A Novel Smooth Variable Structure Filter for Target Tracking Under Model Uncertainty

Model uncertainty is a serious challenge for robustness of tracking algorithms in radar systems. The smooth variable structure filter (SVSF) achieves error-bounded estimations for target state by scaling the magnitude of kinematic modeling error and accordingly performing a flexible switching strategy for the correction gain. However, the SVSF, without any smoothing functions, suffers from undesired chattering phenomenon since the measurement noise causes random disturbance to the identification of actual level of uncertainties, leading to obvious deterioration of tracking accuracy. In this paper, we present a new switching function for SVSF, i.e. the hyperbolic tangent function, for effective chattering suppression. Then we propose a new algorithm named as the Tanh-SVSF, which reformulates the correction gain with the new switching function, to improve the estimation accuracy for target state. A mathematical definition of SVSF chattering is proposed to quantify the chattering amplitude. It is demonstrated that the new switching function exerts a nonlinear compressing effect on the likelihood of measurement innovation and substantially reduces the disturbance of measurement noise, leading to elimination of the chattering problem. The stability of the Tanh-SVSF is analyzed, based on a proposed stability theorem and the numerical exhaustion strategy. Finally, the proposed method is tested on a simulated vehicle tracking scenario and real-world radar data from the Oxford Radar RobotCar Dataset, and shows superior performance over existing SVSF formulations and the Kalman filter, in view of tracking accuracy, track continuity and the proposed chattering indicator.