Calculating some exact MMOSPA estimates for particle distributions

In this work, we present some exact algorithms for calculating the minimum mean optimal sub-pattern assignment (MMOSPA) estimate for probability densities that are represented with particles. First, a polynomial-time algorithm for two targets is derived by reducing the problem to the enumeration of the cells of a hyperplane arrangement. Second, we present a linear-time algorithm for an arbitrary number of scalar target states, which is based on the insight that the MMOSPA estimate coincides with the mean of the order statistics.