Effect of common process noise on two-sensor track fusion

In a multisensor environment for surveillance systems, each sensor tracks multiple targets. It is assumed that sensors are equipped with optimal Kalman filters for target tracking. These tracks are correlated because the common process noise resulting from target maneuver enters the estimate of the state vector of the target being tracked. To obtain better quality tracks, the tracks from each sensor are associated using the nearest neighbor criterion for track matching and then kinematic track fusion is performed using the matched tracks. For this purpose, the cross-correlation matrix between tracks is introduced in the test statistic to test the hypothesis that the two tracks originated from the same target. It is shown that the probability distribution of correct track association is increased if the cross-covariance matrix introduced in the test statistic is positive. Necessary and sufficient conditions for the existence, uniqueness, and positivity of the cross-covariance matrix are derived. In addition, an expression for the steady-state cross-covariance matrix is obtained, which is shown to be a function of the parameters of the two filters associated with the candidate tracks being fused. It is shown that for two identical sensors, if the cross-covariance matrix is to be positive definite, certain restrictions on steady-state performance of the individual Kalman filters must be placed. Other measures of performance on the effect of cross correlation on kinematic track fusion are also discussed.