A Concave Optimization-Based Approach for Joint Multi-Target Track Initialization

The performance of track initialization methods based on real-time filtering depends heavily on the state estimation accuracy of the track head, which cannot be accurately obtained in many cases. This paper proposes the joint optimization problem of multi-target track initialization, in which the data association and track parameters of targets are obtained simultaneously. To this end, the target trajectory is first modeled as a weighted sum of a set of continuous time basis functions, and the corresponding track initialization is to determine discrete-value decision related to data association and continuous-value estimate related to function weights (i.e., track parameters). Such binary optimization is further transformed into the equivalent quadratic concave optimization of the data association vector by track parameter elimination, while each target definitely corresponds to one of the local minima that satisfy the target existence condition. In implementation, a modified normal rectangular algorithm is presented to obtain such minima, instead of the global minimum gotten by the standard normal rectangular algorithm. Finally, simulation results show the effectiveness of the proposed algorithm.