New Recursive Parameter Estimation Algorithms in Impulsive Noise Environment with Application to Frequency Estimation and System Identification

This dissertation, "New Recursive Parameter Estimation Algorithms in Impulsive Noise Environment With Application to Frequency Estimation and System Identification" by Wing-yi, Lau, 劉穎兒, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of the Thesis Entitled New Recursive Parameter Estimation Algorithms in Impulsive Noise Environment with Application to Frequency Estimation and System Identification submitted by Wing-Yi LAU for the degree of Master of Philosophy at The University of Hong Kong in August 2006 Least-squares (LS) parameter estimation algorithms are very useful in applications such as frequency estimation and system identification. In order to support online applications with a much lower arithmetic complexity, new QR-decomposition-(QRD)-based recursive algorithms for estimating the frequency components of multiple sinusoids based on the linear prediction (LP) approach and identifying the system under colored noise are proposed in this study. Furthermore, since the LS-based algorithms are sensitive to impulsive noise, new QRD- based recursive algorithms with M-estimation are introduced so that the robustness of the proposed algorithms can be improved and the impulsive noise can be de-emphasized and removed effectively. Simulation results show that the proposed algorithms give better performance with lower arithmetic complexity than the conventional LS algorithms. Besides parameter estimation, this thesis presents a new Kalman filter-based power spectral density (PSD) estimation algorithm for nonstationary pressure signals. The pressure signals are modeled as an autoregressive (AR) process and a stochastically perturbed difference equation constraint model is used to describe the dynamics of the AR coefficients. The proposed algorithm uses variable numbers of measurements to estimate the coefficients instead of fixed number of measurements in the conventional Kalman filter. In addition, the number of the measurements of the proposed algorithm is adaptively chosen by the intersection of confidence intervals (ICI) rule. Simulation results show that the proposed algorithm achieves a better time-frequency resolution and better tracking performance than the conventional Kalman filter-based algorithm which only updates the fixed number of measurements for each estimation. The above algorithms are proposed for linear models. For nonlinear models, this thesis proposes a new recursive parameter estimation algorithm for the nonlinear adaptive function coefficients autoregressive (AFAR) models. The AFAR model is a generalization of the familiar linear AR model and it is suitable for modeling nonlinear correlation of a time series governed by unknown nonlinearities. The nonlinearities are estimated using local polynomial regression (LPR), which gives a better bias-variance tradeoff than traditional polynomial approximations. Experimental results show that the model parameters can be estimated accurately using the proposed method. Moreover, using the close relationship between a simplified AFAR model and the nonlinear Wiener system, a new recursive algorithm for identifying the nonlinear Wiener system is proposed. Another new recursive algorithm for identifying the nonlinear Wiener-Hammerstein system (WHS) model is also proposed using the relationship between the AFAR model and the WHS model. DOI: 10.5353/th_b3759586 Subjects: Signal processing - Statistical methods Parameter estimation Algorithms