Note on Autocorrelation of the Residuals of the NCV Kalman Filter Tracking a Maneuvering Target

The Kalman filter is the optimal estimator for tracking a nearly constant velocity (NCV) target with white noise acceleration errors. However, when the target maneuvers the white noise input assumption is violated and the filter estimate will become biased or worse, lead to the loss of the target track. Selection of a larger process noise will reduce the bias in the state estimates during a maneuver, but when the target is not maneuvering the filter performance is far from optimal. In decision-directed techniques for tracking maneuvering targets, the estimation process is impacted by hard decisions regarding onset and termination of target maneuvers. In this work, the autocorrelation of consecutive residuals for a maneuvering target is derived and a new test for maneuver detection is proposed. When the process noise covariance of an NCV Kalman filter is artificially high for tracking maneuvering targets, achieving a specified false alarm rate for maneuver detection is a challenge. A remedy to this challenge is also presented.