Nonlinear Target Tracking Methods for Near-Radially Inbound Targets
Ford, Kevin Robert
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Maneuvering, near-radially inbound (NRI) anti-ship missile (ASM) targets pose a difficult problem for ship self-defense systems. The ongoing evolution of these targets is a primary driver of the research and development tracking algorithms. A series of studies have been performed to develop new endpoint-constrained (EPC) filtering algorithms to track these targets in real time and to evaluate the tracking error performance compared with legacy methods. The findings from these studies demonstrate that EPC filters deliver superior tracking accuracy, with many doing so in real time. The EPC model is developed by first deriving the spherical constant velocity kinematic model. Taken together with the proportional navigation acceleration model, the spherical constant velocity model can be reformulated to include an endpoint constraint. This constraint was used to develop an EPC extended Kalman filter (EKF) with superior NRI target tracking performance when compared with the legacy spherical EKF (S-EKF) and the Cartesian EKF (C-EKF). Stepping beyond the EPC EKF, two additional discrete-time filters are developed in order to provide higher order nonlinear estimation capabilities. These two filters are the EPC unscented Kalman filter (UKF) and EPC bootstrap particle filter (BPF). Both filters offer even greater tracking performance improvements than legacy filters for the set of NRI targets. Broadening the scope of this research, multiple-model algorithms have been developed to address the non-NRI target motion behavior. A pair of mixed EPC interacting multiple-model (IMM) algorithms have been shown to be more flexible than any of the EPC or legacy filters alone, allowing for accurate tracking of a larger array of target types. EPC IMM algorithms also deliver real-time performance, making them viable for use in self-defense combat systems. The final chapter returns to first principles of stochastic filtering. The Zakai equation is leveraged to develop a set of continuous-discrete (C-D) filters via the robust Duncan-Mortensen-Zakai (DMZ) equation. These C-D methods are not widely used to track targets in spherical coordinates. A pair of C-D EPC optimal Bayesian filters (OBFs) are developed and found to offer superior performance to all legacy filters and most discrete-time EPC filters, albeit with a higher computational burden.