Analysis of Costs for the GNP Problem

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1 June 2021

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Track-to-track data association in a multisensor framework involves score functions to determine a solution. When sensor errors include both random noise and unknown bias terms, several options are available. Of these, two options are the global nearest pattern match (GNPM) and marginal track-to-track association (MTTA) scores. The former involves a joint likelihood of bias and association hypothesis and the latter is the result of integrating the total probability space over the unknown bias to remove the bias likelihood. Analytically, we show that the difference between these scores is the determinant of the a-posteriori bias covariance, and that the same bias estimation is inherent in both. Using a simple numerical example, we compare the weight each score formulation apportions to track assignment hypotheses based on the quality of the bias estimate, and show that GNPM tends to favor hypotheses with low a-posteriori bias covariance. Additionally, through evaluation of the incremental cost structure, we argue that the non-assignment cost used in both scores is nearly optimal, in the sense of correct associations, for GNPM. However, the same non-assignment cost is not optimal for the MTTA score, and the significance depends upon the uncertainty of bias and the number of associations made.