ANALYSIS AND DATA PROCESSING SYSTEMS

Abstract
Procedures for active parametric identification are a combination of traditional methods of parametric estimation and experiment design methods. Given a certain structure of the mathematical model active parametric identification involves the following stages: the calculation of the unknown parameter estimates based on measurement data corresponding to an experiment plan based on the estimates of an optimal experiment and conversion of parameter estimates based on measurement data corresponding to an optimal plan. The application of ideas and methods of the modern theory of experiment design in the construction of mathematical models of stochastic dynamical systems enhances the efficiency and quality of the research conducted. The calculation of the Fisher information matrix takes a central place in the procedures of active parametric identification. The Fisher information matrix appears in the relevant optimality criteria of the plan. This work provides a theoretical analysis of the Fisher information matrix expression for Gaussian models of linear discrete and continuous-discrete systems. It is stated that with certain parameterizations of model structures the Fisher information matrix remains constant and the unknown parameters in various combinations are included in the covariance matrix of a system noise, noise measurements and the vector of initial conditions. Thus, being constant the Fisher information matrix does not depend on the input signal and the mathematical expectation of the vector of initial conditions. The authors come to a practical conclusion about parameterizations of discrete models and continuous-discrete systems in which the scheduling of input signals and initial conditions does not allow improving the quality of parametric estimation. In this case, the use of active parametric identification procedure does not provide a positive effect compared to the conventional estimation of the unknown parameters.

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