Counter equation: smoothing, filtration, identification
Keywords:
counter equation, double-sided orthogonalization, smoothing, filtration, identification, linear-length approximation, estimation, nonlinear optimization, optimization of the subspaces, difference equations, matrixes inversion, Riccati matrix equations, renovation equation, renovation process, homogeneous vector system.Abstract
Inverse problems of analysis, mathematical modeling, and identification of dynamical systems on base linear stationary models is studying. The analysis method is approximation of the signals and functions determined on uniform nets in limited lengths. Approximation function and theirs models category is transition processes of linear difference or differential equations with constant, possibly unknown coefficients. In last case realize theirs estimation (identification) on base using square means criterion approximation of observing processes and dated function. Showed, that all considering problems may be effective decided with help computer algorithms, based on counter equations of of double-sided orthogonalization of homogeneous vector systems, begetting approximating models.
