# Quantization with adaptation - estimation of Gaussian linear models

Gerencsér, László and Kmecs, Ildikó and Torma, Balázs
(2008)
*Quantization with adaptation - estimation of Gaussian linear models.*
Communications in Information and Systems, 8 (3).
pp. 223-244.

## Abstract

Quantization is a basic operation in communication, having a considerable impact also on control, in particular on control over communication networks, see cite{BROCKETT-QUANT} for an early reference. In this paper we consider a classic, seemingly innocent problem of reconstructing a single signal value $theta^*$ when measured with additive Gaussian noise, followed by uniform quantization of sensitivity $h$, with or without saturation. A peculiar feature of the above estimation problem is that its Fisher information varies considerably with the noise variance and the location of the true parameter. It is therefore a meaningful objective to adjust (shift) the quantization levels so as to maximize the Fisher information or to inject additional measurement noise for the same purpose. We shall focus on the first problem. Empirical evidence shows that, for given noise variance, the Fisher information is maximal when the location parameter is of the form $theta^*= kh + h/2$. Adjusting the quantization levels is equivalent, from the statistical point of view, to adjusting, say increasing the location parameter by an amount of $delta>0$ to achieve a {it known} target, say $eta^*=kh + h/2$ for some integer $k$. The problem that we address in this paper is if such an adjustment of the problem can be done adaptively, in the context of a previously developed recursive, real-time estimation method for estimating $theta^*$, that was called a randomized $EM$-method for estimating $theta^*$. We give a positive answer to this question. The proposed method results in considerable improvement in efficiency, supported both by the algebra of the asymptotic theory of stochastic approximation, and by extensive experimental evidence. The basic ideas developed and presented for this benchmark problem can be easily generalized for the multi-variable case.

Item Type: | Article |
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Subjects: | Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány |

Depositing User: | Eszter Nagy |

Date Deposited: | 11 Dec 2012 15:31 |

Last Modified: | 11 Dec 2012 15:31 |

URI: | http://eprints.sztaki.hu/id/eprint/5523 |

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