Study on the Hungarian algorithm for the maximum likelihood data association problem

A specialized Hungarian algorithm was developed here for the maximum likelihood data association problem with two implementation versions due to presence of false alarms and missed detections. The maximum likelihood data association problem is formulated as a bipartite weighted matching problem. Its duality and the optimality conditions are given. The Hungarian algorithm with its computational steps, data structure and computational complexity is presented. The two implementation versions, Hungarian forest (HF) algorithm and Hungarian tree (HT) algorithm, and their combination with the nave auction initialization are discussed. The computational results show that HT algorithm is slightly faster than HF algorithm and they are both superior to the classic Munkres algorithm.