Efficient extended cubature Kalman filtering for nonlinear target tracking

Abstract

For states estimation problem of continuous–discrete systems, the numerical approximation methods with high order of accuracy are commonly used to build the continuous–discrete filtering algorithms. However, there is a common contradiction between the computational efficiency and the accuracy. In order to improve the efficiency of state estimation in the continuous–discrete filtering method, continuous–discrete extended cubature Kalman filtering based on Adams–Bashforth–Moulton (ABM) numerical approximation is proposed. ABM is the linear multi-step numerical method, which can achieve the fourth-order accuracy for solving the differential state equation, and its ‘predictor–corrector’ mathematic structure is relatively simple. The performances of ABM method are theoretically analysed; the mixed-type filtering method for continuous–discrete nonlinear states estimation is proposed to integrate the best features of extended Kalman filtering and cubature Kalman filtering. More precisely, the time updates are deduced by extended Kalman filtering whereas the measurement updates are conducted by the third-degree spherical-radial cubature rule. The superior performances of proposed method are illustrated in the simulations under the conditions of different step-sizes and sampling periods.