Optical EngineeringCentralized fusion of remote tracks
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A centralized track fusion algorithm that incorporates crosscorrelation between tracks originating from multiple platforms at remote sites is described. Remote stations transmit the information contained in these track updates to a central station where the tracks are kinematically fused to create composite tracks. it has been established that the probability distribution of correct track-to-track association can be improved if the cross-covariance matrix between the candidate tracks for fusion is positive. Necessary and sufficient conditions for positivity were derived and the steady state solution of the cross-covariance matrix was obtained in terms of the parameters of the candidate tracks to be fused. However, system-theoretic implications of these constraints were unclear. We obtain the steady state solution of the cross-covariance matrix in terms of a line integral. It is shown that evaluation of this integral involves inversion of an asymmetric matrix. For fusion of tracks created by similar sensors, this matrix is reduced to that of the Schur matrix, which arises in the analysis of steady state stability of the tracker associated with each sensor. However, for fusion of tracks created by dissimilar sensors, the structure of the matrix to be inverted is complicated and can not readily be partitioned in terms of the Schur matrices associated with each tracker. An efficient algorithm for the inversion of this matrix is also presented.