Converted state equation Kalman filter for nonlinear maneuvering target tracking

Abstract

Handling the nonlinearity between the measurement and kinematic states is the core issue in target tracking based on radar or sonar. The main novelty of this paper is the proposal of a new filter with a linear structure to achieve nonlinear tracking by integrating information in the polar coordinate system. The state vectors composed of the range, bearing and their differentials are constructed to make the measurement equations linear. After discretizing the ordinary differential dynamic equations in the polar coordinate system, linear time-varying state transition matrixes are established for two common Cartesian motions: constant velocity (CV) and constant acceleration (CA). For the process noises converted from the Cartesian coordinate system to the polar coordinate system, the first and second moments are derived with a closed form. Consequently, the coordinate system of the conventional state equations is converted so that the tracking can be conducted by a standard Kalman filter. Several simulation scenarios show that such a new filter effectively improves the tracking accuracy. The reasons for the superior performance of the proposed method are analyzed and exemplified. In addition, different posterior Cramer–Rao lower bounds (PCRLBs) for fusion estimation in Cartesian coordinates and polar coordinates are given and compared.