Sequential unbiased converted measurement non-linear filter with range rate in ECEF coordinates

Air-to-air target tracking is a challenging task for practical military and civilian applications. In this study, an unbiased converted measurement Kalman filter in Earth-centred Earth-fixed (ECEF) coordinates (E-UCMKF) is proposed for air-to-air target tracking, which takes account for noisy measurements from the airborne radar and the inertial navigation system/global navigation satellite system. The unbiased measurement conversion approach from spherical coordinates to ECEF coordinates is presented, and the Kalman filter is implemented for target state estimation with the unbiased converted measurements and the corresponding measurement error covariances. Besides, when range-rate measurements are available to the processor, a sequential unbiased converted measurement non-linear filter in ECEF coordinates with range-rate measurements (E-SUCMNFwR) is developed, which constructs a pseudo measurement to decorrelate the range-rate measurement noise from the unbiased converted measurement noise, and estimates the state sequentially by the E-UCMKF and a modified cubature Kalman filter. Target tracking scenarios with different sensor accuracies are presented to demonstrate the validity of the proposed algorithms. Simulation results validate the consistency of the proposed unbiased measurement conversion. The results also show that the proposed E-UCMKF and E-SUCMNFwR outperform the conventional algorithms in terms of the position and velocity root-mean-square error, demonstrating their effectiveness and practicality.