A new relaxation algorithm and passive sensor data association
TL;DR: In this paper, the measurement-target association problem is formulated as one of maximizing the joint likelihood function of the measurement partition, which leads to a generalization of the 3D assignment (matching) problem, which is known to be NP hard.
Abstract: The static problem of associating measurements at a given time from three angle-only sensors in the presence of clutter, missed detections, and an unknown number of targets is addressed. The measurement-target association problem is formulated as one of maximizing the joint likelihood function of the measurement partition. Mathematically, this formulation leads to a generalization of the 3-D assignment (matching) problem, which is known to be NP hard. The solution to the optimization problem developed is a Lagrangian relaxation technique that successively solves a series of generalized two-dimensional (2-D) assignment problems. The algorithm is illustrated by several application examples. >
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TL;DR: This article places data fusion into the greater context of data integration, precisely defines the goals of data fusion, namely, complete, concise, and consistent data, and highlights the challenges of data Fusion.
Abstract: The development of the Internet in recent years has made it possible and useful to access many different information systems anywhere in the world to obtain information. While there is much research on the integration of heterogeneous information systems, most commercial systems stop short of the actual integration of available data. Data fusion is the process of fusing multiple records representing the same real-world object into a single, consistent, and clean representation.This article places data fusion into the greater context of data integration, precisely defines the goals of data fusion, namely, complete, concise, and consistent data, and highlights the challenges of data fusion, namely, uncertain and conflicting data values. We give an overview and classification of different ways of fusing data and present several techniques based on standard and advanced operators of the relational algebra and SQL. Finally, the article features a comprehensive survey of data integration systems from academia and industry, showing if and how data fusion is performed in each.
1,797 citations
TL;DR: The survey discusses the application of the various algorithms at different layers of the JDL model and highlights the weaknesses and strengths of the approaches in the context of different applications
Abstract: The tracking of objects using distributed multiple sensors is an important field of work in the application areas of autonomous robotics, military applications, and mobile systems. In this survey, we review a number of computationally intelligent methods that are used for developing robust tracking schemes through sensor data fusion. The survey discusses the application of the various algorithms at different layers of the JDL model and highlights the weaknesses and strengths of the approaches in the context of different applications
379 citations
Cites background or methods from "A new relaxation algorithm and pass..."
...However, in a dense environment, this may lead to many pairings with a similar probability, so errors are typically large [28]....
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...In this algorithm, the nearest measurement to the established track is chosen to update the track....
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TL;DR: An efficient and recursive generalized S-D assignment algorithm (S/spl ges/3) employing a successive Lagrangian relaxation technique is presented, with application to the localization of an unknown number of emitters using multiple high frequency direction finder sensors.
Abstract: We develop a new algorithm to associate measurements from multiple sensors to identify the real targets in a surveillance region, and to estimate their states at any given time. The central problem in a multisensor-multitarget state estimation problem is that of data association-the problem of determining from which target, if any, a particular measurement originated. The data association problem is formulated as a generalized S-dimensional (S-D) assignment problem, which is NP-hard for S/spl ges/3 sensor scans (i.e., measurement lists). We present an efficient and recursive generalized S-D assignment algorithm (S/spl ges/3) employing a successive Lagrangian relaxation technique, with application to the localization of an unknown number of emitters using multiple high frequency direction finder sensors (S=3, 5, and 7).
358 citations
Cites background or methods from "A new relaxation algorithm and pass..."
...Although the S-D assignment problem is NP-hard for S ̧ 3, there exist techniques [7, 28] to solve the 2-D assignment problem in O(n3) time....
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...In our earlier effort [28], we solved a 3-D assignment problem as a series of 2-D subproblems, by relaxing the third constraint and appending it to the cost function using Lagrangian multipliers....
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...Thus, optimal solution techniques, based for example on branch and bound strategies, requiring unacceptably long times for 10 or more targets, are of little practical value [28]....
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...We use the generalized 2-D assignment problem presented in [28]....
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...1 Therefore, an optimal algorithm may be impractical even for 10 targets and S = 3 lists in a dense scenario [28]....
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TL;DR: The design of a Variable Structure Interacting Multiple Model (VS-IMM) estimator for tracking groups of ground targets on constrained paths using Moving Target Indicator reports obtained from an airborne sensor is presented, significantly improving performance and reducing computational load.
