Consistent parameter bounding identification for linearly parametrized model sets
The paper deals with the parameter bounding identification of linear dynamical systems. In contrast to the standard bounded error identification approach, three alternative error bounds are introduced, guaranteeing consistency of the identification procedure i.e. convergence of the feasible parameter region (parameter bounds) to the true value of the system parameter if the number of measurement data grows large. These are: a bound on the cross-covariance between the noise and some specified instrumental input signal, a frequency-domain bound on the discrete Fourier transform of the noise (the square root of the periodogram) in combination with sinusoidal excitation, and a standard time-domain bound on the noise after measurement averaging in a repeated experiment. For these bounds, sufficient consistency conditions are derived. They are fairly general, even when a conservative (not tight) bound on the noise has been chosen, and require for instance persistence of excitation and the knowledge of the second-order noise statistics. A deterministic as well as a stochastic interpretation of the noise bounds are given and the corresponding empirical procedures for estimating the bounds from measured data are presented. Efficiency of the new types of noise constraints is illustrated by means of a simulation example.
scientific article; zbMATH DE number 806680
scientific article