Performance analysis of the converted range rate and position linear Kalman filter

In active sonar and radar applications measurements consist of range, bearing and often range rate - all nonlinear functions of the target state (usually modeled in Cartesian coordinates). The converted measurement Kalman filter (CMFK) first converts the range and bearing measurements into Cartesian coordinates to allow for the use of a linear Kalman filter. The extension of the CMKF to use range rate as a linear measurement however has been limited to cases with small bearing errors. The use of range rate as a nonlinear measurement requires the use of a nonlinear filter such as the extended Kalman filter (EKF). Due to the uncertain performance of the EKF, various modifications have been proposed, including use of a pseudo measurement, an alternative linearization of the measurement prediction function, and sequentially processing the converted position and range rate measurements (applied to the EKF and the Unscented Kalman Filter). Common to these approaches is that the measurement prediction function remains nonlinear. A measurement conversion from range, bearing and range rate to Cartesian position and velocity has recently been proposed [4]. This manuscript expands the evaluation of this new approach by comparing to the Sequential EKF, the Sequential Unscented Kalman Filter (UKF) and the posterior Cramer-Rao lower bound (PCRLB). The new method is shown to have improved mean square error performance and exhibits improved constancy over the previously proposed methods, especially in cases with poor bearing accuracy.