Design of NCA Filters for Tracking Maneuvering Targets

When tracking maneuvering targets with a nearly constant acceleration (NCA) Kalman filter with discrete white noise acceleration (DWNA), the selection of the process noise variance is complicated by the fact that the process noise errors are modeled as white Gaussian, while target maneuvers are deterministic or highly correlated in time. In recent years for nearly constant velocity (NCV) Kalman filters, the deterministic tracking index was introduced and used to develop a relationship between the maximum acceleration of the target and the process noise variance that minimizes the maximum mean squared error (MMSE) in position. A lower bound on the process noise variance was also expressed in terms of the maximum acceleration and deterministic tracking index. In this paper, the design methods for NCV Kalman filters with DWNA are extended to develop design methods for NCA Kalman filters with DWNA tracking maneuvering targets. The effectiveness of the design methods are illustrated via Monte Carlo simulations.