MSE Design of Nearly Constant Velocity Kalman Filters for Tracking Targets With Deterministic Maneuvers

Abstract

When tracking maneuvering targets with a nearly constant velocity (NCV) Kalman filter with white noise acceleration, the selection of the process noise variance is complicated by the fact that the process noise errors are modeled as white Gaussian in the Kalman filter, while target maneuvers are deterministic or highly correlated in time. In recent years, the deterministic maneuver index was introduced for NCV Kalman filters and used to develop a relationship between the anticipated maximum acceleration of the target and the process noise variance that minimizes the maximum mean squared error (MaxMSE) in position. Lower bounds on the process noise variance that prevent the position MSE from exceeding the measurement noise variance were also expressed in terms of the maximum acceleration and deterministic maneuver index. In this paper, those results are summarized and codified for practical application by the target tracking community. The design methods for NCV Kalman filters with discrete white noise acceleration (DWNA) and continuous white noise acceleration (CWNA) are presented for sustained and brief maneuvers. The application of the design methods to radar tracking of maneuvering targets is also addressed. The effectiveness of the design methods is illustrated via Monte Carlo simulations.