A reliable maximum likelihood algorithm for bearing-only target motion analysis

This work presents a high performance, reliable algorithm for bearing-only target motion analysis. A general Nth-order target dynamics model is assumed. We analyze and implement, in discrete time, finite horizon setup, the maximal likelihood (ML) algorithm. The Cramer-Rao bound, for a general case of Nth-order target dynamics, is first calculated. Then, an ideal least square (ILS) estimate is defined. We show that the ILS estimate meets the Cramer-Rao, and we calculate an equation for the difference between the error of the ML estimate and the error of the ILS estimate. We conclude that as long as the error is not extremely large, the difference between the estimates is much smaller than the error itself. By utilizing the pseudo linear structure of the problem, the number of variables is reduced from 3N to N. The final result is an efficient, reliable, high performance bearings-only target motion analysis algorithm.