Research On Blind Source Separation Algorithms Of Chaotic Signals And Their Applications

The blind source separation (BSS) issues descend from a cocktail party problem, whilethe corresponding theoretical framework established has been widely applied in the field ofspeech signal processing, wireless communication, and biological signal processing. For thetime being, the BSS algorithms encompass a wide range of methods in those of signal andimage processing, where their common characteristics all feature extracting the underlinedsources from the mixed observables, though any priori about the sources is unavailable. Theblind separation of chaotic signals is a special case in the BSS family. Since chaotic signalsexhibit unpredictability, their blind separation and denoising problems cannot simply solvedby the traditional BSS methods.The first chapter largely introduces the background information of BSS, whose signalmixed models includes linear mixed signals, nonlinear mixed signals, as well asover-determined and under-determined mixing matrix. This well-established area relies onthree fundamental branches, i.e., independent component analysis, sparse component analysis,and non-negative matrix factorization, while their implementations are also briefly presentedin this thesis. Also, how the BSS theory works in the biomedical sciences and wirelesscommunication is articulated using some examples.The second chapter presents the definition of chaotic signal and its specialties in BSS.Firstly, the iteration functions of discrete chaotic signals and the partial derivation equationsof continual chaotic signals are given, where the examples are all rather typical. After that,some common tools used in analyzing chaotic signals, such as phase space reconstruction,solving the Lyapunov exponent, constructing the recurrence map, etc., are shown with theircalculation steps and principles. Lastly, the probability density function of Logistic signal andthat of Lorenz signal both shows that they are sub-Gaussian signals. However, unlike theLorenz system, the Logistic signal is not sparse after unitary transformation, and because ofthis, its BSS and denoising problems cannot be solved in a least total variation perspective.Starting from observing the self-increasing characteristics of chaotic signal in a phasespace, the third chapter articulates a novel BSS method for chaotic signals. Firstly, it takesadvantage of the underlying features in the phase space to identify various chaotic sources.After that, based on the newly defined proliferation exponent (PE), this chapter derives itscorresponding steepest descent method for BSS, which features fast convergence rate withoutincorporating any prior information about the source equations. Simulation results show that the proposed algorithm also outperforms the fast independent component analysis (FastICA)method when noise contamination is considerable.The denoising problems of BSS can be separated into pre-processing andpost-processing perspectives. Pre-processing primarily refers to smooth filtering the mixedsignals before separation, while post-processing means removing noise from the individualseparated signals using human cognition, which belongs to semi-blind denoising issues.Within a semi-blind analyzing framework, the parameter estimating problem for chaoticsystems can be boiled down to a least square evaluating procedure. In the fourth chapter, itstarts with estimating the evolution parameters of chaotic maps by using a least square fittingmethod. After that, phase space reconstruction and projection operation are employed to getnoise suppression for the observed data. The simulation results indicate that the proposedalgorithm surpasses the extended Kalman filter (EKF) and the unscented Kalman filter (UKF)in denoising, as well as maintaining the characteristic quantities of chaotic maps.Chaotic signal is essentially a nonlinear and non-Gaussian signal, which involves signalquantization when used in wireless sensor networks (WSN). It makes the blind sourceseparation of chaotic signal in WSN more difficult to address. To solve the problem, the fifthchapter of this thesis proposes a new source separation algorithm based on cubature Kalmanparticle filter (CPF). First the probability density function of the observed signal is derivedand the optimal quantization is used; this can achieve the optimal quantization of signal underthe limited budget of quantization bits. After that, the algorithm uses cubature Kalman filter(CKF) to generate the important probability distribution of the particle filter (PF), integratingthe latest observation and improving the approximation to the system posterior distribution,which will improve the performance of the signal separation. Simulation results show that thealgorithm can separate mixed chaotic signal effectively, it is superior over the unscentedKalman particle filter (UPF) counterpart in accuracy and computation overhead. The runningtime is88.77%compared to the UPF counterpart.