Research On Blind Signal Separation And Its Application In Passive Location

Blind signal processing (BSP) is an important research aspect in signal processing field, which has a solid theoretical foundation and many potential applications, and has been developed in many fields. In the case that the transmission channel characteristics and the true source signals are both unknown, extracting or separating the original signal from the sensor arrays can be described as blind source separation (BSS). BSS can be divided into instantaneous and convolutive according to the mixture manner. BSS of instantaneous type means the observed signals are the linear mixtures of sources. Convolutive mixture, whose observed signals are mixtured by convolving sources with the transmitting channels, is a more general model. Independent component analysis (ICA) is one of the main methods to solve the BSS problems. This thesis studies on blind signal separation technique and its application in passive location. The main results of this thesis are:1,For the second order statistics of noncircular signals, a new fast ICA algorithm is proposed. By constructing a new cost function, we can obtain a new update rule, which can get more exact result. As the characters of some complex signals are more obvious in frequency domain, it is a new idea to take Fourier transformation to mixtures of noncircular source in time domain to the frequency domain. After separating on the frequency spectra of noncircular source in frequency domain, we can apply the inverse Fourier transformation to get the original source, which can get a better separation performance than separating directly in time domain.2,Independent vector analysis (IVA), an extension of ICA from univariate components to multivariate components, is a method to tackle BSS in frequency domain. IVA utilizes both the statistical independence among multivariate signals and the statistical inner dependency of each multivariate signal. However, so far there is no research on IVA for convolutive mixtures of noncircular sources. We focus on this problem and propose noncircular independent vector analysis (nc-IVA) algorithm, by deriving a new fixed-point algorithm that uses the information of pseudo-covariance matrix in each frequency bin. This modification provides more widely application scenarios with noncircular sources. Simulations demonstrate the effectiveness of our proposed method.3,By applying Expectation-Maximization (EM) algorithm to the noisy ICA model, i.e., assuming the statistical independence of the source signals and formulating it in a Bayesian estimation framework, an EM algorithm to tackle the noisy ICA model is proposed. In the noisy ICA model, the proposed EM algorithm provides an efficient approach to estimate model parameters and then the sources, with the statistic model of sources known. Simulation results show that the proposed method can perform BSS problem with the noisy ICA model.4,We extend the Linear Program algorithm of convex analysis of mixtures of non-negative sources (CAMNS-LP) algorithm to the more general case of real sources, i.e., without restricting sources non-negative, and term it as real CAMNS-LP (R-CAMNS-LP) algorithm. On the assumption that the minimum values of the sources are equal and same, we subtract this minimum from the observations such that the subtracted observations can be expressed as an non-negative blind source separation (NBSS) problem. Then after separating the observations using the CAMNS-LP algorithm, we can add the minimum to the separated signals to get the original real sources. This expands the application fields. Simulation results are presented to demonstrate the obvious efficacy of our proposed method over the traditional FastICA algorithm of Hyv?rinen.5,The proximity operator of a convex function, a natural extension of the notion of a projection operator onto a convex set, plays a central role in the analysis and the numerical solution of convex optimization problems. It has recently been introduced in the area of signal processing, where it has become increasingly important. However, so far, there is no research on ICA in this framework. We propose the fast proximal gradient method for ICA, termed as FastPG-ICA, in BSS problem. We derive the new update rule of the unmixing matrix in the viewpoint of fast proximal gradient. It achieves a better separation performance than that of the traditional ICA method, such as complex FastICA (c-FastICA) proposed by Bingham and Hyv?rinen. Simulation results demonstrate the effectiveness of our proposed method.6,ICA is one of the most important methods for BSS, in which the pre-whitening procedure of the observed signals plays an important role. Usually, principal component analysis (PCA) is employed for this preprocessing task. In practice, the observed signals of a passive radar system are usually corrupted by strong interference and noice, which greatly reduces the performance of BSS methods. However, this problem is rarely taken into account in the whitening step of traditional BSS methods. We propose a new whitening framework for noisy BSS. The idea is that the noise variance is removed from the eigenvalues of the signal subspace before whitening the convariance matrix of the observed signals. The experiments show that the BSS performance is greatly improved using the proposed whitening framework.