Detection thresholds for tracking in clutter--A connection between estimation and signal processing

In the Kalman-Bucy filter and other trackers, the dependence of tracking performance upon the quality of the measurement data is well understood in terms of the measurement noise covariance matrix, which specifies the uncertainty in the values of the measurement inputs. The measurement noise and process noise covariances determine, via the Riccati equation, the state estimation error covariance. When the origin of the measurements is also uncertain, one has the widely studied problem of data association (or data correlation), and tracking performance depends critically on signal processing parameters, primarily the probabilities of detection and false alarm. In this paper we derive a modified Riccati equation that quantifies (approximately) the dependence of the state error covariance on these parameters. We also show how to use a receiver operating characteristic (ROC) curve in conjunction with the above relationship to determine the detection threshold in the signal processing system that provides measurements to the tracker so as to minimize tracking errors. The approach presented in this paper provides a feedback mechanism from the information processing (tracking) subsystem to the signal processing subsystem so as to optimize the overall performance in clutter.