Generalizations of Blom And Bloem´s PDF decomposition for permutation-invariant estimation

Minimum mean squared error estimates generally are not optimal in terms of a common track error statistic used in tracking benchmarks, namely a form of the Mean Optimal Sub-pattern Assignment (MOSPA) metric. We derive an explicit solution for the MOSPA-optimal estimates for two scalar targets. We also generalize previous work on permutation variant and invariant PDF decompositions by Blom and Bloem (avoiding the use of measure theory), demonstrating how the means of these PDFs may be used to approximate minimum MOSPA estimates. These methods based upon PDF manipulation may be used with general PDFs for an arbitrary number of targets having states of arbitrary dimensionality. The results are also applicable within the context of channel estimation.