Two unbiased converted measurement Kalman filtering algorithms with range rate

Abstract

The strong non‐linear relationship between the range rate and the target state can be introduced using the range rate to track a target. A linear measurement equation can be constructed based on the geometrical relationship between the range rate and the velocity components. Then, the linear Kalman filtering (KF) algorithm can be used. To improve the performance of the converted measurement method, a novel multiplicative unbiased converted measurement KF algorithm with range rate (UCMKF‐R) is developed. To eliminate the conversion bias, one‐step prediction estimation is used to replace the position measurement to calculate the converted measurement error covariance in the UCMKF‐R algorithm, which removes the correlation between the converted measurement error covariance and the measurement noise. Thus, a Decorrelated UCMKF‐R (DUCMKF‐R) is proposed. The experimental results show that the measurement conversion of the DUCMKF‐R algorithm is unbiased, consistent and has an estimation bias that is close to zero. The proposed UCMKF‐R and DUCMKF‐R algorithms are compared with the state‐of‐the‐art approaches, namely, the Sequential Extended KF algorithm, the Sequential Unscented KF algorithm, and the Converted Measurement KF with Range Rate algorithm. The experimental results show that the proposed algorithms have good performance.