<title>Effect of cross-correlation on track-to-track fusion</title>

Abstract

Since the advent of target tracking systems employing a diverse mixture of sensors, there has been increasing recognition by air defense system planners and other military system analysts of the need to integrate these tracks so that a clear air picture can be obtained in a command center. A popular methodology to achieve this goal is to perform track-to-track fusion, which performs track-to-track association as well as kinematic state vector fusion. This paper seeks to answer analytically the extent of improvement achievable by means of kinetic state vector fusion when the tracks are obtained from dissimilar sensors (e.g., Radar/ESM/IRST/IFF). It is well known that evaluation of the performance of state vector fusion algorithms at steady state must take into account the effects of cross-correlation between eligible tracks introduced by the input noise which, unfortunately, is often neglected because of added computational complexity. In this paper, an expression for the steady-state cross-covariance matrix for a 2D state vector track-to-track fusion is obtained. This matrix is shown to be a function of the parameters of the Kalman filters associated with the candidate tracks being fused. Conditions for positive definiteness of the cross-covariance matrix have been derived and the effect of positive definiteness on performance of track-to-track fusion is also discussed.