Research On Approximation Method Based On TM System And Learning Theory And Its Application In System Identification

System identification is to determine a model which is equivalent to the real system from the fitted model after given the measured input and output data.This paper will mainly study identification of Linear Time-Invariant(LTI)system.Since the LTI system can be regarded as a rational function model in the complex filed,the problem can be regarded to the fitting problem of the rational function model.What's more,the fitting problem of a rational function also can be transformed into a problem of finding its poles and zeros.However,this problem is often very difficult.Many scholars use TM systems to approximate rational functions.Among them,the Adaptive Fourier Decomposition(AFD)method gave a method of finding the pole which is based on the principle of maximum selection.AFD is an effective algorithm which can give an approximation of the analytic function with the linear combination of the TM systems.However,the maximum selection principle requires exhaustive units which will need a long time to run the program.Therefore,it is still worth for exploring how to effectively and quickly use TakenakaMalmquist(TM)system to approximate the rational function model.Sparse Bayesian learning has been a hot spot in machine learning research in recent years.The Complex Relevant Vector Machine(CRVM)algorithm based on the TM system can provide sparse rational approximation.This method is based on sparse Bayesian theory which can provide sparse rational approximation and iterative optimization without parameters control.This article is roughly arranged as follows: First,we introduce some related content of system identification,Hilbert transform calculation and Adaptive Fourier Decomposition.And then,we will introduce the CRVM in detail.At last,we apply the CRVM method to system identification and Hilbert transform calculation.