Expression for the Probability of Correlation Error in Data Fusion

In a previous paper we proposed an expression for the probability of association (or correlation) error between two lists of objects, subject to known Gaussian distributions and a Poisson field of such objects. The expression requires only summing a few terms in a series, and is quite accurate, especially so when the probability of such an error is low. It does, however, depend on an assumption that correlation errors were caused by isotropic observations of the truth. Hence, in this paper, we extend the analysis to non-isotropic sensor noise, and find that in many practical situations of interest it is quite simple to adapt the isotropic analysis thereto. A natural extension of our results is to the case of multiple (more than two) sensors, and we find that in the case of a simple sequential fusion strategy the analysis is straightforward. These multi-sensor results suggest that the analysis might fruitfully be applied to suggest a good sequential ordering; we do so, and find that significant benefits accrue even when based on observations alone (no need for clairvoyant knowledge of target “truth”). Finally, we explore translational sensor bias.