Design of nearly constant velocity track filters for brief maneuvers

When tracking maneuvering targets with conventional algorithms, the process noise standard deviation used in the nearly constant velocity Kalman filter is selected vaguely in relation to the maximum acceleration of the target. The deterministic tracking index has been introduced and used to develop a relationship between the maximum acceleration and the process noise variance that minimizes the maximum mean squared error (MMSE) in position. A lower bound on the process noise variance has also been expressed in terms of the maximum acceleration and deterministic tracking index. Both of these results were developed for sustained maneuvers in that all of the transient effects of the maneuver have diminished. In this paper, the results for sustained maneuvers are extended to brief maneuvers. For each case, the process noise variance is expressed in terms of the maximum acceleration, duration of the maneuver in number of measurements, and deterministic tracking index for both the discrete white noise acceleration and continuous white noise acceleration models for nearly constant velocity motion. With the use of Monte Carlo simulations, the method for choosing process noise variance for tracking maneuvering targets is demonstrated to be effective for both sustained and brief maneuvers.