Rapid advances in speech recognition theory, as well as computing hardware, have led to the development of machines that can take human speech as input, decode the information content of the speech, and respond accordingly. Real-time performance of such systems is often dominated by the evaluation of likelihoods in the statistical modeling component of the system. Statistical models are typically implemented using Gaussian mixture distributions. The primary objective of this thesis was to develop an extension of the Bucket Box Intersection algorithm in which the dimension with the optimal number of splits can be selected when multiple minima are present. The effects of normalization of mixture weights and Gaussian clipping have also been investigated. We show that the Extended BBI algorithm (EBBI) reduces run-time by 21% without introducing any approximation error. EBBI also produced a 12% lower word error rate than Gaussian clipping for the same computational complexity. These approaches were evaluated on a wide variety of tasks including conversational speech.

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Signal detection and modulation classification are becoming increasingly important in a variety of wireless communication systems such as those involving spectrum management and electronic warfare and surveillance, among others. The majority of the signal detection and modulation classification algorithms available in the literature assume that the additive noise has a Gaussian distribution. However, while this is a good model for thermal noise, various studies have shown that the noise experienced in most radio channels, due to a variety of man-made and natural electromagnetic sources, is non-Gaussian and exhibits impulsive characteristics. Unfortunately, conventional signal processing algorithms developed for Gaussian noise conditions are known to perform poorly in the presence of non-Gaussian noise. For this reason, the main goal of this dissertation is to develop statistical signal processing algorithms for the detection and modulation classification of signals in radio channels where the additive noise is non-Gaussian. One of the major challenges involved in the design of these algorithms is that they are expected to operate with limited or no prior knowledge of the signal of interest, the fading experienced by the signal, and the distribution of the noise added in the channel. Therefore, this dissertation develops new techniques for estimating the parameters that characterize the additive non-Gaussian noise process, as well as the fading process, in the presence of unknown signals. These novel estimators are an integral contribution of this dissertation. The signal detection and modulation classification problems considered here are treated as hypothesis testing problems. Using a composite hypothesis testing procedure, the unknown fading and noise process parameters are first estimated and then used in a likelihood ratio test to detect the presence or identify the modulation scheme of a signal of interest. The proposed algorithms, which are developed for different non-Gaussian noise models, are shown to outperform conventional algorithms which assume Gaussian noise conditions and also algorithms based on other impulsive noise mitigation techniques. This dissertation has three major contributions. First, in environments where the noise can be modeled using a Gaussian mixture distribution, a new expectation-maximization algorithm based technique is developed for estimating the unknown fading and noise distribution parameters. Using these estimates, a hybrid likelihood ratio test is used for modulation classification. Second, a five-stage scheme for signal detection in symmetric α stable noise environments, based on a class of robust filters called the matched myriad filters, is presented. New algorithms for estimating the noise distribution parameters are also developed. Third, a modulation classifier is proposed for environments in which the noise can be modeled as a time-correlated non-Gaussian random process. The proposed classifier involves the use of a whitening filter followed by likelihood-based classification. A new H_â filter-based technique for estimating the whitening filter coefficients is presented. / Ph. D.

The proliferation of renewables, electric vehicles, and power electronic devices calls for innovative approaches to learn, optimize, and plan the power system. The uncertain and volatile nature of the integrated components necessitates using swift and probabilistic solutions. Gaussian process regression is a machine learning paradigm that provides closed-form predictions with quantified uncertainties. The key property of Gaussian processes is the natural ability to integrate the sensitivity of the labels with respect to features, yielding improved accuracy. This dissertation tailors Gaussian process regression for three applications in power systems. First, a physics-informed approach is introduced to infer the grid dynamics using synchrophasor data with minimal network information. The suggested method is useful for a wide range of applications, including prediction, extrapolation, and anomaly detection. Further, the proposed framework accommodates heterogeneous noisy measurements with missing entries. Second, a learn-to-optimize scheme is presented using Gaussian process regression that predicts the optimal power flow minimizers given grid conditions. The main contribution is leveraging sensitivities to expedite learning and achieve data efficiency without compromising computational efficiency. Third, Bayesian optimization is applied to solve a bi-level minimization used for strategic investment in electricity markets. This method relies on modeling the cost of the outer problem as a Gaussian process and is applicable to non-convex and hard-to-evaluate objective functions. The designed algorithm shows significant improvement in speed while attaining a lower cost than existing methods. / Doctor of Philosophy / The proliferation of renewables, electric vehicles, and power electronic devices calls for innovative approaches to learn, optimize, and plan the power system. The uncertain and volatile nature of the integrated components necessitates using swift and probabilistic solutions. This dissertation focuses on three practically important problems stemming from the power system modernization. First, a novel approach is proposed that improves power system monitoring, which is the first and necessary step for the stable operation of the network. The suggested method applies to a wide range of applications and is adaptable to use heterogeneous and noisy measurements with missing entries. The second problem focuses on predicting the minimizers of an optimization task. Moreover, a computationally efficient framework is put forth to expedite this process. The third part of this dissertation identifies investment portfolios for electricity markets that yield maximum revenue and minimum cost.