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Cramér—Rao Type Bounds for Random Set Problems

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Random Sets

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 97))

Abstract

Two lower bounds on the error covariance matrix are described for tracking in a dense multiple target environment. The first bound uses Bayesian theory and equivalence classes of random sets. The second bound, however, does not use random sets, but rather it is based on symmetric polynomials An interesting and previously unexplored connection between random sets and symmetric polynomials at an abstract level is suggested. Apparently, the shortest path between random sets and symmetric polynomials is through a Banach space.

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Authors and Affiliations

  1. Raytheon Company, 1001 Boston Post Road, Marlborough, MA, 01752, USA

    Fred E. Daum

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  1. Fred E. Daum
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Editors and Affiliations

  1. Department of Electrical and Computer Engineering, The Johns Hopkins University, Baltimore, MD, 21218, USA

    John Goutsias

  2. Tactical Defense Systems, Lockheed Martin Corporation, Eagan, MN, 55121, USA

    Ronald P. S. Mahler

  3. Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, 88003, USA

    Hung T. Nguyen

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Daum, F.E. (1997). Cramér—Rao Type Bounds for Random Set Problems. In: Goutsias, J., Mahler, R.P.S., Nguyen, H.T. (eds) Random Sets. The IMA Volumes in Mathematics and its Applications, vol 97. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1942-2_8

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  • DOI: https://doi.org/10.1007/978-1-4612-1942-2_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7350-9

  • Online ISBN: 978-1-4612-1942-2

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