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Optimal Estimation of Multidimensional Data with Limited Measurements

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Sensors: Theory, Algorithms, and Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 61))

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Abstract

Recent results indicate how to optimally schedule transmissions of a measurement to a remote estimator when there are limited uses of the communication channel available. The resulting optimal encoder and estimation policies solve an important problem in networked control systems when bandwidth is limited. Previous results were obtained only for scalar processes, and the previous work was unable to address questions regarding informational relevance. We extend the state-of-the art by treating the case where the source process and measurements are multidimensional. To this end, we develop a nontrivial re-working of the underlying proofs. Specifically, we develop optimal encoder policies for Gaussian and Gauss–Markov measurement processes by utilizing a measure of the informational value of the source data. Explicit expressions for optimal hyper-ellipsoidal regions are derived and utilized in these encoder policies. Interestingly, it is shown in this chapter that analytical expressions for the hyper-ellipsoids exist only when the state’s dimension is even; in odd dimensions (as in the scalar case) the solution requires a numerical look up (e.g., use of the erf function). We have also extended the previous analyses by introducing a weighting matrix in the quadratic cumulative cost function, whose purpose is to allow the system designer to designate which states are more important or relevant to total system performance.

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Author information

Authors and Affiliations

  1. Embry-Riddle Aeronautical University, Daytona Beach, FL, 32114, USA

    William MacKunis

  2. Air Force Research Laboratory Munitions Directorate, Eglin AFB, FL, 32542, USA

    J. Willard Curtis & Pia E. K. Berg-Yuen

Authors
  1. William MacKunis
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  2. J. Willard Curtis
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  3. Pia E. K. Berg-Yuen
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Corresponding author

Correspondence to William MacKunis .

Editor information

Editors and Affiliations

  1. Department of Industrial and Systems Eng, University of Florida, Weil Hall 303, Gainesville, 32611, Florida, 32611, USA

    Vladimir L. L. Boginski

  2. Munitions Directorate, Air Force Research Laboratory, Eglin Air Force Base, West Eglin Blvd 101, Eglin AFB, 32542, Florida, 32542, USA

    Clayton W. W. Commander

  3. Dept. Industrial & Systems, Engineering, University of Florida, Weil Hall 303, Gainesville, 32611-6595, Florida, 94305, USA

    Panos M. M. Pardalos

  4. School of Engineering, Department of Management Science and Eng, Stanford University, Via Ortega 475, Stanford, 94305, California, USA

    Yinyu Ye

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MacKunis, W., Curtis, J.W., Berg-Yuen, P.E.K. (2012). Optimal Estimation of Multidimensional Data with Limited Measurements. In: Boginski, V.L., Commander, C.W., Pardalos, P.M., Ye, Y. (eds) Sensors: Theory, Algorithms, and Applications. Springer Optimization and Its Applications(), vol 61. Springer, New York, NY. https://doi.org/10.1007/978-0-387-88619-0_4

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