Smooth Variable Structure Filtering Theory with Applications to Target Tracking and Trajectory Prediction

Abstract

Target tracking and trajectory prediction are state estimation applications. Popular state estimation techniques include the Kalman Filter (KF), Extended KF (EKF), Unscented KF (UKF), and the Particle Filter (PF). A limitation of these filters is that the model must be largely known; if this is violated, it may cause instability. A filter known as the Smooth Variable Structure Filter (SVSF) has been developed to address modeling errors. It is hypothesized that SVSFs will improve tracking and trajectory prediction performance due to their robustness against modeling uncertainties. To begin, two trajectory prediction algorithms for autonomous driving based on Interacting Multiple Model (IMM) estimation are developed. One combines the IMM and KF, called IMM-KF, and the other combines IMM with the Generalized Variable Boundary Layer - Smooth Variable Structure Filter (GVBL-SVSF), called IMM-GVBL-SVSF. The performance of both algorithms is comparatively analyzed using synthetic and real datasets. A comparison is made to machine learning strategies as well. Moreover, a general framework for SVSF formulation is proposed, putting a subset of SVSF variants under one umbrella. A strategy to combine nonlinear KFs with SVSFs is proposed, which results in six hybrid filters. Since a subset of SVSF variants can be discovered as special cases of these filters, the proposed framework puts these variants under one umbrella. The hybrid filters are applied to perform aircraft target tracking using synthetic radar measurements. Their performance is compared to the EKF, UKF, Cubature KF, PF, and other SVSFs. Furthermore, the covariance is reformulated for the Dynamic Second-Order Smooth Variable Structure Filter. A new PDAF is formulated that uses this covariance. An optimal filter that minimizes the trace of the covariance is also proposed. The new PDAF and the optimal filter are applied to perform aircraft tracking using synthetic radar data, and the performance is compared with other filters.