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Identifying an autoregressive process disturbed by a moving-average noise using inner–outer factorization

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Abstract

This paper deals with the identification of an autoregressive (AR) process disturbed by an additive moving-average (MA) noise. Our approach operates as follows: Firstly, the AR parameters are estimated by using the overdetermined high-order Yule–Walker equations. The variance of the AR process driving process can be deduced by means of an orthogonal projection between two types of estimates of AR process correlation vectors. Then, the correlation sequence of the MA noise is estimated. Secondly, the MA parameters are obtained by using inner–outer factorization. To study the relevance of the resulting method, we compare it with existing algorithms, and we analyze the identifiability limits. The identification approach is then combined with Kalman filtering for channel estimation in mobile communication systems.

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Notes

  1. In this case, the exterior of the unit disk in the z-plane plays the role of the unit disk when using the z-transform.

  2. More particularly, the square of its 2-norm defined by: \(\parallel .\parallel _2^2=\tilde{\mathbf {a}}\tilde{\mathbf {a}}^T\) and its \(\infty \)-norm defined by \(\parallel .\parallel _{\infty }=max \lbrace (a_i-\hat{a}_i)\rbrace _{i=1 \ldots p}\).

  3. It should be noted that the channel is approximated with high-order AR model. Here, we assume a second-order AR model to approximate the channel as an example.

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Authors and Affiliations

  1. Department of Electronics and Communications Engineering, Al-Quds University, P.O. Box 20002, Jerusalem, Palestine

    Ahmed Abdou

  2. Université Bordeaux-Bordeaux-INP-ENSEIRB-MATMECA, UMR CNRS 5218 IMS - 351 cours de la Libération, 33405, Talence Cedex, France

    Flavius Turcu, Eric Grivel & Guillaume Ferré

  3. Department of Electrical, Electronic and Information Engineering, University of Bologna, Viale del Risorgimento 2, 40136, Bologna, Italy

    Roberto Diversi

Authors
  1. Ahmed Abdou
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  2. Flavius Turcu
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  3. Eric Grivel
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  4. Roberto Diversi
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  5. Guillaume Ferré
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Correspondence to Ahmed Abdou.

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Abdou, A., Turcu, F., Grivel, E. et al. Identifying an autoregressive process disturbed by a moving-average noise using inner–outer factorization. SIViP 9 (Suppl 1), 235–244 (2015). https://doi.org/10.1007/s11760-015-0803-3

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  • DOI: https://doi.org/10.1007/s11760-015-0803-3

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