Letter to the Editor—An Algorithm for Ranking all the Assignments in Order of Increasing Cost

Abstract

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

“…Based on this, one assumes that if j-th measurement does not fall in the gate of target i, then the value, associated with this pairing ( , ) ij in the assignment matrix could be set to be big enough (in our case it equals 100), in order to prepare the assignment matrix for the next step. The classical Munkres and Katta-Murty methods [15] are used in order to obtain the first and the second best assignment solutions for measurement-to-track associations. By minimizing the sum of the chosen pairings' distances, a binary association matrix…”

“…Among the well known are KuhnMunkres algorithm (known as Hungarian) [12,13] and its extension proposed by Bourgeois and Lassalle in [14] to rectangular matrices. More sophisticated Murty's method [15] provides not only the first best assignment, but also the m-best assignments in order of increasing the cost, as shown in the examples of [10,11].…”

“…The pignistic transformation [15] is applied in order to obtain pignistic probabilities, built on the basis of fused basic belief assignments, such as …”

Sea ice tracking with a Spatially Indexed Labeled Multi-Bernoulli filter

“…It can, however, be enumerated in order of decreasing probability and truncated to the k-best hypotheses [17]. For each hypothesis, it is assumed that each track can be modeled as a standard single-target estimation problem, conditioned on the validity of the hypothetical assignments, and that its evolution is described by the single-target transition density f k (x k, |x k−1, , ) for target at time step k.…”

Tolerances Applied in Combinatorial Optimization

“…preserving the optimality of the given optimal solution. The first successful implicit application of upper tolerances for improving the Transportation Simplex Algorithm is appeared in the so called Vogel's Approximation Method [4] and has been used for a straightforward enumeration of the k -best solutions for some positive integer k [5,6] as well as a base of the MAX-REGRET heuristic for solving the three-index assignment problem [7] .…”