Recursive Bearings-Only TMA via Unscented Kalman Filter: Cartesian vs. Modified Polar Coordinates

This paper considers the classic problem of bearings-only target motion analysis. This has extensively been studied in the past and the novelty here is the use of the unscented Kalman filter (UKF) with the modified polar coordinates state representation. To take advantage of this filter, we keep the exact non linear plant equation of the model in the prediction stage with the coupling between the different state vector components. In this representation, the prediction equation is not straightforward, but the counterpart is a trivial measurement equation. We compare the performance, in terms of estimation rms (root mean square) error and bias, of this filter with the widely used Cartesian representation in which the plant equation is trivial and the non linearity is reported in the measurement equation. The Cramer Rao Lower Bound is finally computed and helps as a reference.