Four contributions to the multitaper method of applied spectrum estimation are presented. These are a generalization of the multitaper method of spectrum estimation to time-series possessing irregularly spaced samples, a robust spectrum estimate suitable for cyclostationary, or quasi cyclostationary time-series, an improvement over the standard, multitaper spectrum estimates using quadratic inverse theory, and finally a method of scan-free spectrum estimation using a rotational shear-interferometer. Each of these topics forms a chapter in this thesis. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2009-02-05 18:01:45.187

Este trabalho envolve dois diferentes aspectos da estimação de espectros direcionais de onda a partir de movimentos de 1a ordem da embarcação. Sendo a estimação do espectro de ondas feita por meio de um método Bayesiano, existe a necessidade da calibração dos hiperparâmetros derivados da modelagem Bayesiana. O primeiro assunto abordado é a determinação de uma metodologia de calibração dos hiperparâmetros necessários à estimação do espectro direcional de ondas. Desenvolve-se ao longo deste uma primeira análise de um método aplicável a qualquer embarcação do tipo FPSO para a determinação a priori de valores de dois hiperparâmetros de controle da suavização da estimativa. Obtém-se resultados indicativos de que é possível definir valores destes hiperparâmetros dependentes de quantidades observáveis como calado da embarcação e período das ondas, de modo que os erros de estimação ainda se mantém muito próximos aos encontrados por valores ótimos dos hiperparâmetros. Isto leva à conclusão de que na abordagem atual, com valores fixos a cada calado, erros excessivos e desnecessários podem ocorrer no processo de estimação. O segundo tema trata da estimação paramétrica de espectros, utilizando modelos paramétricos de descrição de espectros como forma de obtenção de estatísticas de mar. Abordam-se também os assuntos de mares cruzados, donde se faz necessária a identificação da bimodalidade dos espectros para a estimação correta das estatísticas de mar. / In this work, two differents aspects of directional wave spectra estimation from 1st order ship motions are presented. As the estimation of wave spectrum is made by means of a Bayesian method, it is necessary to calibrate the hyperparameters derived from Bayesian modeling. The first addressed subject is the determination of a calibration methodology of the hyperparameters needed for the directional wave spectrum estimation. It is developed through this work a first analysis of an applicable method to any vessel of FPSO type for the prior determination of values for this two hyperparameters depending on observable quantities, such as draft of the vessel and wave period, in such a way that the estimation errors are still very close to those found by optimum values of the hyperparameters. This leads to the conclusion that in the current approach excessive and unnecessary errors can occur on the estimation process. The second subject addresses the parametric estimation of spectra, using parametric models of spectrum description to acquire the sea statistics. For this purpose, it became necessary the study of crossed-sea states, which was employed in the bimodal spectrum identification for the correct estimation of sea statistics.

Designing estimators based on low rank signal models is a common practice in signal processing. Some of these estimators are designed to use a single low rank snapshot vector, while others employ multiple snapshots. This dissertation deals with both these cases in different contexts. Separable nonlinear least squares is a popular tool to extract parameter estimates from a single snapshot vector. Asymptotic statistical properties of the separable non-linear least squares estimates are explored in the first part of the thesis. The assumptions imposed on the noise process and the data model are general. Therefore, the results are useful in a wide range of applications. Sufficient conditions are established for consistency, asymptotic normality and statistical efficiency of the estimates. An expression for the asymptotic covariance matrix is derived and it is shown that the estimates are circular. The analysis is extended also to the constrained separable nonlinear least squares problems. Nonparametric estimation of the material functions from wave propagation experiments is the topic of the second part. This is a typical application where a single snapshot vector is employed. Numerical and statistical properties of the least squares algorithm are explored in this context. Boundary conditions in the experiments are used to achieve superior estimation performance. Subsequently, a subspace based estimation algorithm is proposed. The subspace algorithm is not only computationally efficient, but is also equivalent to the least squares method in accuracy. Estimation of the frequencies of multiple real valued sine waves is the topic in the third part, where multiple snapshots are employed. A new low rank signal model is introduced. Subsequently, an ESPRIT like method named R-Esprit and a weighted subspace fitting approach are developed based on the proposed model. When compared to ESPRIT, R-Esprit is not only computationally more economical but is also equivalent in performance. The weighted subspace fitting approach shows significant improvement in the resolution threshold. It is also robust to additive noise.

