Statistical signal processing with nonnegativity constraints

Nonnegativity constraints arise frequently in statistical learning and pattern recognition. Multiplicative updates provide natural solutions to optimizations involving these constraints. One well known set of multiplicative updates is given by the Expectation-Maximization algorithm for hidden Markov models, as used in automatic speech recognition. Recently, we have derived similar algorithms for nonnegative deconvolution and nonnegative quadratic programming. These algorithms have applications to low-level problems in voice processing, such as fundamental frequency estimation, as well as high-level problems, such as the training of large margin classifiers. In this paper, we describe these algorithms and the ideas that connect them

Statistical signal processing for mechanical systems

Random processes such as temperature and acoustic noise are found in all types of mechanical systems. Knowledge of these processes can lead to improved design and detection methods related to faulty operation. The goal of this dissertation is to contribute to the knowledge base of such processes. Specifically, we address statistical signal processing methods that are appropriate and consistent relative to the physics of these systems. Two generic problems associated with random signal measurements from mechanical systems are addressed.;Random processes associated with mechanical systems usually have complex spectral structure containing both continuous and line spectral components. Accordingly, they are called mixed random processes. One problem addressed is to use variability related to families of spectral estimators for a mixed random process to better characterize its spectral information. We show that tones are a significant source of bias and variability of families of spectral estimators. Expressions for estimating statistical and arithmetic variability of three common families of spectral estimators are provided. An important and immediate application of these results is tone detection.;We also address the statistical problem of estimating the bandwidth parameter of a Gauss-Markov process from a realization of fixed and finite duration at selectable sampling interval. The motivation is that continuous-time processes are often sampled at a rate far higher than their underlying dynamics. It is commonly assumed a faster sample rate is better. But in many real world situations, such as in adaptive feedback control schemes design, short time changes demand only limited time being utilized. Thus this problem is investigated. The bias and variance expressions of the parameter estimator are derived with a second order expansion. Three sample rate regions---finite, large and very large ones, corresponding to substantial, gradual, and very slight variance drop, are quantitatively identified. Guidelines in choosing sampling rate based on estimator performance requirement are provided.;The results are used to characterize the stochastic structure of the sound pressure process from an engine cooling fan with and without mock engine, and to perform a hypothesis test for deciding whether a design change has a significant effect on the sound

Multiscale statistical signal processing

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Statistical signal processing of nonstationary tensor-valued data

Real-world signals, such as the evolution of three-dimensional vector fields over time, can exhibit highly structured probabilistic interactions across their multiple constitutive dimensions. This calls for analysis tools capable of directly capturing the inherent multi-way couplings present in such data. Yet, current analyses typically employ multivariate matrix models and their associated linear algebras which are agnostic to the global data structure and can only describe local linear pairwise relationships between data entries. To address this issue, this thesis uses the property of linear separability -- a notion intrinsic to multi-dimensional data structures called tensors -- as a linchpin to consider the probabilistic, statistical and spectral separability under one umbrella. This helps to both enhance physical meaning in the analysis and reduce the dimensionality of tensor-valued problems. We first introduce a new identifiable probability distribution which appropriately models the interactions between random tensors, whereby linear relationships are considered between tensor fibres as opposed to between individual entries as in standard matrix analysis. Unlike existing models, the proposed tensor probability distribution formulation is shown to yield a unique maximum likelihood estimator which is demonstrated to be statistically efficient. Both matrices and vectors are lower-order tensors, and this gives us a unique opportunity to consider some matrix signal processing models under the more powerful framework of multilinear tensor algebra. By introducing a model for the joint distribution of multiple random tensors, it is also possible to treat random tensor regression analyses and subspace methods within a unified separability framework. Practical utility of the proposed analysis is demonstrated through case studies over synthetic and real-world tensor-valued data, including the evolution over time of global atmospheric temperatures and international interest rates. Another overarching theme in this thesis is the nonstationarity inherent to real-world signals, which typically consist of both deterministic and stochastic components. This thesis aims to help bridge the gap between formal probabilistic theory of stochastic processes and empirical signal processing methods for deterministic signals by providing a spectral model for a class of nonstationary signals, whereby the deterministic and stochastic time-domain signal properties are designated respectively by the first- and second-order moments of the signal in the frequency domain. By virtue of the assumed probabilistic model, novel tests for nonstationarity detection are devised and demonstrated to be effective in low-SNR environments. The proposed spectral analysis framework, which is intrinsically complex-valued, is facilitated by augmented complex algebra in order to fully capture the joint distribution of the real and imaginary parts of complex random variables, using a compact formulation. Finally, motivated by the need for signal processing algorithms which naturally cater for the nonstationarity inherent to real-world tensors, the above contributions are employed simultaneously to derive a general statistical signal processing framework for nonstationary tensors. This is achieved by introducing a new augmented complex multilinear algebra which allows for a concise description of the multilinear interactions between the real and imaginary parts of complex tensors. These contributions are further supported by new physically meaningful empirical results on the statistical analysis of nonstationary global atmospheric temperatures.Open Acces

Multiscale statistical signal processing : stochastic processes indexed by trees

Cover title.Includes bibliographical references.Supported in part by CRNS. GO134 Supported in part by AFOSR. AFOSR-88-0032 Supported in part by NSF. ECS-8700903 Supported in part by ARO. DAAL03-86-K-0171M. Basseville ... [et al.]

Advanced statistical signal processing for next generation trajectory prediction

Trajectory Prediction (TP) is fundamental in Air Traffic Management (ATM). This research focuses on TP for the execution phase of the flight. In contrast to exploit black-box machine learning-based solutions, we tackle TP as an estimation problem, resorting to mathematical tools arising from statistical signal processing. Our first goal is to find an optimal and robust 4D (3D space plus time) TP solution, and the real-time estimation of the aircraft's active guidance mode, observing flight data collected from Automatic Dependent Surveillance-Broadcast (ADS-B), and transponder selective mode (Mode S) transmissions. Notice that this work is at a very early stage and only preliminary results are available.Peer ReviewedPostprint (published version