Covariance reformulations of the dynamic second-order smooth variable structure filter with applications to target tracking

A popular filter in target tracking is the Kalman Filter (KF). However, its performance degrades when modeling error is present and it may become unstable. Target maneuvers introduce modeling errors. The Smooth Variable Structure Filter (SVSF) is a robust filter formulated based on variable structure system theory to address modeling errors, which are common in practice. This paper reformulates the covariance of an SVSF variant known as the Dynamic Second-Order Smooth Variable Structure Filter (DSO-SVSF). It is reformulated because the current covariance of that filter is approximate, and in this work, an exact covariance is derived. An accurate filter covariance is necessary for data association in target tracking. Although the DSO-SVSF does not require a covariance to update the state, the covariance is necessary for target tracking to perform data association. This paper involves the following original theoretical contributions: i) covariance reformulation of the DSO-SVSF for linear systems with square and non-square output matrices, and ii) formulation of a Probabilistic Data Association Filter (PDAF) that uses the reformulated covariance. The applied contributions are: iii) application of the proposed covariance for data association in target tracking, and iv) comparison of the target tracking performance of the proposed PDAF to other PDAFs in simulations. The proposed covariance is referred to as Stochastic Gain Covariance (SGC). The proposed PDAF is applied to perform target tracking in simulations. The baselines include the KF-based formulation of PDA, a PDAF that employs the DSO-SVSF and its approximate covariance, and a PDAF that uses the original Second-Order SVSF (SO-SVSF) and its approximate covariance.