Target Tracking Using Time Delay and Doppler Shift with Nonnegligible Motion Effect in Bistatic Sonar

This article investigates the target tracking problem using time delay and Doppler shift measurements obtained by bistatic sonar. The motions of the target, transmitter and receiver result in their real locations to be different from the initial locations during every observation period. Knowing that the measurement model is related to the locations, neglecting the motion effect will bring model bias, especially when the motion speeds are significant relative to underwater sound speed. Incorporating the motion effect into the measurement model to address the model bias problem will introduce the unknown real locations to make the tracking problem challenging. We shall transform the unknown real locations to be expressions with respect to the target state by solving their corresponding quadratic equations. The motion-compensated extended Kalman filter (MC-EKF) is next developed by deriving exact Jacobian and using EKF. Theoretical analysis corroborates the importance of taking the motion effect into consideration during the observation period by contrasting with the posterior Cramér-Rao lower bound (PCRLB) and motion-neglected EKF (MN-EKF). Comprehensive simulations are conducted to study the effectiveness of the proposed MC-EKF algorithm and the results show that the larger mean square error (MSE) arises when neglecting the motion effect than that of the proposed MC-EKF which reaches PCRLB.