Target tracking algorithm for underwater ranges-only long baseline system with incomplete measurements

A Least Squares-Cubature Kalman Filter (LS-CKF) algorithm is proposed, aiming at increasing the tracking accuracy of underwater maneuvering target with incomplete measurements of the long baseline system. Firstly, a practical two-dimensional mathematical model of underwater target tracking with incomplete measurements is established. Secondly, a two-layer CKF is introduced where the expression of the cubature point under the latest measurement constraint is derived via least square estimation in the first layer to improve the accuracy of the measurement updating process. Finally, considering the underwater tracking system is power-limited, a simplified form of the new algorithm with ranges-only measurements is derived. The accuracy of the proposed algorithm is improved because the latest measurement is effectively integrated into each cubature point with the Least-Squares method, which allows the cubature points to move from the a prior area to the high likelihood region. The results of the simulation and the lake trial both show that the new algorithm significantly improves the tracking accuracy on condition that severe incomplete measurements and large initial error. Compared with the standard CKF algorithm, the convergence speed of LS-CKF is double while the tracking error is reduced by more than 10%.