When the Closest Targets Make the Difference: An Analysis of Data Association Errors

Multi-object data fusion - combining measurements or estimates of more than one truth object from more than one observer - requires a first "data association" step of deciding which data have common truth objects. Here we focus on the case of two observers only, with the data association engine powered by a polynomially-complex list-matching algorithm such as of Jonker-Volgenant-Castanon (JVC), auction or Munkres. The paper's purpose is to develop an approximation for the probability of assignment error: How often does the data association engine tell the fuser to combine data from truth objects that do not go together? We assume data with Gaussian errors and a Poisson field of truth objects, and we focus on the low-noise case where errors are infrequent and fusion makes sense. In this article, for isotropic, independent identically distributed errors, a single scalar parameter representative of the scene complexity is identified and, exploiting that, a reasonably simple approximate expression for the association error is derived.