Abstract: In this paper we present the design of a Variable Structure Interacting Multiple Model (VS-IMM) estimator for tracking groups of ground targets on constrained paths using Moving Target Indicator (MTI) reports obtained from an airborne sensor. The targets are moving along a highway, with varying obscuration due to changing terrain conditions. In addition, the roads can branch, merge or cross-the scenario represents target convoys along a realistic road network with junctions, changing terrains, etc. Some of the targets may also move in an open field. This constrained motion estimation problem is handled using an IMM estimator with varying mode sets depending on the topography, The number of models in the IMM estimator, their types and their parameters are modified adaptively, in real-time, based on the estimated position of the target and the corresponding road/visibility conditions. This topography-based variable structure mechanism eliminates the need for carrying all the possible models throughout the entire tracking period as in the standard IMM estimator, significantly improving performance and reducing computational load. Data association is handled using an assignment algorithm. The estimator is designed to handle a very large number of ground targets simultaneously. A simulated scenario consisting of over one hundred targets is used to illustrate the selection of design parameters and the operation of the tracker. Performance measures are presented to contrast the benefits of the VS-IMM estimator over the Kalman filter and the standard IMM estimator, The VS-IMM estimator is then combined with multidimensional assignment to gain "time-depth." The additional benefit of using higher dimensional assignment algorithms for data association is also evaluated.
336 citations
Cites background or methods from "A new relaxation algorithm and pass..."
...The dummy notation is used to formulate the assignment problem in a uniform manner, where the nonassociation possibilities are also considered, making it computer-solvable [17, 21]....
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...Recently, assignment algorithms have been shown to be effective in data association for multitarget tracking in the presence of clutter [9, 11, 12, 17, 18, 21]....
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...The candidate associations, subject to the above constraints, are given to the modified auction algorithm5 [17] along with the corresponding association costs....
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References
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01 Jan 1979
42,654 citations
Book•
01 Jan 1979
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Abstract: This is the second edition of a quarterly column the purpose of which is to provide a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NP-Completeness,’’ W. H. Freeman & Co., San Francisco, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed. Readers having results they would like mentioned (NP-hardness, PSPACE-hardness, polynomial-time-solvability, etc.), or open problems they would like publicized, should send them to David S. Johnson, Room 2C355, Bell Laboratories, Murray Hill, NJ 07974, including details, or at least sketches, of any new proofs (full papers are preferred). In the case of unpublished results, please state explicitly that you would like the results mentioned in the column. Comments and corrections are also welcome. For more details on the nature of the column and the form of desired submissions, see the December 1981 issue of this journal.
40,020 citations
TL;DR: This paper has always been one of my favorite children, combining as it does elements of the duality of linear programming and combinatorial tools from graph theory, and it may be of some interest to tell the story of its origin this article.
Abstract: This paper has always been one of my favorite “children,” combining as it does elements of the duality of linear programming and combinatorial tools from graph theory. It may be of some interest to tell the story of its origin.
11,096 citations
TL;DR: This clearly written, mathematically rigorous text includes a novel algorithmic exposition of the simplex method and also discusses the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms, local search heuristics for NPcomplete problems, more.
Abstract: This clearly written , mathematically rigorous text includes a novel algorithmic exposition of the simplex method and also discusses the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms, local search heuristics for NPcomplete problems, more All chapters are supplemented by thoughtprovoking problems A useful work for graduate-level students with backgrounds in computer science, operations research, and electrical engineering Mathematicians wishing a self-contained introduction need look no further—American Mathematical Monthly 1982 ed
7,221 citations
03 May 1971
TL;DR: It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology.
Abstract: It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology. Here “reduced” means, roughly speaking, that the first problem can be solved deterministically in polynomial time provided an oracle is available for solving the second. From this notion of reducible, polynomial degrees of difficulty are defined, and it is shown that the problem of determining tautologyhood has the same polynomial degree as the problem of determining whether the first of two given graphs is isomorphic to a subgraph of the second. Other examples are discussed. A method of measuring the complexity of proof procedures for the predicate calculus is introduced and discussed.
6,675 citations