Misassociation Probability in M2TA and T2TA

This paper deals with the closed form misassociation probability formula for measurement-to-track association (M2T) and track-to-track association (T2T). The emphasis of this work is in closely spaced targets, which is much more prevalent in the real world than association of clutter to target tracks. Thus clutter is not considered in the sequel. In the first sections we develop the procedure to calculate the probability that the measurement associated by a likelihood based assignment algorithm to a target of interest originates from another (extraneous) target as a function of the state estimates and covariances of the tracks. Both a Nearest Neighbor1 (NN) as well as Global2 (G) assignment are considered. An approximate procedure is developed for the T2T association, as a closed form of the probability density function is very hard to find, due to the existing correlation between the track estimates. These closed form expressions should be useful when the knowledge of the performance of a system is to be quantified, for example, in the selection of a radar given it accuracy and the expected scenarios it could encounter. Also as in [6], it could be used to predict the number of measurements needed to achieve a certain performance. The model used for the targets is deterministic–they are located at a certain separation distance in the measurement space, expressed in terms of the track state estimates mapped into the measurement space. The association problem3 was investigated in [10] for a different model, namely, the targets were assumed randomly distributed (i.i.d. uniform in a hyperball of a sufficiently large radius). Extensive work on the association of tracks from two sources, using kinematic, feature and classification information was done in [14, 7]. In [9] a more complex T2TA problem accounting for registration errors and mismatch in the number of tracks is considered. To obtain meaningful results, the track model considered is simplistic, assuming isotropic errors of the same variance. The model considered here allows performance evaluation of association algorithms under more realistic conditions, namely, with arbitrary measurement prediction covariances and the results are expressed in terms of the target separation distance. Section 2 formulates the M2T association problem. The calculation of the misassociation probability for a Nearest Neighbor association is described in Section 3