In this paper, we propose to employ an extension to the natural gradient algorithm for robust Independent Component Analysis against outliers. The standard natural gradient algorithm does not exhibit this property since it employs nonrobust sample estimates for computing higher order moments. In order to overcome this drawback, we propose to use robust alternatives to higher order moments, which are comparatively less sensitive to outliers in the observed data. Some computer simulations are presented to show that the proposed method, as compared to the standard natural gradient algorithm, gives better performance in the presence of outlying data.

In this paper, a novel cumulant-based adaptive notch filtering technique for the enhancement and tracking of a single sinusoid in additive noise is presented. In this technique, the enhanced signal is obtained as the output of a narrow bandpass filter implemented using a second-order pole-zero constraint IIR adaptive notch filter, which needs only one coefficient to be updated. The filter coefficient, which leads to identifying and tracking the sinusoidal frequency, is updated using a suggested adaptive algorithm employing a recursive estimate of the kurtosis and only one-sample-lag point of a selected one-dimensional fourth-order cumulant slice of the input signal. Therefore, the proposed technique provides automatically resistance to additive Gaussian noise. It is also shown that the presented technique outperforms the correlation-based counterpart in handling additive non-Gaussian noise. Simulation results are provided to show the effectiveness of the proposed algorithm in comparison with the correlation-based lattice algorithm.

This paper describes a new high resolution algorithm for the two-dimensional (2-D) frequency estimation problem, which, in particular, is noise insensitive in view of the fact that in many practical applications the contaminated noise may not be white noise. For this purpose, the approach is set in the context of higher-order statistics (HOS), which has demonstrated to be an effective approach under a colored noise environment. The algorithm begins with the consideration of the fourth-order moments of the available 2-D data. Two auxiliary matrices, constituted by a novel stacking of the diagonal slice of the computed fourth-order moments, are then introduced and through which the two frequency components can be precisely determined, respectively, via matrix factorizations along with the subspace rotational invariance (SRI) technique. Simulation results are also provided to verify the proposed algorithm.

This study is aimed to derive a new theoretical solution for blind equalizers. Undr the common assumptions for this framework, it is found that the condition for blind equalization is directly associated with an eigenproblem, i.e. the tap coefficients of the equalizer appear as an eigenvector of a higher order statistics matrix. Computer simulations show that very fast convergence can be achieved based on the approach.