Observation noise-gain detection for Markov chains observed through scaled Brownian motion

W. P. Malcolm; Alain Bensoussan

doi:10.1109/CDC.2008.4739239

Observation noise-gain detection for Markov chains observed through scaled Brownian motion

W. P. Malcolm, Alain Bensoussan

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this preliminary article we consider the problem of estimating an unknown noise-gain for a Markov chain observed through a scaled Brownian motion. It is assumed that the unknown noise-gain is time invariant. Two objectives are addressed in this work, 1) compute an estimation scheme that is fast, and 2) compute an estimation scheme without recourse to stochastic integration. To address the first objective we avoid the Expectation Maximization (EM) algorithm, instead we develop an estimation scheme for a finite number of candidate model hypotheses. To address the second objective we develop a version of the Gauge-Transformation technique introduced by J. M. C. Clark.

Original language	English
Title of host publication	Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3227-3232
Number of pages	6
ISBN (Print)	9781424431243
DOIs	https://doi.org/10.1109/CDC.2008.4739239
Publication status	Published - 2008
Event	47th IEEE Conference on Decision and Control, CDC 2008 - Cancun, Mexico Duration: 9 Dec 2008 → 11 Dec 2008

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	47th IEEE Conference on Decision and Control, CDC 2008
Country/Territory	Mexico
City	Cancun
Period	9/12/08 → 11/12/08

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10.1109/CDC.2008.4739239

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Malcolm, W. P., & Bensoussan, A. (2008). Observation noise-gain detection for Markov chains observed through scaled Brownian motion. In Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008 (pp. 3227-3232). Article 4739239 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2008.4739239

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title = "Observation noise-gain detection for Markov chains observed through scaled Brownian motion",

abstract = "In this preliminary article we consider the problem of estimating an unknown noise-gain for a Markov chain observed through a scaled Brownian motion. It is assumed that the unknown noise-gain is time invariant. Two objectives are addressed in this work, 1) compute an estimation scheme that is fast, and 2) compute an estimation scheme without recourse to stochastic integration. To address the first objective we avoid the Expectation Maximization (EM) algorithm, instead we develop an estimation scheme for a finite number of candidate model hypotheses. To address the second objective we develop a version of the Gauge-Transformation technique introduced by J. M. C. Clark.",

keywords = "Detection, Filtering, Martingales, Reference probability, Wonham filter",

author = "Malcolm, {W. P.} and Alain Bensoussan",

year = "2008",

doi = "10.1109/CDC.2008.4739239",

language = "English",

isbn = "9781424431243",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "3227--3232",

booktitle = "Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008",

address = "United States",

note = "47th IEEE Conference on Decision and Control, CDC 2008 ; Conference date: 09-12-2008 Through 11-12-2008",

}

Malcolm, WP & Bensoussan, A 2008, Observation noise-gain detection for Markov chains observed through scaled Brownian motion. in Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008., 4739239, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 3227-3232, 47th IEEE Conference on Decision and Control, CDC 2008, Cancun, Mexico, 9/12/08. https://doi.org/10.1109/CDC.2008.4739239

Observation noise-gain detection for Markov chains observed through scaled Brownian motion. / Malcolm, W. P.; Bensoussan, Alain.
Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008. Institute of Electrical and Electronics Engineers Inc., 2008. p. 3227-3232 4739239 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Observation noise-gain detection for Markov chains observed through scaled Brownian motion

AU - Malcolm, W. P.

AU - Bensoussan, Alain

PY - 2008

Y1 - 2008

N2 - In this preliminary article we consider the problem of estimating an unknown noise-gain for a Markov chain observed through a scaled Brownian motion. It is assumed that the unknown noise-gain is time invariant. Two objectives are addressed in this work, 1) compute an estimation scheme that is fast, and 2) compute an estimation scheme without recourse to stochastic integration. To address the first objective we avoid the Expectation Maximization (EM) algorithm, instead we develop an estimation scheme for a finite number of candidate model hypotheses. To address the second objective we develop a version of the Gauge-Transformation technique introduced by J. M. C. Clark.

AB - In this preliminary article we consider the problem of estimating an unknown noise-gain for a Markov chain observed through a scaled Brownian motion. It is assumed that the unknown noise-gain is time invariant. Two objectives are addressed in this work, 1) compute an estimation scheme that is fast, and 2) compute an estimation scheme without recourse to stochastic integration. To address the first objective we avoid the Expectation Maximization (EM) algorithm, instead we develop an estimation scheme for a finite number of candidate model hypotheses. To address the second objective we develop a version of the Gauge-Transformation technique introduced by J. M. C. Clark.

KW - Detection

KW - Filtering

KW - Martingales

KW - Reference probability

KW - Wonham filter

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U2 - 10.1109/CDC.2008.4739239

DO - 10.1109/CDC.2008.4739239

M3 - Conference contribution

SN - 9781424431243

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 3227

EP - 3232

BT - Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 47th IEEE Conference on Decision and Control, CDC 2008

Y2 - 9 December 2008 through 11 December 2008

ER -

Malcolm WP, Bensoussan A. Observation noise-gain detection for Markov chains observed through scaled Brownian motion. In Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008. Institute of Electrical and Electronics Engineers Inc. 2008. p. 3227-3232. 4739239. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2008.4739239

Observation noise-gain detection for Markov chains observed through scaled Brownian motion

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