Combinatorial problems in multitarget tracking—a comprehensive solution

Nagarajan, V.; Chidambara, M. R.; Sharma, Rishu

doi:10.1049/ip-f-1.1987.0019

Cited by 15 publications

(21 citation statements)

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“…In the limit, MHT builds an exponentially sized tree of all possible target states. However, in practice an approximation such as tree-pruning [48], k-best hypotheses, [42] or greedy tracking [51] can be used. It is also possible to use dynamic programming to optimize the target trajectories [56], however, this method is best suited to tracking a small number of objects, as the computational complexity may become prohibitive when the number of tracked objects grows large.…”

Section: A State-of-the Artmentioning

confidence: 99%

Dense Multiperson Tracking with Robust Hierarchical Linear Assignment

McLaughlin

Rincón

Miller

2015

IEEE Trans. Cybern.

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Section: A State-of-the Artmentioning

confidence: 99%

Dense Multiperson Tracking with Robust Hierarchical Linear Assignment

McLaughlin

Rincón

Miller

2015

IEEE Trans. Cybern.

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“…Instead, we have shown so far how to carry out this minimization for each case: if the allocation was known, it would be possible to minimize (11) with respect to the hyperparameters using simple conjugate gradient descent, which is standard practice when learning regular GPs. If the hyperparameters were known, it would possible to approximately compute the optimal allocation h * , casting the problem as a MaxCut algorithm, as per Section V-B, and using the SDP relaxation described in Section V-C.…”

Section: Worked Examplementioning

confidence: 99%

“…Another strategy to improve performance relies on postponing the decisions until enough information is available to exclude ambiguities [2], although this causes the number of possible trajectories to grow exponentially. Several attempts have been made to restrain this combinatorial explosion, including [11]- [13].…”

Section: Introductionmentioning

confidence: 99%

A Gaussian Process Model for Data Association and a Semidefinite Programming Solution

Lázaro-Gredilla

Vaerenbergh

2014

IEEE Trans. Neural Netw. Learning Syst.

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In this paper, we propose a Bayesian model for the data association problem, in which trajectory smoothness is enforced through the use of Gaussian process priors. This model allows to score candidate associations using the evidence framework, thus casting the data association problem into an optimization problem. Under some additional mild assumptions, this optimization problem is shown to be equivalent to a constrained Max K-section problem. Furthermore, for K=2, a MaxCut formulation is obtained, to which an approximate solution can be efficiently found using an SDP relaxation. Solving this MaxCut problem is equivalent to finding the optimal association out of the combinatorially many possibilities. The obtained clustering depends only on two hyperparameters, which can also be selected by maximum evidence.

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“…from a KF state estimator and the composite measurement probability given by Eq. (20). The numerator denotes the likelihood that composite measurement z from the t-th (static) rn-best S D assignment problem solution originated from track y2, and the denominator is the likelihood that measurement z3 corresponds to none of the existing tracks (i.e., a false alarm).…”

Section: Dynamic 2 D Assignment Problemmentioning

confidence: 99%

<title>M-best SD assignment algorithm with application to multitarget tracking</title>

Popp¹,

Pattipati²,

Bar‐Shalom³

1998

SPIE Proceedings

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In this paper we describe a novel data association algorithm, termed rn-best S D, that determines in O(mSkn3) time (m assignments, S lists of size ii, k relaxations) the rn-best solutions to an S D assignment problem. This algorithm is applied to the following problem. Given line of sight (i.e., incomplete position) measurements from S sensors, sets of complete position measurements are extracted, namely, the 1-st, 2-nd, . . . , rn-th best (in terms of likelihood) sets of composite measurements are determined solving a static S D assignment problem. Utilizing the joint likelihood functions used to determine the in-best S D assignment solutions, the composite measurements are then quantified with a probability of being correct using a JPDA-like technique. Lists of composite measurements from successive scans, along with their corresponding probabilities, are then used in turn with a state estimator in a dynamic 2 D assignment algorithm to estimate the states of the 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) rn-best S D assignment solutions. We demonstrate this algorithm on a multitarget passive sensor track formation and maintenance problem, consisting of multiple time samples of line of sight (LOS) measurements originating from multiple (S = 7) synchronized high frequency direction finding sensors. Another significance of this work is that the rn-best S D assignment algorithm (in a sliding window mode) provides for an efficient implementation of a Multiple Hypothesis Tracking (MHT) algorithm by obviating the need for a brute force enumeration of an exponential number of joint hypotheses.

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Combinatorial problems in multitarget tracking—a comprehensive solution

Cited by 15 publications

References 0 publications

Dense Multiperson Tracking with Robust Hierarchical Linear Assignment

Dense Multiperson Tracking with Robust Hierarchical Linear Assignment

A Gaussian Process Model for Data Association and a Semidefinite Programming Solution

<title>M-best SD assignment algorithm with application to multitarget tracking</title>

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