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Analytic Combinatorics for Multiple Object Tracking [electronic resource] / by Roy Streit, Robert Blair Angle, Murat Efe.

By: Streit, Roy [author.].
Contributor(s): Angle, Robert Blair [author.] | Efe, Murat [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookPublisher: Cham : Springer International Publishing : Imprint: Springer, 2021Edition: 1st ed. 2021.Description: XVI, 221 p. 16 illus., 15 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783030611910.Subject(s): Signal processing | Computer science—Mathematics | Mathematical statistics | Probabilities | Signal, Speech and Image Processing | Probability and Statistics in Computer Science | Probability TheoryAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 621.382 Online resources: Click here to access online
Contents:
Introduction -- Extended object tracking -- Multiple sensors -- Other high computational complexity tracking problems -- Multiframe assignment and combinatorial optimization -- Saddle Point Method -- Multicomplex Algebra -- Automatic Differentiation -- Conclusion.
In: Springer Nature eBookSummary: The book shows that the analytic combinatorics (AC) method encodes the combinatorial problems of multiple object tracking—without information loss—into the derivatives of a generating function (GF). The book lays out an easy-to-follow path from theory to practice and includes salient AC application examples. Since GFs are not widely utilized amongst the tracking community, the book takes the reader from the basics of the subject to applications of theory starting from the simplest problem of single object tracking, and advancing chapter by chapter to more challenging multi-object tracking problems. Many established tracking filters (e.g., Bayes-Markov, PDA, JPDA, IPDA, JIPDA, CPHD, PHD, multi-Bernoulli, MBM, LMBM, and MHT) are derived in this manner with simplicity, economy, and considerable clarity. The AC method gives significant and fresh insights into the modeling assumptions of these filters and, thereby, also shows the potential utility of various approximation methods that are well established techniques in applied mathematics and physics, but are new to tracking. These unexplored possibilities are reviewed in the final chapter of the book. .
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Introduction -- Extended object tracking -- Multiple sensors -- Other high computational complexity tracking problems -- Multiframe assignment and combinatorial optimization -- Saddle Point Method -- Multicomplex Algebra -- Automatic Differentiation -- Conclusion.

The book shows that the analytic combinatorics (AC) method encodes the combinatorial problems of multiple object tracking—without information loss—into the derivatives of a generating function (GF). The book lays out an easy-to-follow path from theory to practice and includes salient AC application examples. Since GFs are not widely utilized amongst the tracking community, the book takes the reader from the basics of the subject to applications of theory starting from the simplest problem of single object tracking, and advancing chapter by chapter to more challenging multi-object tracking problems. Many established tracking filters (e.g., Bayes-Markov, PDA, JPDA, IPDA, JIPDA, CPHD, PHD, multi-Bernoulli, MBM, LMBM, and MHT) are derived in this manner with simplicity, economy, and considerable clarity. The AC method gives significant and fresh insights into the modeling assumptions of these filters and, thereby, also shows the potential utility of various approximation methods that are well established techniques in applied mathematics and physics, but are new to tracking. These unexplored possibilities are reviewed in the final chapter of the book. .

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