Counter equations: smoothing, filtration, identification

A. O. Egorshin

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1322-1351

Résumé

Inverse problems of analysis, mathematical modeling, and identification of dynamical systems and processes are studied on the base of linear stationary models. The method of analysis is dynamical approximation of signals and functions determined on uniform grids on finite intervals. One class of approximating functions and their models is transition processes of linear difference or differential equations with constant, possibly unknown, coefficients. In the latter case, their estimation (identification) is performed on the basis of the least square method of approximation of observed processes and specified functions. We show that all the considered problems may be effectively solved using computer algorithms based on counter equations of bilateral orthogonalization of homogeneous vector systems, generated by approximating models.

Détail

Keywords: counter equations, bilateral orthogonalization, smoothing, piecewise-linear approximation, nonlinear optimization, optimization of subspaces, difference equations, renewal equation, renewal process, homogeneous vector system.
Mots-clés : filtration, identification, estimation, matrix inversion, Riccati matrix equation