Assignment costs for multiple sensor track-to-track association

Successful track-to-track data association in a multisensor, multitarget scenario is predicated on a proper cost function. The cost function for associating two tracks is well established. This paper investigates different versions of the likelihood that more than two tracks represent the same target. These likelihoods lead to different cost functions for the general track-to-track association problem. Two of the likelihoods are approximations based on ad-hoc extensions of the well-known two-track expression. The next approximation is the generalized likelihood (GL), where the true state is replaced by the maximum likelihood (ML) estimate of the target state in the true likelihood. The final likelihood is derived exactly from a diffuse prior of the target state and is referred to as the diffuse prior likelihood (DPL). This paper reveals the connection between the DPL and GL. The last two likelihood expressions incorporate the cross-track error covariance matrices, which are not readily available in distributed track fusion. Therefore, the paper considers three forms of the DPL or GL: (1) the correlated tracks (CT) form by using the actual cross-covariance matrices, (2) the independent tracks (IT) form by assuming the cross-covariance matrices are zero, and (3) the approximated correlated tracks (ACT) form by approximating the cross-covariance matrices. Simulations compare the performance of all likelihood versions.