Continuous-Time Identification of SISO Systems using Laguerre Functions
Chou, C. T. ; Verhaegen, Michel and Johansson, Rolf LU
(1999)
In IEEE Transactions on Signal Processing
47(2).
p.349-362
- Abstract
- This paper looks at the problem of estimating the coefficients of a continuous-time transfer function given samples of its input and output data. We first prove that any nth-order continuous-time transfer function can be written as a fraction of the form /spl Sigma//sub k=0//sup n/b~/sub k/L/sub k/(s)//spl Sigma//sub k=0//sup n/a~/sub k/L/sub k/(s), where L/sub k/(s) denotes the continuous-time Laguerre basis functions. Based on this model, we derive an asymptotically consistent parameter estimation scheme that consists of the following two steps: (1) filter both the input and output data by L/sub k/(s), and (2) estimate {a~/sub k/, b~/sub k/} and relate them to the coefficients of the transfer function. For practical implementation, we... (More)
- This paper looks at the problem of estimating the coefficients of a continuous-time transfer function given samples of its input and output data. We first prove that any nth-order continuous-time transfer function can be written as a fraction of the form /spl Sigma//sub k=0//sup n/b~/sub k/L/sub k/(s)//spl Sigma//sub k=0//sup n/a~/sub k/L/sub k/(s), where L/sub k/(s) denotes the continuous-time Laguerre basis functions. Based on this model, we derive an asymptotically consistent parameter estimation scheme that consists of the following two steps: (1) filter both the input and output data by L/sub k/(s), and (2) estimate {a~/sub k/, b~/sub k/} and relate them to the coefficients of the transfer function. For practical implementation, we require the discrete-time approximation of L/sub k/(s) since only sampled data is available. We propose a scheme that is based on higher order Pade approximations, and we prove that this scheme produces discrete-time filters that are approximately orthogonal and, consequently, a well-conditioned numerical problem. Some other features of this new algorithm include the possibility to implement it as either an off-line or a quasi-on-line algorithm and the incorporation of constraints on the transfer function coefficients. A simple example is given to illustrate the properties of the proposed algorithm. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/8497051
- author
- Chou, C. T.
; Verhaegen, Michel
and Johansson, Rolf
LU
- organization
- publishing date
- 1999
- type
- Contribution to journal
- publication status
- published
- subject
- in
- IEEE Transactions on Signal Processing
- volume
- 47
- issue
- 2
- pages
- 349 - 362
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- scopus:0033079788
- ISSN
- 1053-587X
- language
- English
- LU publication?
- yes
- id
- 301c084e-788c-4e5b-b1aa-da038cd35daa (old id 8497051)
- date added to LUP
- 2016-04-04 13:14:27
- date last changed
- 2022-03-23 19:35:55
@article{301c084e-788c-4e5b-b1aa-da038cd35daa,
abstract = {{This paper looks at the problem of estimating the coefficients of a continuous-time transfer function given samples of its input and output data. We first prove that any nth-order continuous-time transfer function can be written as a fraction of the form /spl Sigma//sub k=0//sup n/b~/sub k/L/sub k/(s)//spl Sigma//sub k=0//sup n/a~/sub k/L/sub k/(s), where L/sub k/(s) denotes the continuous-time Laguerre basis functions. Based on this model, we derive an asymptotically consistent parameter estimation scheme that consists of the following two steps: (1) filter both the input and output data by L/sub k/(s), and (2) estimate {a~/sub k/, b~/sub k/} and relate them to the coefficients of the transfer function. For practical implementation, we require the discrete-time approximation of L/sub k/(s) since only sampled data is available. We propose a scheme that is based on higher order Pade approximations, and we prove that this scheme produces discrete-time filters that are approximately orthogonal and, consequently, a well-conditioned numerical problem. Some other features of this new algorithm include the possibility to implement it as either an off-line or a quasi-on-line algorithm and the incorporation of constraints on the transfer function coefficients. A simple example is given to illustrate the properties of the proposed algorithm.}},
author = {{Chou, C. T. and Verhaegen, Michel and Johansson, Rolf}},
issn = {{1053-587X}},
language = {{eng}},
number = {{2}},
pages = {{349--362}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
series = {{IEEE Transactions on Signal Processing}},
title = {{Continuous-Time Identification of SISO Systems using Laguerre Functions}},
url = {{https://lup.lub.lu.se/search/files/6076391/8498158.pdf}},
volume = {{47}},
year = {{1999}},
}