Consistent linear tracker with position and range rate measurements

Abstract

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).

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

“…The consistency of the conversion method was examined using the Normalized Error Squared (NES) [2] and shown to be consistent in [4]. Note that although the converted measurement has dimension 4, the expected NES [2, eq.…”

“…The converted measurement is then used in a linear Kalman filter. The method, referred to here as the converted measurement Kalman filter with range rate (CMKFRR), was shown in [4] to have improved performance over an EKF and an EKF with alternate linearization as describe in [3]. In this manuscript the evaluation is expanded to include the sequential EKF using a pseudo measurement [7], [11], [12] and the sequential UKF using the raw range range measurement [8], [13].…”

“…A recently proposed method [4], however, provides a natural extension of the CMKF to include range rate by converting range, bearing and range rate to Cartesian position and velocity. The converted measurement is then used in a linear 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).…”

Tracking maneuver target using interacting multiple model-square root cubature Kalman filter based on range rate measurement

“…The Doppler radar not only can obtain the position information of the target, but also the range rate or Doppler velocity. The literature [4][5][6] shows that the range rate measurement can improve the tracking performance. Yuan et al 7 and Frencl and colleagues 8,9 try to get the angle velocity estimation from the Doppler velocity.…”