Performance of the NCV Kalman Filter with ECAE for Tracking Maneuvering Targets

When tracking maneuvering targets with a nearly constant velocity (NCV) Kalman filter, the selection of the process noise variance is complicated by the fact that the process errors are modeled as white Gaussian, while target maneuvers are deterministic or highly correlated in time. Due to this model mismatch, the NCV Kalman filter is a biased estimator for an accelerating target. In recent years, 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 NCV model Kalman filter with exponentially-correlated acceleration errors (ECAE) is studied. While the model mismatch of the NCV Kalman filter with ECAE is less than that for the NCV Kalman filter with white noise errors for a constant acceleration target, it is a biased estimator. Expressions for the MMSE of an NCV Kalman filter with ECAE tracking a constant acceleration target are developed and those expressions are verified via Monte Carlo simulations.