The Asymptotic Normality Of The Estimation Of The Impulse Transfer Function For Two-dimensional Linear Systems

In some fields, such as automatic control, radio technology, mechanical vibrations, we frequently meet the stochastic process which is relates with "system " , moreover the estimation and the recognition linear system characteristic also is the main research topics which extensively applied in the radio physics, the underwater sound survey study, the seismography, the biology, the medicine and so on. The theory of probability has the widespread application in the aspect of the fundamental research of the linear system. This paper mainly utilizes the methods of the stochastic process of the spectrum analysis to estimate the impulse transfer function of the two-dimensional linear system, and discuss the property of the estimation of impulse transfer function of the two-dimensional linear system.This paper divides into four chapters:In first chapter, we summarize the research background, present development situation and we give the basic concept and known conclusions which we need to quote, at last we give the estimation of the impulse transfer function H_kj^Δ,N.In second chapter,we introduce the stochastic process Z_kj^Δ,N which is closely related with the estimation of the impulse transfer function,and give the property and correlation function of the stochastic process Z_kj^Δ,N.In third chapter,we research the asymptotic normality of finite-dimensional distributions of the process Z_kj^Δ,N , prove the estimation H_kj^Δ,N is asymptotic unbiased estimation, also we discuss the asymptotic normality of finite-dimensional distributions of the estimation error W_kj^Δ,N , and give the condition which make the asymptotic normality hold.In four chapter, we discuss the asymptotic normality of the process Z_kj^Δ,N, W_kj^Δ,N in the space of continuous functions, also give the conditions which make the asymptotic normality hold.