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Distributed and Recursive Parameter Estimation

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Sensor Networks

Part of the book series: Signals and Communication Technology ((SCT))

Abstract

Parametric estimation is a canonical problem in sensor networks. The intrinsic nature of sensor networks requires regression algorithms based on sensor data to be distributed and recursive. Such algorithms are studied in this chapter for the problem of (conditional) least squares regression when the data collected across sensors is homogeneous, i.e., each sensor observes samples of the dependent and independent variable in the regression problem. The chapter is divided into three parts. In the first part, distributed and recursive estimation algorithms are developed for the nonlinear regression problem. In the second part, a distributed and recursive algorithm is designed to estimate the unknown parameter in a parametrized state-space random process. In the third part, the problem of identifying the source of a diffusion field is discussed as a representative application for the algorithms developed in the first two parts.

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Notes

  1. 1.

    When Z k = R k–1 , the model set is auto-regressive.

  2. 2.

    Not knowing anything about the joint statistics of the sensor measurements, should not be confused with knowing that they are independent.

  3. 3.

    When the function in (1) has multiple minima, then each minimum is a CLSE estimate. For example, this would be the case if less than three sensors were used in the acoustic source localization. In most cases, by increasing the number of sensors, and thus the spatial diversity of the measurements, it is possible to ensure that the estimation problem is well defined and there is a unique least squares estimate. Such an assumption would be analogous the observability condition of [10].

  4. 4.

    We make the zero mean assumption to keep the presentation simple. The algorithm can be extended to the case when they are not zero mean.

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This work was supported in part by a Vodafone Fellowship, Motorola, and the National Science Foundation, under CAREER grant CMMI 07-42538.

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Authors and Affiliations

  1. Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Srinivasan Sundhar Ram & Venugopal V. Veeravalli

  2. Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Angelina Nedić

Authors
  1. Srinivasan Sundhar Ram
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  2. Venugopal V. Veeravalli
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  3. Angelina Nedić
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Correspondence to Srinivasan Sundhar Ram .

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Editors and Affiliations

  1. Dipto. Ingegneria dell'Informazione, Università Parma, Parco Area delle Scienze 181A, Parma, 43100, Italy

    Gianluigi Ferrari

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Ram, S.S., Veeravalli, V.V., Nedić, A. (2010). Distributed and Recursive Parameter Estimation. In: Ferrari, G. (eds) Sensor Networks. Signals and Communication Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01341-6_2

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  • DOI: https://doi.org/10.1007/978-3-642-01341-6_2

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