ContinuousTime Identification of SISO Systems using Laguerre Functions
(1999) In IEEE Transactions on Signal Processing 47(2). p.349362 Abstract
 This paper looks at the problem of estimating the coefficients of a continuoustime transfer function given samples of its input and output data. We first prove that any nthorder continuoustime 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 continuoustime 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 continuoustime transfer function given samples of its input and output data. We first prove that any nthorder continuoustime 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 continuoustime 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 discretetime 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 discretetime filters that are approximately orthogonal and, consequently, a wellconditioned numerical problem. Some other features of this new algorithm include the possibility to implement it as either an offline or a quasionline 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:
http://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
 IEEEInstitute of Electrical and Electronics Engineers Inc.
 external identifiers

 scopus:0033079788
 ISSN
 1053587X
 language
 English
 LU publication?
 yes
 id
 301c084e788c4e5bb1aada038cd35daa (old id 8497051)
 date added to LUP
 20151227 13:05:07
 date last changed
 20170101 08:10:39
@article{301c084e788c4e5bb1aada038cd35daa, abstract = {This paper looks at the problem of estimating the coefficients of a continuoustime transfer function given samples of its input and output data. We first prove that any nthorder continuoustime 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 continuoustime 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 discretetime 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 discretetime filters that are approximately orthogonal and, consequently, a wellconditioned numerical problem. Some other features of this new algorithm include the possibility to implement it as either an offline or a quasionline 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 = {1053587X}, language = {eng}, number = {2}, pages = {349362}, publisher = {IEEEInstitute of Electrical and Electronics Engineers Inc.}, series = {IEEE Transactions on Signal Processing}, title = {ContinuousTime Identification of SISO Systems using Laguerre Functions}, volume = {47}, year = {1999}, }