also extended to the state estimation of fractional-order systems.…”