Variable learning rate EASI-based adaptive blind source separation in situation of nonstationary source and linear time-varying systems

In the case of multiple nonstationary independent source signals and linear instantaneous time-varying mixing systems, it is difficult to adaptively separate the multiple source signals. Therefore, the adaptive blind source separation (BSS) problem is firstly formally expressed and compared with tradition BSS problem. Then, we propose an adaptive blind identification and separation method based on the variable learning rate equivariant adaptive source separation via independence (EASI) algorithm. Furthermore, we analyze the scope and conditions of variable-learning rate EASI algorithm. The adaptive BSS simulation results also show that the variable learning rate EASI algorithm provides better separation effect than the fixed learning rate EASI and recursive least-squares algorithms

Variable step-size sign natural gradient algorithm for sequential blind source separation

A novel variable step-size sign natural gradient algorithm (VS-S-NGA) for online blind separation of independent sources is presented. A sign operator for the adaptation of the separation model is obtained from the derivation of a generalized dynamic separation model. A variable step size is also derived to better match the dynamics of the input signals and unmixing matrix. The proposed sign algorithm is appealing in practice due to its computational simplicity. Experimental results verify the superior convergence performance over conventional NGA in both stationary and nonstationary environments

Sequential blind source separation based exclusively on second-order statistics developed for a class of periodic signals

A sequential algorithm for the blind separation of a class of periodic source signals is introduced in this paper. The algorithm is based only on second-order statistical information and exploits the assumption that the source signals have distinct periods. Separation is performed by sequentially converging to a solution which in effect diagonalizes the output covariance matrix constructed at a lag corresponding to the fundamental period of the source we select, the one with the smallest period. Simulation results for synthetic signals and real electrocardiogram recordings show that the proposed algorithm has the ability to restore statistical independence, and its performance is comparable to that of the equivariant adaptive source separation (EASI) algorithm, a benchmark high-order statistics-based sequential algorithm with similar computational complexity. The proposed algorithm is also shown to mitigate the limitation that the EASI algorithm can separate at most one Gaussian distributed source. Furthermore, the steady-state performance of the proposed algorithm is compared with that of EASI and the block-based second-order blind identification (SOBI) method

A novel adaptive algorithm for the blind separation of periodic sources

An adaptive algorithm for the blind separation of periodic sources is proposed in this paper. The method uses only the second order statistics of the data, and exploits the periodic nature of the source signals. Simulation results show that the proposed approach has the ability to restore statistical independence, and its performance is comparable to that of a well established, higher order, blind source separation method

Stationary subspace analysis based on second-order statistics

In stationary subspace analysis (SSA) one assumes that the observable p-variate time series is a linear mixture of a k-variate nonstationary time series and a (p-k)-variate stationary time series. The aim is then to estimate the unmixing matrix which transforms the observed multivariate time series onto stationary and nonstationary components. In the classical approach multivariate data are projected onto stationary and nonstationary subspaces by minimizing a Kullback-Leibler divergence between Gaussian distributions, and the method only detects nonstationarities in the first two moments. In this paper we consider SSA in a more general multivariate time series setting and propose SSA methods which are able to detect nonstationarities in mean, variance and autocorrelation, or in all of them. Simulation studies illustrate the performances of proposed methods, and it is shown that especially the method that detects all three types of nonstationarities performs well in various time series settings. The paper is concluded with an illustrative example

On-line blind separation of non-stationary signals

This paper addresses the problem of blind separation of non-stationary signals. We introduce an on-line separating algorithm for estimation of independent source signals using the assumption of non-stationary of sources. As a separating model, we apply a self-organizing neural network with lateral connections, and define a contrast function based on correlation of the network outputs. A separating algorithm for adaptation of the network weights is derived using the state-space model of the network dynamics, and the extended Kalman filter. Simulation results obtained in blind separation of artificial and real-world signals from their artificial mixtures have shown that separating algorithm based on the extended Kalman filter outperforms stochastic gradient based algorithm both in convergence speed and estimation accuracy