### Abstract

A non-linear operator approach to estimation in discrete-time multivariable systems is described. It involves inferential estimation of a signal which enters a communication channel that contains non-linearities and transport delays. The measurements are assumed to be corrupted by a coloured noise signal correlated with the signal to be estimated. The solution of the non-linear estimation problem is obtained using nonlinear operators. The signal and noise channels may be grossly non-linear and are represented in a very general non-linear operator form. The resulting so-called Wiener non-linear minimum variance estimation algorithm is relatively simple to implement. The optimal non-linear estimator is derived in terms of the nonlinear operators and can be implemented as a recursive algorithm using a discrete-time non-linear difference

equation. In the limiting case of a linear system, the estimator has the form of a Wiener filter in discrete-time polynomial matrix system form. A non-linear channel equalisation problem is considered for the design example.

equation. In the limiting case of a linear system, the estimator has the form of a Wiener filter in discrete-time polynomial matrix system form. A non-linear channel equalisation problem is considered for the design example.

Original language | English |
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Pages (from-to) | 618-629 |

Number of pages | 12 |

Journal | IET Signal Processing |

Volume | 4 |

Issue number | 6 |

DOIs | |

Publication status | Published - Dec 2010 |

### Keywords

- channel estimation
- equalisers
- polynomial matrices
- stochastic processes

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## Cite this

Grimble, M. J., & Ali Naz, S. (2010). Optimal minimum variance estimation for nonlinear discrete-time multichannel systems.

*IET Signal Processing*,*4*(6), 618-629. https://doi.org/10.1049/iet-spr.2009.0001