Design of nearly constant velocity track filters for tracking maneuvering targets

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 is introduced and used to develop a relationship between the maximum acceleration and the process noise variance that either minimizes the maximum mean squared error (MMSE) in position or weighted sum of the noise variance plus maneuver bias. For each case, the process noise standard deviation is expressed in terms of the maximum acceleration and deterministic tracking index for both piecewise constant and discretized continuous acceleration error models. A lower bound on the process noise variance is also expressed in terms of the maximum acceleration and deterministic tracking index. With the use of Monte Carlo simulations, the method for choosing process noise variance for tracking maneuvering targets is demonstrated.