Nonexistence of finite-dimensional filters for conditional statistics of the cubic sensor problem

M. Hazewinkel; S. I. Marcus; H. J. Sussmann

doi:10.1016/0167-6911(83)90074-9

Nonexistence of finite-dimensional filters for conditional statistics of the cubic sensor problem

M. Hazewinkel, S. I. Marcus, H. J. Sussmann

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

47 Scopus citations

Abstract

Consider the cubic sensor dx = dw, dy = x³dt + dv where w, v are two independent Brownian motions. Given a function φ(x) of the state x let φ_t(x) denote the conditional expectation given the observations y_s, 0 ≤ s ≤ t. This paper consists of a rather detailed discussion and outline of proof of the theorem that for nonconstant φ there cannot exist a recursive finite-dimensional filter for φ driven by the observations.

Original language	English (US)
Pages (from-to)	331-340
Number of pages	10
Journal	Systems and Control Letters
Volume	3
Issue number	6
DOIs	https://doi.org/10.1016/0167-6911(83)90074-9
State	Published - Dec 1983

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
General Computer Science
Mechanical Engineering
Electrical and Electronic Engineering

Keywords

Cubic sensor
Recursive filter
Robust filtering
Weyl Lie algebra

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10.1016/0167-6911(83)90074-9

Cite this

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title = "Nonexistence of finite-dimensional filters for conditional statistics of the cubic sensor problem",

abstract = "Consider the cubic sensor dx = dw, dy = x3dt + dv where w, v are two independent Brownian motions. Given a function φ(x) of the state x let φt(x) denote the conditional expectation given the observations ys, 0 ≤ s ≤ t. This paper consists of a rather detailed discussion and outline of proof of the theorem that for nonconstant φ there cannot exist a recursive finite-dimensional filter for φ driven by the observations.",

keywords = "Cubic sensor, Recursive filter, Robust filtering, Weyl Lie algebra",

author = "M. Hazewinkel and Marcus, {S. I.} and Sussmann, {H. J.}",

note = "Funding Information: * Supported in part by the National Science Foundation under Grant ECS-8022033 and in part by the Joint Services Elec-tronics program under contract F-49620-77-C-0101.",

year = "1983",

month = dec,

doi = "10.1016/0167-6911(83)90074-9",

language = "English (US)",

volume = "3",

pages = "331--340",

journal = "Systems and Control Letters",

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publisher = "Elsevier B.V.",

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T1 - Nonexistence of finite-dimensional filters for conditional statistics of the cubic sensor problem

AU - Hazewinkel, M.

AU - Marcus, S. I.

AU - Sussmann, H. J.

N1 - Funding Information: * Supported in part by the National Science Foundation under Grant ECS-8022033 and in part by the Joint Services Elec-tronics program under contract F-49620-77-C-0101.

PY - 1983/12

Y1 - 1983/12

N2 - Consider the cubic sensor dx = dw, dy = x3dt + dv where w, v are two independent Brownian motions. Given a function φ(x) of the state x let φt(x) denote the conditional expectation given the observations ys, 0 ≤ s ≤ t. This paper consists of a rather detailed discussion and outline of proof of the theorem that for nonconstant φ there cannot exist a recursive finite-dimensional filter for φ driven by the observations.

AB - Consider the cubic sensor dx = dw, dy = x3dt + dv where w, v are two independent Brownian motions. Given a function φ(x) of the state x let φt(x) denote the conditional expectation given the observations ys, 0 ≤ s ≤ t. This paper consists of a rather detailed discussion and outline of proof of the theorem that for nonconstant φ there cannot exist a recursive finite-dimensional filter for φ driven by the observations.

KW - Cubic sensor

KW - Recursive filter

KW - Robust filtering

KW - Weyl Lie algebra

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DO - 10.1016/0167-6911(83)90074-9

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AN - SCOPUS:0003655388

SN - 0167-6911

VL - 3

SP - 331

EP - 340

JO - Systems and Control Letters

JF - Systems and Control Letters

IS - 6

ER -

Nonexistence of finite-dimensional filters for conditional statistics of the cubic sensor problem

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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