Misassociation Probability in M2TA and T2TA

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1 December 2007
J. Areta, Y. Bar-Shalom, R. Rothrock

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This paper presents procedures to calculate the probability that the measurement or the track originating from an extraneous tar-get will be (mis)associated with a target of interest for the cases of Nearest Neighbor and Global association. For the measurement-to-track (M2T) case, it is shown that these misassociation probabilities depend, under certain assumptions, on a particular–covariance weighted–norm of the difference between the targets’ predicted measurements. For the Nearest Neighbor M2T association, the exact solution, obtained for the case of equal track covariances, is based on a noncentral chi-square distribution. An approximate solution is also presented for the case of unequal track prediction covariances. For the Global M2T association case an approximation is presented for the case of “similar” track covariances. In the general case of unequal track covariances where this approximation fails, a more complicated but exact method based on the inversion of the characteristic function is presented. The track-to-track (T2T) association case involves correlated random variables for which the exact prob-ability density function is very hard to obtain. Moment matching approximations are used that provide very accurate results. The theoretical results, confirmed by Monte Carlo simulations, quantify the benefit of Global vs. Nearest Neighbor M2T association. These results are applied to problems of single sensor as well as centralized fusion architecture multiple sensor tracking.