(A) study on non-minimum phase system identification with additive white noise

Abstract

The identification problem of time invariant, causal, nonminimum phase ARMA(p,q) systems with known order from output measurements is considered. It is assumed that the system was driven by nongaussian white random sequence and the output measurements were contaminated with additive white noise. This problem can only be solved if higher order statistics(HOS) are used since, as it is well known, second order statistics(SOS) are phase blind, i.e., they contain only magnitude information. There are two categories in using HOS in order to extract phase information. The first one is the method to extract the system parameters from HOS directly. The other one uses the SOS in order to find the spectrally equivalent minimum phase (SEMP) system of the ARMA(p,q). And higher order statistics are used solely to resolve the locations(phases) of the zeros of the SEMP system function. The latter can estimate the system more accurately than the former. But it is sensitive to noise and there is no efficient method to determine the phase of each zero of the SEMP system. The main contributions of this dissertation are as follows : ● We propose a new method which can determine phases of all zeros of MA(q) with computational burden proportion to q but not to $2^q$ and prove the robustness of the proposed method. ● We present two techniques to remove the effect of additive white noise in estimating the SEMP system function using second order statistics. ● We analyze the global convergence of a known SEMP estimate even though the considering system is non-minimum phase system. ● We observed that the estimation error of HOS is greater than that of SOS in general. It theoretically supports that our scheme is a good approach. Thus, the proposed nonminimum phase system identification method can estimate the parameters more accurately than the ones in the first category and have robustness against additive white gaussian noise. Many experimental results approve our assertion.