A Fundamental Limitation on Maximum Parameter Dimension for Accurate Estimation with Quantized Data

Abstract

It is revealed that there is a link between the quantization approach employed and the dimension of the vector parameter which can be accurately estimated by a quantized estimation system. A critical quantity called inestimable dimension for quantized data (IDQD) is introduced, which doesn't depend on the quantization regions and the statistical models of the observations but instead depends only on the number of sensors and on the precision of the vector quantizers employed by the system. It is shown that the IDQD describes a quantization induced fundamental limitation on the estimation capabilities of the system. To be specific, if the dimension of the desired vector parameter is larger than the IDQD of the quantized estimation system, then the Fisher information matrix for estimating the desired vector parameter is singular, and moreover, there exist infinitely many nonidentifiable vector parameter points in the vector parameter space. Furthermore, it is shown that under some common assumptions on the statistical models of the observations and the quantization system, a smaller IDQD can be obtained, which can specify an even more limiting quantization induced fundamental limitation on the estimation capabilities of the system.

Department(s)

Electrical and Computer Engineering

Comments

Early Access

Keywords and Phrases

Distributed Sensor Parameter Estimation; Inestimable Dimension for Quantized Data; Singular Fisher Information Matrix; Identifiability; Quantization

International Standard Serial Number (ISSN)

0018-9448; 1557-9654

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2018 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

27 Jun 2018

Link to Full Text

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