Compressive System Identification

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

The first part of this chapter presents a novel Kalman filtering-based method for estimating the coefficients of sparse, or more broadly, compressible autoregressive models using fewer observations than normally required. By virtue of its (unscented) Kalman filter mechanism, the derived method essentially addresses the main difficulties attributed to the underlying estimation problem. In particular, it facilitates sequential processing of observations and is shown to attain a good recovery performance, particularly under substantial deviations from ideal conditions, those which are assumed to hold true by the theory of compressive sensing. In the remaining part of this chapter we derive a few information-theoretic bounds pertaining to the problem at hand. The obtained bounds establish the relation between the complexity of the autoregressive process and the attainable estimation accuracy through the use of a novel measure of complexity. This measure is suggested herein as a substitute to the generally incomputable restricted isometric property.
Original languageEnglish
Title of host publicationCompressed Sensing & Sparse Filtering
EditorsA. Carmi, S.J. Godsill, L. Mihaylova
PublisherSpringer Heidelberg
Pages281-324
Number of pages44
ISBN (Print)978-3-642-38397-7
DOIs
StatePublished - 2014

Keywords

  • Compressed Sensing (CS)
  • Good Recovery Performance
  • Kalman Filter-based Method
  • Entropy Estimation Error
  • Sigma Points

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