An approximate Minimum MOSPA estimator

Optimizing over a variant of the Mean Optimal Subpattern Assignment (MOSPA) metric is equivalent to optimizing over the track accuracy statistic often used in target tracking benchmarks. Past work has shown how obtaining a Minimum MOSPA (MMOSPA) estimate for target locations from a Probability Density Function (PDF) outperforms more traditional methods (e.g. maximum likelihood (ML) or Minimum Mean Squared Error (MMSE) estimates) with regard to track accuracy metrics. In this paper, we derive an approximation to the MMOSPA estimator in the two-target case, which is generally very complicated, based on minimizing a Bhattacharyya-like bound. It has a particularly nice form for Gaussian mixtures. We thence compare the new estimator to that obtained from using the MMSE and the optimal MMOSPA estimators.