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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)
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author
organization
publishing date
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
2015-12-27 13:05:07
date last changed
2016-04-16 10:57:40
@misc{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    = {ARRAY(0x8be8480)},
  series       = {IEEE Transactions on Signal Processing},
  title        = {Continuous-Time Identification of SISO Systems using Laguerre Functions},
  volume       = {47},
  year         = {1999},
}