A comparison of two algorithms for determining ranked assignments with application to multitarget tracking and motion correspondence

Abstract

Recently, it has become clear that determining a ranked set of assignments allows computation of very good approximationsto the data association problem. Several algorithms have been proposed but only two return the k-best assignments in reasonable time. One is Danchick and Newnams' [1] algorithm, which is based on the recognition that determining the best assignment is a classical assignment problem, and that determining a ranked set of assignments may be accomplished by solving a series of modified copies of the initial assignment problem. The other algorithm is originally due to Murty [2] and was most recently described by [3] within the context of multitarget tracking. We evaluate the two algorithms using randomly generated data and data obtained from an electrooptical sensor simulation in which 90 missiles are launched. These evaluations show that Murty's algorithm performs significantly better in all scenarios. We show the relationship between the two algorithms and how Danchick and Newnams' algorithm can be very easily modified to Murty's algorithm. Experimental results using Murty's algorithm suggest that a solution to the real-time data association problem is now feasible.

Multiple hypothesis track-to-truth assignment with a minimum sojourn time

“…Let φ i k denote the ith best assignment of tracks to truth in a likelihood sense at time t k . Murty's algorithm provides an efficient method for generating the K best assignments [8], [9].…”

“…An artificial switch is defined as a very brief assignment of a track to a truth object that results from a minimum cost assignment of the set of tracks to the set of truth objects, but the assignment is unrealistic from a physics perspective. For each scoring time, the K-best hypotheses of track-totruth assignments are found via Murty's algorithm [8], [9], and these assignments are connected across scoring times so that the constraint on the minimum sojourn time is not violated. The multiple hypothesis or multiple frame approach to track-to-truth assignment are applied to simulated data and the results are compared to the assignments from the single frame approach with no constraint on the sojourn time and content vectors.…”

Extraction and temporal segmentation of multiple motion trajectories in human motion

“…The MHT attempts to solve the data association problem by finding the best hypothesis when each hypothesis represents an assignment of measurements to features. There have been efforts to make the MHT more practical by restraining the number of hypothesis [2,3]. Another statistical approach is the joint probabilistic data association filter (JPDAF) [8].…”

Matrix permanent inequalities for approximating joint assignment matrices in tracking systems

“…A strategy for generating multiple hypotheses within the context of the optimal assignment approach is to identify the k best assignments and take the union of their respective pairings [6,[10][11][12]. The assumption is that pairs in the most likely assignments are most likely to be correct.…”