Вибiркова неперервнiсть з iмовiрнiстюодиниця для оцiнки iмпульсноїперехiдної функцiї

I V Rozora

doi:10.17721/1812-5409.2020/3.10

Abstract

The problem of estimation of a stochastic linear system has been a matter of active research for the last years. One of the simplest models considers a ‘black box’ with some input and a certain output. The input may be single or multiple and there is the same choice for the output. This generates a great amount of models that can be considered. The sphere of applications of these models is very extensive, ranging from signal processing and automatic control to econometrics (errors-in-variables models). In this paper a time-invariant continuous linear system is considered with a real-valued impulse response function. We assume that impulse function is square-integrable. Input signal is supposed to be Gaussian stationary stochastic process with known spectral density. A sample input–output crosscorrelogram is taken as an estimator of the response function. The conditions on sample continuousness with probability one for impulse response function are investigated.

Highlights

The problem of estimation of a stochastic linear system has been a matter of active research for the last years
The input may be single or multiple and there is the same choice for the output
In this paper a time-invariant continuous linear system is considered with a real-valued impulse response function

Summary

Introduction

Sample continuity with probability one for the estimator of impulse response function В роботах [1], [2] розглядаються послiдовностi коварiацiйних функцiй, якi залежать вiд параметру ∆, i знаходяться умови, коли оцiнка HT,∆(τ ) є асимптотично незмiщеною для H(τ ) при ∆ → ∞. Що умови попередньої леми виконуються для функцiї ψ(u) = K · uα, u 0, α ∈ Нехай функцiя ψ(u), u 0, задовольняє всi умови леми 2 та збiгається iнтеграл

Results

Conclusion