Book chapter
Open problems in sequential parametric estimation
Open Problems in Mathematical Systems and Control Theory, pp.19-22
Communications and Control Engineering, Springer London
1998
DOI: 10.1007/978-1-4471-0807-8_5
Abstract
In this paper, we consider a single input-single output discrete-time system \documentclass[12pt]{minimal}
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\begin{document}$${{y}_{i}} = \phi _{i}^{T}\theta + {{e}_{i}},\;{\text{ }}{\mkern 1mu} i = {\mkern 1mu} 1,2,...,n$$\end{document} where yi ∈ R is the system output, ϕi ∈ Rm the measurable regressor, θ ∈ Rm the unknown parameter vector to be identified and ei ∈ R the output noise. This system can be re-written more compactly as (5.1)\documentclass[12pt]{minimal}
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\begin{document}$$
y = \Phi \theta + e
$$\end{document} were \documentclass[12pt]{minimal}
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\begin{document}$$
y = \left( {\begin{array}{*{20}{c}}
{{y_1}} \\
{{y_2}} \\
\vdots \\
{{y_n}}
\end{array}} \right),\;\Phi = \left( {\begin{array}{*{20}{c}}
{\phi _1^T} \\
{\phi _2^T} \\
\vdots \\
{\phi _n^T}
\end{array}} \right)\;and\;e = \left( {\begin{array}{*{20}{c}}
{{e_1}} \\
{{e_2}} \\
\vdots \\
{{e_n}}
\end{array}} \right).
$$\end{document}
Details
- Title: Subtitle
- Open problems in sequential parametric estimation
- Creators
- Er-Wei BaiRoberto Tempo - Polytechnic University of TurinYinyu Ye - University of Iowa
- Resource Type
- Book chapter
- Publication Details
- Open Problems in Mathematical Systems and Control Theory, pp.19-22
- Publisher
- Springer London; London
- Series
- Communications and Control Engineering
- DOI
- 10.1007/978-1-4471-0807-8_5
- ISSN
- 0178-5354
- Language
- English
- Date published
- 1998
- Academic Unit
- Electrical and Computer Engineering
- Record Identifier
- 9984573819202771
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