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Design of quadratic estimators using covariance information in linear discrete‐time stochastic systems

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  • Seiichi Nakamori
  • Aurora Hermoso‐Carazo
  • Josefa Linares‐Pérez

Abstract

. This article describes a polynomial estimation technique based on the state‐space model and develops an estimation method for the quadratic estimation problem by applying the multivariate recursive least squares (RLS) Wiener estimator to the quadratic estimation of a stochastic signal in linear discrete‐time stochastic systems. The augmented signal vector includes the signal to be estimated and its quadratic quantity. The augmented signal vector is modelled in terms of an autoregressive model of appropriate order. A numerical simulation example for the speech signal as a practical stochastic signal is implemented and its estimation accuracy is found to be considerably improved in comparison with the existing RLS Wiener estimators. The proposed method may be applied advantageously to the quadratic estimations of wide‐sense stationary stochastic signals in general.

Suggested Citation

  • Seiichi Nakamori & Aurora Hermoso‐Carazo & Josefa Linares‐Pérez, 2008. "Design of quadratic estimators using covariance information in linear discrete‐time stochastic systems," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(3), pages 501-512, May.
    • Handle: RePEc:bla:jtsera:v:29:y:2008:i:3:p:501-512
    DOI: 10.1111/j.1467-9892.2007.00566.x
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