Exact bias removal for the track-to-track association problem

In the track-to-track association problem, the fundamental quantity to calculate is the probability of an association given the data. Algorithms which are based on such a calculation can make meaningful statements about the probabilities of associations and of related events, and are more accurate and robust than algorithms which do not. This paper presents the required probability calculation for the case of two or more biased sensors. Two demonstrations are then made of its superiority to currently used approaches for handling bias - in particular to what is currently considered the state-of-the-art approach, which is to remove the most likely bias candidate for each association individually. The first demonstration is a simple, illustrative scenario where commonly used bias removal methods fail drastically because they attempt to compute the wrong quantity. The second is a procedure for validating the probabilities produced by any association algorithm. This procedure demonstrates the correctness of the probability formula, and the degree to which the probabilities produced by other methods are erroneous.