Consistent linear tracker with position and range rate measurements

In active sonar and radar applications measurements consist of range, bearing and often range rate. When tracking using range and bearing measurements only, the performance of a Converted Measurement Kalman Filter (CMFK) exceeds that of a mixed coordinate Extended Kalman Filter (EKF) if an unbiased conversion from polar to Cartesian coordinates is used. Performance is further enhanced if estimation bias is eliminated by evaluating the converted measurement error covariance using the state prediction. The extension of the CMKF to use range rate as a linear measurement is possible, but limited to cases with small bearing errors. The use of range rate as a nonlinear measurement requires the use of an EKF. Due to the poor performance of the EKF in some situations, 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. The goal of this work is to develop a measurement conversion from range, bearing and range rate to Cartesian position and velocity that is unbiased and consistent. The approach is then applied to a CMKF with appropriate elimination of conversion bias and estimation bias. Performance is compared to the conventional EKF and the EKF with alternative linearization (AEKF).