Improved relaxation algorithm for passive sensor data association

The Lagrangian relaxation algorithm is widely used for passive sensor data association. However, there are two major problems about it. Firstly, the cost function of the algorithm is computed by using least square estimation of the target position without taking the estimation errors into account. To solve this problem, a modified cost function is derived, which is more proper to reflect the correlation between measurements owing to the integration of estimation errors. Secondly, owing to the fact that building the candidate assignment tree would take a lot of CPU time, the authors propose a statistic test based on indicator function with a great improvement in the computational efficiency. It is shown analytically that this method can obtain the same result as that of Lagrangian relaxation algorithm in some special cases, so a part of correct pairs can be selected directly without redundant relaxation and enforcement processes, then the possible set can be simplified according to the constraint conditions so that more correct pairs can be picked out by repeating such a process. Simulation results show that both the correlation accuracy and the computational efficiency of the improved relaxation algorithm are higher than that of the traditional one.