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39
The Fundamental Role of General Orthonormal Bases in System Identification
 IEEE Transactions on Automatic Control
, 1997
"... The purpose of this paper is threefold. Firstly, it is to establish that contrary to what might be expected, the accuracy of well known and frequently used asymptotic variance results can depend on choices of fixed poles or zeros in the model structure. Secondly, it is to derive new variance express ..."
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Cited by 14 (10 self)
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The purpose of this paper is threefold. Firstly, it is to establish that contrary to what might be expected, the accuracy of well known and frequently used asymptotic variance results can depend on choices of fixed poles or zeros in the model structure. Secondly, it is to derive new variance expressions that can provide greatly improved accuracy while also making explicit the influence of any fixed poles or zeros. This is achieved by employing certain new results on generalised Fourier series and the asymptotic properties of Toeplitzlike matrices in such a way that the new variance expressions presented here encompass preexisting ones as special cases. Via this latter analysis a new perspective emerges on recent work pertaining to the use of orthonormal basis structures in system identification. Namely, that orthonormal bases are much more than an implementational option offering improved numerical properties. In fact, they are an intrinsic part of estimation since, as shown here, or...
Generalised Fourier and Toeplitz Results for Rational Orthonormal Bases
, 1997
"... This paper provides a generalisation of certain classical Fourier convergence and asymptotic Toeplitz matrix properties to the case where the underlying orthonormal basis is not the conventional trigonometric one, but a rational generalisation which encompasses the trigonometric one as a special cas ..."
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Cited by 11 (8 self)
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This paper provides a generalisation of certain classical Fourier convergence and asymptotic Toeplitz matrix properties to the case where the underlying orthonormal basis is not the conventional trigonometric one, but a rational generalisation which encompasses the trigonometric one as a special case. These generalised Fourier and Toeplitz results have particular application in dynamic system estimation theory.
Orthonormal Basis Functions for Modelling ContinuousTime Systems
, 1999
"... This paper studies continuoustime system model sets that are spanned by xed pole orthonormal bases. The nature of these bases is such as to generalise the well known Laguerre and two{parameter Kautz bases. The contribution of the paper is to establish that the obtained model sets are complete in al ..."
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Cited by 10 (2 self)
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This paper studies continuoustime system model sets that are spanned by xed pole orthonormal bases. The nature of these bases is such as to generalise the well known Laguerre and two{parameter Kautz bases. The contribution of the paper is to establish that the obtained model sets are complete in all of the Hardy spaces H p (); 1 < p < 1 and the right half plane algebra A() provided that a mild condition on the choice of basis poles is satis ed. A characterisation of how modelling accuracy is aected by pole choice, as well as an application example of exible structure modelling are also provided. Key words: Rational basis functions, orthonormal, completeness, continuoustime systems. Technical Report EE9819, Department of Electrical and Computer Engineering, University of Newcastle,AUSTRALIA 1 Notation C the eld of complex numbers.
Model Order Reduction for Strictly Passive and Causal Distributed Systems
 ACM/IEEE Design Automation Conference
, 2002
"... This paper presents a class of algorithms suitable for model reduction of distributed systems. Distributed systems are not suitable for treatment by standard modelreduction algorithms such as PRIMA, PVL, and the Arnoldi schemes because they generate matrices that are dependent on frequency (or othe ..."
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Cited by 9 (2 self)
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This paper presents a class of algorithms suitable for model reduction of distributed systems. Distributed systems are not suitable for treatment by standard modelreduction algorithms such as PRIMA, PVL, and the Arnoldi schemes because they generate matrices that are dependent on frequency (or other parameters) and cannot be put in a lumped or statespace form. Our algorithms build on wellknown projectionbased reduction techniques, and so require only matrixvector product operations and are thus suitable for operation in conjunction with electromagnetic analysis codes that use iterative solution methods and fastmultipole acceleration techniques. Under the condition that the starting systems satisfy systemtheoretic properties required of physical systems, the reduced systems can be guaranteed to be passive. For distributed systems, we argue that causality of the underlying representation is as important a consideration as passivity has become.
Variance Error Quantifications that are Exact for Finite Model Order
 IEEE Transactions on Automatic Control
, 2003
"... This paper is concerned with the frequency domain quantification of noise induced errors in dynamic system estimates. Preceding seminal work on this problem provides general expressions that are approximations whose accuracy increases with observed data length and model order. In the interests of ..."
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Cited by 9 (5 self)
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This paper is concerned with the frequency domain quantification of noise induced errors in dynamic system estimates. Preceding seminal work on this problem provides general expressions that are approximations whose accuracy increases with observed data length and model order. In the interests of improved accuracy, this paper provides new expressions whose accuracy depends only on data length.
Rational Basis Functions for Robust Identification from Frequency and Time Domain Measurements
 Automatica
, 1998
"... This paper investigates the use of general bases with fixed poles for the purposes of robust estimation. These bases, which generalise the common FIR, Laguerre and twoparameter Kautz ones, are shown to be fundamental in the disc algebra provided a very mild condition on the choice of poles is sati ..."
