MMOSPA estimation with unknown number of objects

We consider the problem of estimating unordered sets of objects, which arises when the object labels are irrelevant. The widely used minimum mean square error (MMSE) estimators are not applicable for the estimation of unordered objects. Recently, a new type of estimator, known as the minimum mean OSPA (MMOSPA) estimator, which minimizes the optimal sub-pattern assignment (OSPA) metric, was proposed. Unfortunately, the MMOSPA estimator is unable to deliver a closed form solution when the objects, represented as a random finite set (RFS), are multidimensional or when the underlying posterior density is non-Gaussian; also, the existing MMOSPA estimators have not bee used to estimate unknown numbers of objects. In this paper, we derive a particle-based algorithm for the estimation of unknown number of objects which is optimal in the MMOSPA sense; also, the proposed algorithm is not limited by the dimension of the RFS or the requirement of Gaussian posterior density.