Adaptive filtering via maximization of residual joint density functions

The theory of estimating the position and motion of a randomly maneuvering target given noisy bearing measurements from a single moving observer is presented. The standard Kalman filter formulation, which employs a constant target velocity plant description, is shown to exhibit classical filter divergence in the presence of target maneuvers; further, reliable estimation of the position and motion parameters of an unconstrained target is demonstrated via adaptive control of process noise. Classical application of plant noise is found to be insufficient to handle the maneuvering target problem. An adaptive control algorithm, which estimates the plant noise variance by maximizing the joint probability density function of a sequence of uncorrelated predicted measurement residuals, is developed and offered as a viable solution to the bearings-only maneuvering target problem. Experimental results using laboratory data are presented.