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Signal estimation with binary-valued sensors

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Abstract

This paper introduces several algorithms for signal estimation using binary-valued output sensing. The main idea is derived from the empirical measure approach for quantized identification, which has been shown to be convergent and asymptotically efficient when the unknown parameters are constants. Signal estimation under binary-valued observations must take into consideration of time varying variables. Typical empirical measure based algorithms are modified with exponential weighting and threshold adaptation to accommodate time-varying natures of the signals. Without any information on signal generators, the authors establish estimation algorithms, interaction between noise reduction by averaging and signal tracking, convergence rates, and asymptotic efficiency. A threshold adaptation algorithm is introduced. Its convergence and convergence rates are analyzed by using the ODE method for stochastic approximation problems.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Wayne State University, Detroit, Michigan, 48202, USA

    Leyi Wang

  2. Department of Mathematics, Wayne State University, Detroit, Michigan, 48202, USA

    Gang George Yin

  3. Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China

    Chanying Li

  4. School of Computing and Mathematics, University of Western Sydney, Western Sydney, Australia

    Weixing Zheng

Authors
  1. Leyi Wang
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  2. Gang George Yin
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  3. Chanying Li
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  4. Weixing Zheng
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Corresponding author

Correspondence to Leyi Wang.

Additional information

The research of Leyi Wang was supported in part by the National Science Foundation under ECS-0329597 and DMS-0624849, and in part by the Air Force Office of Scientific Research under FA9550-10-1-0210; the research of Gang George Yin was supported by the National Science Foundation under DMS-0907753 and DMS-0624849, and in part by the Air Force Office of Scientific Research under FA9550-10-1-0210; the research of Weixing Zheng was supported in part by a research grant from the Australian Research Council.

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Wang, L., Yin, G.G., Li, C. et al. Signal estimation with binary-valued sensors. J Syst Sci Complex 23, 622–639 (2010). https://doi.org/10.1007/s11424-010-0149-4

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  • DOI: https://doi.org/10.1007/s11424-010-0149-4

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