Bayesian source separation and system data fusion methodology

Abstract

The probability of correctly selecting a target object from among many objects is a measure of how well one can discriminate. If more than one system modality for object discrimination is available, then one can fuse respective information derived from multiple systems. In this case, performance is dependent upon the accurate association of object tracks seen by one system with common object tracks seen by another system and can be viewed in terms of answering the question: “Which objects seen by one system are associated with which objects seen by another system?” Because discrimination performance is dependent upon how accurately track data from the various systems is associated, the association question has bearing on the discrimination question, i.e., the association question must be answered to facilitate answering the discrimination question. The purpose of this paper is to address the association question using the logical question formalism advocated by Richard Cox instead of the standard approach of random variables. Biases result from random and common object track errors from each system. An association matrix correlates each object track seen by one system with object tracks seen by another system. While estimation of the common bias is essential to robust track association, most current association algorithms do not jointly estimate the association matrix and the common bias. The essential problem is analogous to that of blind source separation [2]. A combined M-on-N track association matrix and common bias inferencing algorithm using a Bayesian source separation methodology is described with a sample 2-on-2 track association problem. While the described Bayesian algorithm deals with common translation biases and currently uses only metric information in the likelihood function, the same algorithmic approach can also effectively deal with errors having the form of any common affine transformation and can be extended to exploit features and any other available track information. Although its effectiveness has some dependence on track positions and relative sizes of the random and common errors which should be further investigated, the algorithm is both statistically efficient in its optimal exploitation of the likelihood information and exhaustive in its delineation of and search over [4] all possible association configurations.