Identification Algorithms

  • Przemysław Śliwiński
Chapter
Part of the Lecture Notes in Statistics book series (LNS, volume 210)

Abstract

Four nonparametric Haarregression estimates are proposed and applied to the system nonlinearity identification (recovery). The algorithms are various implementations of the local average paradigm and produce regressogram of the nonlinearity. Three of them are based on the classic Haarseries expansion. The first is of a quotient form and resembles the Nadaraya-Watson kernel regression estimate. The second utilizes ordered measurements, while the third maps the measurements using the empirical distribution function. The last one is a version of the second algorithm but exploits the unbalanced Haar series. Two variants of each algorithm, linear and nonlinear, are introduced and studied. The former is based on a standard linear Haarapproximation. The latter employs the nonlinear (EZW-based) approximation scheme. Convergence conditions and convergence rates of all algorithms are established. The interpolation routine, based on the regressograms (and applicable when the continuous estimate is desired), is eventually derived.

Keywords

Convergence Rate Convergence Condition Empirical Coefficient Input Measurement Jump Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Przemysław Śliwiński
    • 1
  1. 1.Institute of Computer Engineering, Control and RoboticsWrocław University of TechnologyWrocławPoland

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