Hypothesis Testing over Factorizations for Data Association
The issue of data association arises frequently in sensor networks; whenever multiple sensors and sources are present, it may be necessary to determine which observations from different sensors correspond to the same target. In highly uncertain environments, one may need to determine this correspondence without the benefit of an a priori known joint signal/sensor model. This paper examines the data association problem as the more general hypothesis test between factorizations of a single, learned distribution. The optimal test between known distributions may be decomposed into model-dependent and statistical dependence terms, quantifying the cost incurred by model estimation from measurements compared to a test between known models. We demonstrate how one might evaluate a two-signal association test efficiently using kernel density estimation methods to model a wide class of possible distributions, and show the resulting algorithm's ability to determine correspondence in uncertain conditions through a series of synthetic examples. We then describe an extension of this technique to multisignal association which can be used to determine correspondence while avoiding the computationally prohibitive task of evaluating all hypotheses. Empirical results of the approximate approach are presented.