Theory & Application Of Adaptive Blind Signal Processing

Blind signal separation (BSS) is an important topic and has many applications in practices. In this thesis, the principle and algorithm of adaptive blind source separation are discussed, and the assumption that sources are independent identical distributive (i.i.d.) is extended to more practical situations, just like temporal-correlated sources, non-stationary sources and noisy sources. A simple experiment in water tank is executed to testify some algorithms of this thesis."Blind" means that the information of sources and the mixing system is unknown, so the mission of BSS is to recover the original sources from the observed data when the mixing system is assumed Linear Time Invariant (L.T.I.) system. The object criterion is based on information theory, including Information Maximization, Minimize Mutual Information and Maximization Likelihood, all are equivalent. The nonlinear function relative to probability density function (p.d.f.) of sources affects the performance of adaptive algorithm, as stability, convergence speed, mean square error etc. Gaussian Mixture Model (GMM) is provided to approximate the p.d.f. of sources and leads to a robust adaptive algorithm. By the relationship of the instantaneous mixture model with the convolutive mixture model, some BSS algorithms can be extended to blind deconvolution, which are more practical adaptive algorithms.For temporal-correlated sources and non-stationary sources, the characteristic of sources -- different spectrum or non-stationary, is used to separate signals, so second order statistic is enough. Joint Approximate Diagonalization (JADE) method and adaptive decorrelation have better performance than other algorithms.Noise reduces the algorithm performance and prevent linear transform from getting the exact original sources. The accurate estimation for mixing parameters and source parameter can reconstruct sources in least-square meaning, which can be solved by an adaptive blind estimation algorithm based on GMM. How to deal with noise for temporal-correlated sources and non-stationary sources also is discussed.Finally, data from a simple experimental in water tank is used to analyze the above algorithms.