This paper deals with equation error methods that fit continuous-time transfer function models to discrete-time data recently included in the CONTSID (CONtinuous-Time System IDentification) Matlab toolbox. An overview of the methods is first given where implementation issues are highlighted. The performances of the methods are then evaluated on simulated examples by Monte Carlo simulations. The experiments have been carried out to study the sensitivity of each approach to the design parameters, sampling period, signal-to-noise ratio, noise power spectral density and type of input signal. The effectiveness of the CONTSID toolbox techniques is also briefly compared with indirect methods in which discrete-time models are first estimated and then transformed into continuous-time models. The paper does not consider iterative or recursive algorithms for continuous-time transfer function model identification.

Continuous-time model identification from sampled data: Implementation issues and performance evaluation

System identification is a well-established field. It is concerned with the determination of particular models for systems that are intended for a certain purpose such as control. Although dynamical systems encountered in the physical world are native to the continuous-time domain, system identification has been based largely on discrete-time models for a long time in the past, ignoring certain merits of the native continuous-time models. Continuous-time-model-based system identification techniques were initiated in the middle of the last century, but were overshadowed by the overwhelming developments in discrete-time methods for some time. This was due mainly to the ‘go completely digital’ trend that was spurred by parallel developments in digital computers. The field of identification has now matured and several of the methods are now incorporated in the continuous time system identification (CONTSID) toolbox for use with Matlab. The paper presents a perspective of these techniques in a unified framework. 

Identification of continuous-time systems

When modeling a system from discrete-time data, a continuous-time parameterization is desirable in some situations, In a direct estimation approach, the derivatives are approximated by appropriate differences. For an ARX model this lead to a linear regression. The well-known least squares method would then be very desirable since it can have good numerical properties and low computational burden, in particular for fast or nonuniform sampling. It is examined under what conditions a least squares fit for this linear regression will give adequate results for an ARX model. The choice of derivative approximation is crucial for this approach to be useful. Standard approximations like Euler backward or Euler forward cannot be used directly. The precise conditions on the derivative approximation are derived and analyzed. It is shown that if the highest order derivative is selected with care, a least squares estimate will be accurate. The theoretical analysis is complemented by some numerical examples which provide further insight into the choice of derivative approximation.

Least squares parameter estimation of continuous-time ARX models from discrete-time data

Models of dynamical systems are required for various purposes in the field of systems and control. The models are handled either in discrete time (DT) or in continuous time (CT). Physical systems give rise to models only in CT because they are based on physical laws which are invariably in CT. In system identification, indirect methods provide DT models which are then converted into CT. Methods of directly identifying CT models are preferred to the indirect methods for various reasons. The direct methods involve a primary stage of signal processing, followed by a secondary stage of parameter estimation. In the primary stage, the measured signals are processed by a general linear dynamic operation—computational or realized through prefilters, to preserve the system parameters in their native CT form—and the literature is rich on this aspect. 

In this book: Identification of Continuous-Time Systems-Linear and Robust Parameter Estimation, Allamaraju Subrahmanyam and Ganti Prasada Rao consider CT system models that are linear in their unknown parameters and propose robust methods of estimation. This book complements the existing literature on the identification of CT systems by enhancing the secondary stage through linear and robust estimation.
In this book, the authors


provide an overview of CT system identification,


consider Markov-parameter models and time-moment models as simple linear-in-parameters models for CT system identification,


bring them into mainstream model parameterization via basis functions,


present a methodology to robustify the recursive least squares algorithm for parameter estimation of linear regression models,


suggest a simple off-line error quantification scheme to show that it is possible to quantify error even in the absence of informative priors, and


indicate some directions for further research.

This modest volume is intended to be a useful addition to the literature on identifying CT systems.

Identification of Continuous-Time Systems: Linear and Robust Parameter Estimation

Part I: Deterministic Systems.- Background on Sampling of Signals.-Sampled Data Models for Linear Deterministic Systems.- Incremental Sampled Data Models.- Asymptotic Sampling Zeros.- Generalized Hold Devices.- Robustness.- Approximate Models for Linear Deterministic Systems.- Approximate Models for Deterministic Nonlinear Systems.- Applications of Approximate Sampled-data Models in Estimation and Control.- Part II: Stochastic Systems.- Background on Sampling of Stochastic Signals.- Sampled-data Models for Linear Stochastic Systems.- Incremental Stochastic Sampled-data Models.- Asymptotic Sampling Zeros for Linear Stochastic Systems.- Generalized Sampling Filters.- Approximate Sampled-data Models for Linear Stochastic Systems.- Stochastic Nonlinear Systems.- Approximate Sampled-data Models for Nonlinear Stochastic Systems.- Applications of Approximate Stochastic Sampled-data Models.- Part III: Embellishments and Extensions.- The Euler-Frobenius Polynominals.- Models for Intersample Response.- Approximate Sampled-data Models for Fractional Order Systems.

/pdf/sampled-data-models-for-linear-and-nonlinear-systems-rbckprenre.pdf

Sampled-Data Models for Linear and Nonlinear Systems

An IV-Scheme for Estimating Continuous-Time Stochastic Models from Discrete-Time Data

When modelling a time series from discrete-time data, a continuous-time parametrization is desirable in some situations. It can have good numerical properties and low computational burden, in particular for fast or nonuniform sampling. In a direct estimation approach, the derivatives are approximated by appropriate differences, leading to a linear regression model. It is shown that standard approximations like Euler backward or Euler forward cannot be used. The precise conditions on the derivative approximation are derived and analysed. It is shown that if the highest order derivative is selected with care, a least-squares estimate will be accurate. The theoretical analysis is complemented by some numerical examples.

Can a least-squares fit be feasible for modelling

Can a least-squares fit be feasible for modelling continuous-time autoregressive processes from discrete-time data?

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Least squares parameter estimation of continuous-time ARX models from discrete-time data

An IV-Scheme for Estimating Continuous-Time Stochastic Models from Discrete-Time Data

Can a least-squares fit be feasible for modelling

Can a least-squares fit be feasible for modelling continuous-time autoregressive processes from discrete-time data?