On the NCA Versus NCV Models in Tracking Maneuvering Targets

When tracking maneuvering targets with a nearly constant velocity (NCV) Kalman filter with discrete white noise acceleration (DWNA) or a nearly constant acceleration (NCA) Kalman filter with discrete Wiener process acceleration (DWPA), the selection of the process noise variance is complicated by the fact that the process noise errors are modeled as zero-mean white Gaussian, while target maneuvers are deterministic or highly correlated in time. In recent years, for the NCV Kalman filters with DWNA, the deterministic tracking index was introduced 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. A lower bound on the process noise variance was also expressed in terms of the maximum acceleration and deterministic tracking index. Recently, the design methods for NCV Kalman filters with DWNA were extended to develop design methods for NCA Kalman filters with DWPA for tracking maneuvering targets, and the effectiveness of the design methods were illustrated via Monte Carlo simulations. However, the question of when to use an NCA filter instead of an NCV filter for tracking maneuvering targets remained unanswered. In this paper, this question is addressed utilizing these two design methods to achieve a fair comparison of two filters that are optimally designed.