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Generating Dithering Noise for Maximum Likelihood Estimation from Quantized Data
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Nira Dynamics AB, Linköping, Sweden.
2013 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, no 2, 554-560 p.Article in journal (Refereed) Published
Abstract [en]

The Quantization Theorem I (QT I) implies that the likelihood function can be reconstructed from quantized sensor observations, given that appropriate dithering noise is added before quantization. We present constructive algorithms to generate such dithering noise. The application to maximum likelihood estimation (mle) is studied in particular. In short, dithering has the same role for amplitude quantization as an anti-alias filter has for sampling, in that it enables perfect reconstruction of the dithered but unquantized signal’s likelihood function. Without dithering, the likelihood function suffers from a kind of aliasing expressed as a counterpart to Poisson’s summation formula which makes the exact mle intractable to compute. With dithering, it is demonstrated that standard mle algorithms can be re-used on a smoothed likelihood function of the original signal, and statistically efficiency is obtained. The implication of dithering to the Cramér–Rao Lower Bound (CRLB) is studied, and illustrative examples are provided.

Place, publisher, year, edition, pages
Elsevier, 2013. Vol. 49, no 2, 554-560 p.
Keyword [en]
Maximum likelihood, Estimation, Quantization
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-90218DOI: 10.1016/j.automatica.2012.11.028ISI: 000315003100028OAI: oai:DiVA.org:liu-90218DiVA: diva2:612333
Funder
Swedish Research Council
Note

Funding Agencies|Swedish Research Council through the center of excellence CADICS||project grant "Fundamental issues in sensor fusion"||

Available from: 2013-03-21 Created: 2013-03-21 Last updated: 2017-12-06Bibliographically approved

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