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 Probl. Peredachi Inf., 1974, Volume 10, Issue 1, Pages 39–59 (Mi ppi1018)

Methods of Signal Processing

Estimation of a Signal Parameter in Gaussian White Noise

I. A. Ibragimov, R. Z. Khas'minskii

Abstract: The asymptotic properties of the maximum-likelihood estimator (MLE), truncated MLE, and Bayes estimators of a one-dimensional parameter are investigated for the transmission of a continuous signal in a channel with Gaussian white noise. The conditions are determined under which the consistency and asymptotic efficiency of these estimators (i.e., in the terminology of Kotel'nikov [Theory of Potential Noise Immunity, Moscow–Leningrad, Gosenergoizdat, 1956 (in Russian)], the absence of anomaly) are guaranteed. The results obtained in this connection may be regarded as a mathematically rigorous expression of the assertion in the book cited that anomaly is absent if the noise is sufficiently small and different branches of the signal curve do not pass too close to one another. Frequency modulation is studied in closer detail. In particular, an exponentially exact bound is found for the width of the band in which a consistent estimate of the parameter is obtainable, i.e., anomaly is absent, for a given transmission time.

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English version:
Problems of Information Transmission, 1974, 10:1, 31–46

Bibliographic databases:

UDC: 621.391.1:51

Citation: I. A. Ibragimov, R. Z. Khas'minskii, “Estimation of a Signal Parameter in Gaussian White Noise”, Probl. Peredachi Inf., 10:1 (1974), 39–59; Problems Inform. Transmission, 10:1 (1974), 31–46

Citation in format AMSBIB
\Bibitem{IbrKha74} \by I.~A.~Ibragimov, R.~Z.~Khas'minskii \paper Estimation of a Signal Parameter in Gaussian White Noise \jour Probl. Peredachi Inf. \yr 1974 \vol 10 \issue 1 \pages 39--59 \mathnet{http://mi.mathnet.ru/ppi1018} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=403126} \zmath{https://zbmath.org/?q=an:0305.93047} \transl \jour Problems Inform. Transmission \yr 1974 \vol 10 \issue 1 \pages 31--46 

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• http://mi.mathnet.ru/eng/ppi/v10/i1/p39

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. M. V. Burnashev, “Asymptotic expansions for estimates of a signal parameter in Gaussian white noise”, Math. USSR-Sb., 33:2 (1977), 159–184
2. M. V. Burnashev, “Investigation of second order properties of statistical estimators in a scheme of independent observations”, Math. USSR-Izv., 18:3 (1982), 439–467
3. G. K. Golubev, V. G. Potapov, “On statistical problems in geolocation”, Problems Inform. Transmission, 49:3 (2013), 249–275
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