Modified Murty's Algorithm for Diverse Multitarget Top Hypothesis Extraction

On the Quality of Optimal Assignment for Data Association

“…2 ) = 1/β 2 = 0.25 for k 2 = 1, 2, 3, 4) the following quality indicator matrix: We observe that optimal pairings (2,4) and (3,2) get the same quality value 0.2849 with the method I (based on averaging), even if these pairings have different impacts in the global reward value, which is abnormal. If we use the method I with the belief interval measure based on (5), the situation is worst because the three optimal pairings (1,3), (2,4) and (3,2) will get exactly same belief interval values [0.0465,1]. To take into account, and in a better way, the reward values of each specific association given in the best assignment A 1 and in the 2nd-best assignment A k2 2 , we propose to use the following construction of quality indicators depending on the type of matching (called Method II):…”

“…Clearly, with Method I we obtain the same quality indicator value 0.2849 for the specific associations (2,4) and (3,2) which seems intuitively not very reasonable because the specific rewards of these associations impact differently the global rewards result. If the method II based on the belief interval measure computed from (5) is preferred 7 , we will get respectively for the three optimal pairings (1,3), (2,4) and (3,2) the three distinct belief interval [0.5956,0.8924], [0.4113,0.7699] and [0.3524,0.6529]. These belief intervals show that the ordering of quality of optimal pairings (based either on the lower bound, or on the upper bound of belief interval) is consistent with the ordering of quality of optimal pairings in Q II (A 1 , A 2 ) computed with the averaging approach.…”

“…Fortunately, efficient algorithms have been developed in operational research and tracking communities for formalizing and solving these optimal assignments problems. Several approaches based on different models can be used to establish rewards matrix, either based on the probabilistic framework [1,3], or on the belief function (BF) framework [4][5][6][7]. In this paper, we do not focus on the construction of the rewards matrix 1 , and our purpose is to provide a method to evaluate the quality (interpreted as a confidence score) of each association (pairing) provided in the optimal solution based on its consistency (stability) with respect to all the second best solutions.…”

“…The most wellknown algorithms are Kuhn-Munkres (a.k.as Hungarian) algorithm [8,9] and its extension to rectangular matrices proposed by Bourgeois and Lassalle in [10], Jonker-Volgenant method [11], and Auction [12]. More sophisticated methods using Murty's method [13], and some variants [3,[14][15][16][17][18][19], are also able to provide not only the best assignment, but also the m-best assignments. We will not present in details all these classical methods because they have been already well reported in the literature [20,21], and they are quite easily accessible on the web.…”

The Impact of the Quality Assessment of Optimal Assignment for Data Association in a Multitarget Tracking Context

“…Some of them establish a reward matrix based on Kinematic only Data Association (KDA) and on a probabilistic framework [3,4]. Some of them rely on Belief Functions (BF) [5][6][7][8][9] and motivate the incorporation of the advanced concepts for Generalized Data Association (GDA) [6][7][8], allowing the introduction of a target attribute (target type, radar cross section, etc.)…”