Este trabalho envolve dois diferentes aspectos da estimação de espectros direcionais de onda a partir de movimentos de 1a ordem da embarcação. Sendo a estimação do espectro de ondas feita por meio de um método Bayesiano, existe a necessidade da calibração dos hiperparâmetros derivados da modelagem Bayesiana. O primeiro assunto abordado é a determinação de uma metodologia de calibração dos hiperparâmetros necessários à estimação do espectro direcional de ondas. Desenvolve-se ao longo deste uma primeira análise de um método aplicável a qualquer embarcação do tipo FPSO para a determinação a priori de valores de dois hiperparâmetros de controle da suavização da estimativa. Obtém-se resultados indicativos de que é possível definir valores destes hiperparâmetros dependentes de quantidades observáveis como calado da embarcação e período das ondas, de modo que os erros de estimação ainda se mantém muito próximos aos encontrados por valores ótimos dos hiperparâmetros. Isto leva à conclusão de que na abordagem atual, com valores fixos a cada calado, erros excessivos e desnecessários podem ocorrer no processo de estimação. O segundo tema trata da estimação paramétrica de espectros, utilizando modelos paramétricos de descrição de espectros como forma de obtenção de estatísticas de mar. Abordam-se também os assuntos de mares cruzados, donde se faz necessária a identificação da bimodalidade dos espectros para a estimação correta das estatísticas de mar. / In this work, two differents aspects of directional wave spectra estimation from 1st order ship motions are presented. As the estimation of wave spectrum is made by means of a Bayesian method, it is necessary to calibrate the hyperparameters derived from Bayesian modeling. The first addressed subject is the determination of a calibration methodology of the hyperparameters needed for the directional wave spectrum estimation. It is developed through this work a first analysis of an applicable method to any vessel of FPSO type for the prior determination of values for this two hyperparameters depending on observable quantities, such as draft of the vessel and wave period, in such a way that the estimation errors are still very close to those found by optimum values of the hyperparameters. This leads to the conclusion that in the current approach excessive and unnecessary errors can occur on the estimation process. The second subject addresses the parametric estimation of spectra, using parametric models of spectrum description to acquire the sea statistics. For this purpose, it became necessary the study of crossed-sea states, which was employed in the bimodal spectrum identification for the correct estimation of sea statistics.

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<p>Designing estimators based on low rank signal models is a common practice in signal processing. Some of these estimators are designed to use a single low rank snapshot vector, while others employ multiple snapshots. This dissertation deals with both these cases in different contexts.</p><p>Separable nonlinear least squares is a popular tool to extract parameter estimates from a single snapshot vector. Asymptotic statistical properties of the separable non-linear least squares estimates are explored in the first part of the thesis. The assumptions imposed on the noise process and the data model are general. Therefore, the results are useful in a wide range of applications. Sufficient conditions are established for consistency, asymptotic normality and statistical efficiency of the estimates. An expression for the asymptotic covariance matrix is derived and it is shown that the estimates are circular. The analysis is extended also to the constrained separable nonlinear least squares problems.</p><p>Nonparametric estimation of the material functions from wave propagation experiments is the topic of the second part. This is a typical application where a single snapshot vector is employed. Numerical and statistical properties of the least squares algorithm are explored in this context. Boundary conditions in the experiments are used to achieve superior estimation performance. Subsequently, a subspace based estimation algorithm is proposed. The subspace algorithm is not only computationally efficient, but is also equivalent to the least squares method in accuracy.</p><p>Estimation of the frequencies of multiple real valued sine waves is the topic in the third part, where multiple snapshots are employed. A new low rank signal model is introduced. Subsequently, an ESPRIT like method named R-Esprit and a weighted subspace fitting approach are developed based on the proposed model. When compared to ESPRIT, R-Esprit is not only computationally more economical but is also equivalent in performance. The weighted subspace fitting approach shows significant improvement in the resolution threshold. It is also robust to additive noise.</p>

