Adaptive Masreliez–Martin fractional interpolatory cubature Kalman filter with recursive noise estimation

Abstract

In this study, we propose a Masreliez–Martin fractional interpolatory cubature Kalman filter and an adaptive Masreliez–Martin fractional interpolatory cubature Kalman filter to design the estimators for fractional-order discrete-time nonlinear systems under non-Gaussian measurement noise and unknown process noise covariance. Ther Masreliez–Martin fractional interpolatory cubature Kalman filter is developed by extending the interpolatory cubature Kalman filter to the fractional nonlinear discrete system to increase the robustness of estimation under noisy environment by applying the Masreliez–Martin method, including both time update and measurement update. Meanwhile, the adaptive Masreliez–Martin fractional interpolatory cubature Kalman filter is put forward to enhance the state estimation adaptive to the fractional system with uncertain process noise through recursive estimation. Simulation results on the re-entry target tracking system have demonstrated the adaptiveness, robustness and effectiveness of the propose filters.