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For the time being, the notion of ‘intelligent measurements’ is still rather vague (and, according to these authors, often misused). It is clear, however, that the implicit or explicit use of models in such measurements is quite pronounced. For that reason it is appropriate, perhaps even necessary, to explore the relations with system identification (ie, model building + parameter estimation). That is the subject of this paper. Also discussed are the actual and potential contributions of identification, the availability of appropriate software, and the desirabilities with respect to further contributions to intelligent measurements.

Using cross-validation ideas, two procedures are proposed for making a choice between different model structures used for (approximate) modelling of multivariable systems. The procedures are derived under fairly general conditions: the ‘true’ system does not need to be contained in the model set; model structures do not need to be nested and different criteria may be used for model estimation and validation. The proposed structure selection rules are invariant to parameter scaling. Under certain conditions (essentially requiring that the system belongs to the model set and that the maximum likelihood method is used for parameter estimation) they are shown to be asymptotically equivalent to the (generalized) Akaike structure selection criteria

An account is given of useful and effective applications of information theory in identification and some new problems are indicated, which can be solved within an information-theoretic framework. In the first part of the paper a brief survey is presented of information measures and their mutual relations. Restriction has been made to probabilistic information measures. Non-probabilistic measures did not find any application in identification so far. The second part of the paper deals with the practical applications of information theory in identification. Special attention is paid to problems, the solution of which in the information-theoretic framework seems to be the most effective or perhaps even the only possible one*).

It is well known that the (naive) least squares approach to the estimation problem in functional relationships leads to inconsistent results if the information matrix is not known exactly. In this paper an estimation method, denoted by “Least-Squares-Like”, is developed. This method can be used if two sets of observations of the explaining variables, both containing disturbances, are available. Its statistical properties are derived. The method is discussed from the point of view of system parameter estimation using input and output measurements contaminated by noise. The properties of this estimator are compared to those of the maximum likelihood one. The instrumental variable method can be considered as a special case of this least-squares-like approach.

Using cross-validation ideas, two procedures are proposed for making a choice between different model structures used for (approximate) modelling of multivariable systems. The procedures are derived under fairly general conditions: the ‘true’ system does not need to be contained in the model set; model structures do not need to be nested and different criteria may be used for model estimation and validation. The proposed structure selection rules are shown to be invariant to parameter scaling. Under certain conditions (essentially requiring that the system belongs to the model set and that the maximum likelihood method is used for parameter estimation) they are shown to be asymptotically equivalent to the (generalized) Akaike structure selection criteria.

In this paper the problem of input signal design for system identification is considered. The input signal is amplitude-constrained and the case of a finite-length Input sequence Is Investigated. Various optiraality criteria are used to derive the optimal identifying input sequence. In particular: Rissanen's Minimum Description length (MHL) criterion, the determinant of the information matrix, the information matrix determinant ratio, and the trace of the parameter error covariance matrix are considered as the criteria for optimality of identification. These input design criteria can also be used in structure selection (multivariate systems) or in model order (univariate systems) estimation procedures. The emphasis is pur on autoregressive models, and the input signal sequences are derived using a dynamic programming approach. A comparative study based on analytical results as well as on simulations is presented.

Based on the notions of template functions a multitude of system parameter estimation methods is presented as a coherent picture. This leads to increased insight and to new, practical estimation schemes, adaptable for a wide variety of situations. The goal of parameter estimation is the derivation of quantitative knowledge on unknown characteristics of dynamical systems. Consequently it is of basic interest to determine whether, fundamentally, the particular situation at hand offers enough information, i.e. whether the best estimation algorithm available could indeed provide the knowledge required. The this question is about the efficiency of the various estimation algorithms, i.e. the part of the potentially available information that becomes artually present. In this paper partial answers to these questions are given. This holds for recursive estimation as well as for “one shot” estimation in cases of lin-earity in the parameters.

In this paper the problem of input signal design for parameter and order estimation in linear dynamical systems is considered. The input signal is assumed to be amplitude constrained. The accuracy criterion of the parameter estimates is given by the determinant ratio of the approximated covariance matrix. A model order test is proposed using the instrumental variable approach. The influence of input signal design on the discrimination power of the order test is discussed.

The paper presents a coherent picture of the parameter-estimation problem. Starting from the theory of minimum risk- or Bayes estimation the paper shows how other statistical estimation techniques can be interpreted as special cases (viz. maximum likelihood-, Markov-, and least squares estimation), The most important properties of these estimates are summarized. The engineering approaches based on these statistical techniques can be divided into two classes, viz. ''using explicit mathematical relations'' and ''using adjustment of a model''. Each of these classes is discussed briefly. The majority of parameter estimation techniques can be embodied in this framework. A very brief discussion is given on the problem of process state estimation which is related to parameter estimation. A few examples are used to illustrate the notions presented and to indicate some engineering considerations.

The purpose of this paper is to give a coherent picture of the process-parameter estimation. It offers a philosophy by introducing a "generalized model." From this, two classes of schemes can be derived. In each class there is quite some freedom with respect to the choice of elements of the scheme, the choice of the error criterion, and the choice of signal representation (continuous, sampled, quantized, etc.). These choices account for a whole range of estimating systems. The dynamic properties of many of these systems can be studied by the approach presented in this paper. The extension to estimation of nonlinear processes is also discussed.

A wide variety of parameter estimation techniques can be discussed from the point of view of functional operators working on system input/output signals. The classes of operators can be characterised by time functions, called `template functions?. These notions contribute to a coherent picture of a wide class of estimation techniques, as well as to a discussion of the statistical properties and, in appropriate cases, the information efficiency.