Finite-Set Statistics

Abstract

The purpose of this chapter is to extend the basic elements of practical statistics to multisensor, multitarget data fusion. Specifically, in section 5.1 we show that the basic concepts of elementary statistics—expectations, covariances, prior and posterior densities, etc.—have direct analogs in the multisensor, multitarget realm. In section 5.2 we show how the basic elements of parametric estimation theory—maximum likelihood estimator (MLE), maximum a posteriori estimator (MAPE), Bayes estimators, etc.—lead to fully integrated Level 1 fusion algorithms. That is, they lead to algorithms in which the numbers, I.D.s, and kinematics of multiple targets are estimated simultaneously without any attempt to estimate optimal report-to-track assignments. In particular, we show that two such fully integrated algorithms (analogs of the MLE and MAPE) are statistically consistent. The chapter concludes with section 5.3, in which we prove a Cramér-Rao inequality for multisensor, multitarget problems. The significance of this inequality is that it sets best-possible-theoretical-performance bounds for certain kinds of data fusion algorithms.