Extended Diffuse Kalman Filter in Bearings-Only Tracking Applications

Bearings-only tracking (BOT) problem consists in determining the position and velocities of the target from noisy angular measurements coming from a radar or optoelectronic system. It is well known that nonlinear relationships between measurements and target coordinates, poor observability lead to serious complications when trying to use common nonlinear estimation methods. In this paper, the application of the extended Diffuse Kalman filter (EDFK) to the BOT problem is discussed. Such filter is a limiting case of Kalman filter (KF) with an unlimited increase in the initial covariances and linearization of the state space models in the vicinity of the current estimate. It is shown that the filter has a number of important properties which can be used both for analyzing the BOT problems in various formulations and for modeling. In particular, it was established that the limiting ratios and state estimates for the KF gains do not depend on the initial covariances. At the same time, the estimation error covariance matrix includes a component proportional to a large parameter.