Detection thresholds for multi-target tracking in clutter

Tracking performance depends upon the quality of the measurement data. In the Kalman-Bucy filter and other trackers, this dependence is well-understood in terms of the measurement noise covariance matrix, which specifies the uncertainty in the values of the measurement inputs. 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 additional 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 an ROC curve in conjunction with the above relationship to determine an optimal detection threshold in the signal processing system that provides measurements to the tracker.