<p>This thesis addresses the problem of source localization and time-varying spatial spectrum estimation with maneuverable arrays. Two applications, each having different environmental assumptions and array geometries, are considered: 1) passive broadband source localization with a rigid 2-sensor array in a shallow water, multipath environment and 2) time-varying spatial spectrum estimation with a large, flexible towed array. Although both applications differ, the processing scheme associated with each is designed to exploit array maneuverability for improved localization and detection performance.</p><p>In the first application considered, passive broadband source localization is accomplished via time delay estimation (TDE). Conventional TDE methods, such as the generalized cross-correlation (GCC) method, make the assumption of a direct-path signal model and thus suffer localization performance loss in shallow water, multipath environments. Correlated multipath returns can result in spurious peaks in GCC outputs resulting in large bearing estimate errors. A new algorithm that exploits array maneuverability is presented here. The multiple orientation geometric averaging (MOGA) technique geometrically averages cross-correlation outputs to obtain a multipath-robust TDE. A broadband multipath simulation is presented and results indicate that the MOGA effectively suppresses correlated multipath returns in the TDE.</p><p>The second application addresses the problem of field directionality mapping (FDM) or spatial spectrum estimation in dynamic environments with a maneuverable towed acoustic array. Array processing algorithms for towed arrays are typically designed assuming the array is straight, and are thus degraded during tow ship maneuvers. In this thesis, maneuvering the array is treated as a feature allowing for left and right disambiguation as well as improved resolution towards endfire. The Cramer Rao lower bound is used to motivate the improvement in source localization which can be theoretically achieved by exploiting array maneuverability. Two methods for estimating time-varying field directionality with a maneuvering array are presented: 1) maximum likelihood estimation solved using the expectation maximization (EM) algorithm and 2) a non-negative least squares (NNLS) approach. The NNLS method is designed to compute the field directionality from beamformed power outputs, while the ML algorithm uses raw sensor data. A multi-source simulation is used to illustrate both the proposed algorithms' ability to suppress ambiguous towed-array backlobes and resolve closely spaced interferers near endfire which pose challenges for conventional beamforming approaches especially during array maneuvers. Receiver operating characteristics (ROCs) are presented to evaluate the algorithms' detection performance versus SNR. Results indicate that both FDM algorithms offer the potential to provide superior detection performance in the presence of noise and interfering backlobes when compared to conventional beamforming with a maneuverable array.</p> / Dissertation

This thesis deals with oportunity of ROC curve usage in the description of methods that work with sound signals. Specifically, it focuses on ways of detecting of stress in speech signals. The detection itselfs is done in a range of frequencies of the sound signal. There is also a classifier designed using ROC curves that decides whether the input signal is stressed or not. The output of this thesis are findings gathered from analyses and also some recommendation based on those analyses.

Este texto trata da estimação de espectro direcional de ondas a partir de movimentos de primeira ordem de sistemas oceânicos estacionários utilizando um método de inferência bayesiano. Após descrição do método e discutidas suas principais fontes de incertezas, este foi validado experimentalmente através de ensaios com dois tipos de embarcações para ondas irregulares e mares bimodais, e verificado com dados de monitoração em escala real. Uma comparação preliminar com dados provenientes de um radar próximo ao sistema monitorado também foi feita. Com base nestes resultados, discute-se a eficiência do método e suas limitações. / This text is about estimating directional wave spectra based on first order motions of stationary systems by means of a bayesian inference method. After being described the method and its main sources of uncertainties discussed, an experimental validation was carried out with two different types of hulls for irregular waves and bimodal seas, with a posterior verification using data from a real scale monitoring campaign. Also, a preliminary comparison with data from a radar in the vicinities of the monitored system was made. Based on those results, the methods efficiency is discussed, along with its limitations.

Este texto trata da estimação de espectro direcional de ondas a partir de movimentos de primeira ordem de sistemas oceânicos estacionários utilizando um método de inferência bayesiano. Após descrição do método e discutidas suas principais fontes de incertezas, este foi validado experimentalmente através de ensaios com dois tipos de embarcações para ondas irregulares e mares bimodais, e verificado com dados de monitoração em escala real. Uma comparação preliminar com dados provenientes de um radar próximo ao sistema monitorado também foi feita. Com base nestes resultados, discute-se a eficiência do método e suas limitações. / This text is about estimating directional wave spectra based on first order motions of stationary systems by means of a bayesian inference method. After being described the method and its main sources of uncertainties discussed, an experimental validation was carried out with two different types of hulls for irregular waves and bimodal seas, with a posterior verification using data from a real scale monitoring campaign. Also, a preliminary comparison with data from a radar in the vicinities of the monitored system was made. Based on those results, the methods efficiency is discussed, along with its limitations.