Detection Thresholds for Tracking in Clutter - A Connection Between Estimation and Signal Processing.

摘要

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. 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 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 a 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. A validation of the modified Riccati equation is also presented.