### Abstract

Original language | English |
---|---|

Pages (from-to) | 365-378 |

Number of pages | 14 |

Journal | IET Signal Processing |

Volume | 5 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Jul 2011 |

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### Keywords

- channel estimation
- deconvolution
- discrete time systems
- equalisers
- nonlinear estimation

### Cite this

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**Non-linear minimum variance state-space-based estimation for discrete-time multi-channel systems.** / Grimble, Michael.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Non-linear minimum variance state-space-based estimation for discrete-time multi-channel systems

AU - Grimble, Michael

PY - 2011/7/1

Y1 - 2011/7/1

N2 - A new state equation and non-linear operator-based approach to estimation is introduced for discrete-time multi-channel systems. This is a type of deconvolution or inferential estimation problem, where a signal enters a communications channel involving both non-linearities and transport delays. The measurements are corrupted by a coloured noise signal, which is correlated with the signal to be estimated both at the inputs and outputs of the channel. The communications channel may include either static or dynamic non-linearities represented in a general non-linear operator form. The optimal non-linear estimator is derived in terms of the state equations and non-linear operators that describe the system. The algorithm is relatively simple to derive and to implement in the form of a recursive algorithm. The main advantage of the approach is the simplicity of the non-linear estimator theory and the straightforward structure of the resulting solution. The results may be applied to the solution of channel equalisation problems in communications or fault detection problems in control applications.

AB - A new state equation and non-linear operator-based approach to estimation is introduced for discrete-time multi-channel systems. This is a type of deconvolution or inferential estimation problem, where a signal enters a communications channel involving both non-linearities and transport delays. The measurements are corrupted by a coloured noise signal, which is correlated with the signal to be estimated both at the inputs and outputs of the channel. The communications channel may include either static or dynamic non-linearities represented in a general non-linear operator form. The optimal non-linear estimator is derived in terms of the state equations and non-linear operators that describe the system. The algorithm is relatively simple to derive and to implement in the form of a recursive algorithm. The main advantage of the approach is the simplicity of the non-linear estimator theory and the straightforward structure of the resulting solution. The results may be applied to the solution of channel equalisation problems in communications or fault detection problems in control applications.

KW - channel estimation

KW - deconvolution

KW - discrete time systems

KW - equalisers

KW - nonlinear estimation

U2 - 10.1049/iet-spr.2009.0064

DO - 10.1049/iet-spr.2009.0064

M3 - Article

VL - 5

SP - 365

EP - 378

JO - IET Signal Processing

JF - IET Signal Processing

SN - 1751-9675

IS - 4

ER -