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Cited by 8 (5 self)
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This paper investigates the use of general bases with fixed poles for the purposes of robust estimation. These bases, which generalise the common FIR, Laguerre and twoparameter Kautz ones, are shown to be fundamental in the disc algebra provided a very mild condition on the choice of poles is satisfied. It is also shown, that by using a minmax criterion, these bases lead to robust estimators for which error bounds in different norms can be explicitly quantified. The key idea facilitating this analysis is to reparameterise the model structures into new ones with equivalent fixed poles, but for which the basis functions are orthonormal in H 2 . Key words: Identification, estimation, worstcase analysis, error analysis, robustness. Technical Report EE9718, Department of Electrical and Computer Engineering, University of Newcastle,AUSTRALIA. 1 Introduction In connection with the estimation of dynamic models on the basis of observed inputoutput measurements, many approaches have ...
NonStationary Stochastic Embedding for Transfer Function Estimation
 Automatica
, 1998
"... This paper presents a consistent framework for the quantification of noise and undermodelling errors in transfer function model estimation. We use the, socalled, "stochastic embedding" approach, in which both noise and undermodelling errors are treated as stochastic processes. In contrast to previo ..."
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Cited by 8 (1 self)
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This paper presents a consistent framework for the quantification of noise and undermodelling errors in transfer function model estimation. We use the, socalled, "stochastic embedding" approach, in which both noise and undermodelling errors are treated as stochastic processes. In contrast to previous applications of stochastic embedding, in this paper we represent the undermodeling as a multiplicative error characterised by random walk processes in the frequency domain. The benefit of the present formulation is that it significantly simplifies the estimation of the parameters of the embedded process yielding a closedform expression for the model error quantification. An example illustrates how the random walk effectively captures typical cases of undermodelling found in practice.
Orthonormal Basis Functions for ContinuousTime Systems and L_p Convergence
, 1999
"... In this paper, model sets for continuoustime linear time invariant systems that are spanned by fixed pole orthonormal bases are investigated. These bases generalise the well known Laguerre and twoparameter Kautz cases. It is shown that the obtained model sets are norm dense in the Hardy space H ..."
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Cited by 5 (4 self)
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In this paper, model sets for continuoustime linear time invariant systems that are spanned by fixed pole orthonormal bases are investigated. These bases generalise the well known Laguerre and twoparameter Kautz cases. It is shown that the obtained model sets are norm dense in the Hardy space H 1 (#) under the same condition as previously derived by the authors for the norm denseness in the (# is the open right half plane) Hardy spaces H p (#), 1 < p < #.
Integral Constraints on the Accuracy of Least Squares Estimation
 Automatica
, 1996
"... It is common to need to estimate the frequency response of a system from observed inputoutput data. In this paper we characterise, via integral constraints, the undermodelling induced errors involved in solving this problem via parametric least squares methods. Our approach is to exploit the Hilbert ..."
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Cited by 4 (1 self)
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It is common to need to estimate the frequency response of a system from observed inputoutput data. In this paper we characterise, via integral constraints, the undermodelling induced errors involved in solving this problem via parametric least squares methods. Our approach is to exploit the Hilbert Space structure inherent in the least squares solution in order to provide a geometric interpretation of the nature of frequency domain errors. This allows an intuitive process to be applied in which for a given data collection method and model structure, one identifies the sides of a right triangle, and then by noting the hypotenuse to be the longest side, integral constraints on magnitude estimation error are obtained. By also noting that the triangle sides both lie in a particular plane, integral constraints on phase estimation error are derived. This geometric approach is in contrast to earlier work in this area which has relied on algebraic manipulation. Technical Report EE9502 Departm...
Identification of Multivariable Hammerstein Systems using Rational Orthonormal Bases
"... In this paper, a non iterative algorithm for the simultaneous identification of the linear and nonlinear parts of multivariable Hammerstein systems is presented. The proposed algorithm is numerically robust, since it is based only on least squares estimation and singular value decomposition. Under w ..."
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Cited by 4 (1 self)
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In this paper, a non iterative algorithm for the simultaneous identification of the linear and nonlinear parts of multivariable Hammerstein systems is presented. The proposed algorithm is numerically robust, since it is based only on least squares estimation and singular value decomposition. Under weak assumptions on the persistency of excitation of the inputs, the algorithm provides consistent estimates even in the presence of coloured noise. Key in the derivation of the results is the use of rational orthonormal bases for the representation of the linear part of the system. An additional advantage of this is the possibility of incorporating prior information about the system in a typically blackbox identification scheme. 1 Introduction In the last decades, many research activities have been carried out on modelling, identification, and control design of nonlinear systems. Many dynamical systems can be better represented by nonlinear models, which are able to describe the global be...