Substantiation of algorithms for nonparametric identification (Q1913638)

The paper is devoted to the substantiation of algorithms for nonparametric identification. Linear systems with scalar inputs and outputs are studied. The classical problem of the system's weight function (impulse response) determination is discussed. A classical estimation scheme is used as a basis of the algorithm for nonparametric identification. It is proved that the asymptotic Stirling formula for \(k!\) can be used for the ancillary estimation improving. The convergence of the identification method is rigorously proved. Two basic theorems on equiconvergence are demonstrated. The algorithms under study are particularly important in circumstances where the system may be thought of as being linear only in the set of inputs with limited amplitude and where impulse input signals are inadmissible. The paper will be of interest for the specialists and engineers, working on system identification.