A polynomial-time approximation algorithm for joint probabilistic data association

Abstract

Joint probabilistic data association (JPDA) is a powerful tool for solving data association problems. However, the exact computation of association probabilities {/spl beta//sub jk/} in JPDA is NP-hard, where /spl beta//sub jk/ is the probability that j-th observation is from k-th track. Hence, we cannot expect to compute association probabilities in JPDA exactly in polynomial time unless P = NP. In this paper, we present a simple Markov chain Monte Carlo data association (MCMCDA) algorithm that finds an approximate solution to JPDA in polynomial time. For /spl epsiv/ > 0 and 0 < /spl eta/ < .5, we prove that the algorithm finds good estimates of /spl beta//sub jk/ with probability at least 1 - /spl eta/ in time complexity O(/spl epsiv//sup -2/ log /spl eta//sup -1/N(N log N + log /spl epsiv//sup -1/))), where N is the number of observations.