A Bayesian perspective on why the EKF fails in passive tracking

The problem of passive tracking (estimation of target location and velocity using only bearing to target information) is difficult but very important. Solutions have been proposed using the extended Kalman filter (EKF) based on various state representations. While some perform better than others, all are subject to failure through divergence. In this paper, EKF failure is considered from a Bayesian viewpoint by examining the differences between the EKF approximated conditional densities and the true conditional densities. It is shown that the EKF misses important features of the conditional densities and introduces distortions that can partially explain divergence. It is suggested that comparing the EKF approximated densities and the true densities could guide the design of improved estimators