m-Best S-D Assignment Algorithm with Application to Multitarget Tracking

In this paper we describe a novel data association algorithm, termed m-best S-D, that determines in O(mSkn3) time (m assignments, S ̧ 3 lists of size n, k relaxations) the (approximately) m-best solutions to an S-D assignment problem. The m-best S-D algorithm is applicable to tracking problems where either the sensors are synchronized or the sensors and/or the targets are very slow moving. The significance of this work is that the m-best S-D assignment algorithm (in a sliding window mode) can provide for an efficient implementation of a suboptimal multiple hypothesis tracking (MHT) algorithm by obviating the need for a brute force enumeration of an exponential number of joint hypotheses. We first describe the general problem for which the m-best S-D applies. Specifically, given line of sight (LOS) (i.e., incomplete position) measurements from S sensors, sets of complete position measurements are extracted, namely, the 1st,2nd, : : : ,mth best (in terms of likelihood) sets of composite measurements are determined by solving a static S-D assignment problem. Utilizing the joint likelihood functions used to determine the m-best S-D assignment solutions, the composite measurements are then quantified with a probability of being correct using a JPDA-like (joint probabilistic data association) technique. Lists of composite measurements from successive scans, along with their corresponding probabilities, are used in turn with a state estimator in a dynamic 2-D assignment algorithm to estimate the states of moving targets over time. The dynamic assignment cost coefficients are based on a likelihood function that incorporates the “true” composite measurement probabilities obtained from the (static) m-best S-D assignment solutions. We demonstrate the merits of the m-best S-D algorithm by applying it to a simulated multitarget passive sensor track formation and maintenance problem, consisting of multiple time samples of LOS measurements originating from multiple (S = 7) synchronized high frequency direction finding sensors.