Sharif, W. (2012)
Robust Sensor Array Processing for Non-stationary Signals.
Technische Universität Darmstadt
Dissertation, Erstveröffentlichung

Kurzbeschreibung (Abstract)

Non-stationary signals arise in many practical applications such as radar, sonar and mobile communication. An important task in these applications is to estimate the direction-of-arrival (DOA) of the signals in order to locate the desired signals transmitted via inherently noisy wireless channels. The existing methods for non-stationary DOA estimation are based on the assumption that the noise is Gaussian. However, in practice, the noise is often non-Gaussian and impulsive which leads to a significant performance loss in traditional methods. Therefore, in this thesis, the problem of DOA estimation of non-stationary signals in the presence of impulsive noise is considered.

The developed algorithm for robust DOA estimation is based on the robust instantaneous frequency (IFreq) estimation of the individual sources present in the mixture. Then robustly estimated spatial time-frequency distribution matrices (STFD) are averaged across each IFreq segment to obtain the DOA estimate of that particular signal. For IFreq estimation, the presented approach is based on morphological image processing of the spatially averaged, robustly computed auto time-frequency distribution (TFD) image. This thesis also provides robust methods to compute the STFD matrices which are widely used in array signal processing for blind source separation (BSS) and DOA estimation.

The proposed methods for the robust estimation of STFD matrices can be categorized into three classes: pre-processing based, robust position based and robust non-iterative techniques. The pre-processing based STFDs are computationally lightweight, adaptive, easily implementable and are effective in highly impulsive noise environments. For the second class, methods are based on the robust estimation techniques from the statistical literature. This dissertation provides STFD estimation techniques based on M-estimator, highly robust S-estimator and MM-estimator. The robust position based STFD estimation methods provide improved impulsive rejection capability and at the same time enhanced efficiency when compared to the pre-processing based methods. The robust position based methods, however, require expansive computations in comparison to the pre-processing based techniques. To provide a compromise in terms of robustness, efficiency and computational burden, non-iterative robust methods are proposed. For all the proposed methods, simulations have been conducted to exhibit their efficacy. The proposed methods are compared in terms of their achieved root-mean-square-error (RMSE) for DOA estimation under varying signal-to-noise-ratio (SNR) and under varying amount of impulsive contamination. The proposed robust methods provide an improved (lower) RMSE for DOA estimation as compared to the classical non-robust methods.

This dissertation also presents robustness analysis for STFD matrices. The analysis is based on the influence function. The influence function is also a measure of qualitative robustness of an estimator. It gives us the additional bias due to an infinitesimal contamination at a certain point. For recently proposed robust techniques, analytical expressions for influence functions have been provided. Moreover, finite sample counterpart of influence function, which is called the empirical influence function, has also been evaluated. The results show that the classical non-robust STFD estimators yield unbounded influence functions that confirms the non-robustness of classical approaches. On the other hand the proposed robust methods result in bounded influence functions and thus confirm the robustness of the presented robust estimators.

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