Current efforts to measure child mortality for municipalities in Brazil are hampered by the relative rarity of child deaths, which often results in unstable and unreliable estimates. As a result, it is not possible to accurately assess true levels of child mortality for many areas, hindering efforts towards constructing and implementing effective policy initiatives for the reduction of child mortality. However, with a spatial smoothing process based upon Bayesian Statistics it is possible to “borrow” information from neighboring areas in order to generate more stable and accurate estimates of mortality in smaller areas. The objective of this study is to use this spatial smoothing process to derive estimates of child mortality at the level of the municipality in Brazil. Using data from the 2000 Brazil Census, I derive both Bayesian and non-Bayesian estimates of mortality for each municipality. In comparing the smoothed and raw estimates of this parameter, I find that the Bayesian estimates yield a clearer spatial pattern of child mortality with smaller variances in less populated municipalities, thus, more accurately reflecting the true mortality situation of those municipalities. These estimates can then be used, ultimately, to lead to more effective policies and health initiatives in the fight for the reduction of child mortality in Brazil. / text

In this thesis work, Cyclic Root MUSIC method is integrated with spatial smoothing and interpolation techniques to estimate the direction of arrivals of coherent,cyclostationary signals received via a Uniform Circular Array (UCA). Cyclic Root MUSIC and Conventional Root MUSIC algorithms are compared for various signal scenarios by computer simulations. A cyclostationary process is a random process with probabilistic parameters, such as the autocorrelation function, that vary periodically with time. Most of the man-made communication signals exhibit cyclostationarity due to the periodicity arising from their carrier frequencies, chip rates, baud rates, etc. Cyclic Root MUSIC algorithm exploits the cyclostationarity properties of signals to achieve signal selective direction of arrival estimation. Spatial smoothing is presented to overcome the coherent signals problem in a multipath propagation environment. Forward spatial smoothing and forward backward spatial smoothing techniques are investigated. Interpolation method is presented to cope with the restrictions of spatial smoothing on array structure. Although the array structure that is considered in this thesis (Uniform Circular Array), is not suitable for applying spatial smoothing directly, using interpolation method makes it possible. Performance of Cyclic Root MUSIC and Conventional Root MUSIC algorithms are compared under variation of various factors by computer simulations. Effects of signal type on the performance of the algorithms are observed by using different signal scenarios.

In this thesis, DOA estimation using array interpolation in randomly distributed sensor arrays is considered. Array interpolation is a technique in which a virtual array is obtained from the real array and the outputs of the virtual array, computed from the real array using a linear transformation, is used for direction of arrival estimation. The idea of array interpolation techniques is to make simplified and computationally less demanding high resolution direction finding methods applicable to the general class of non-structured arrays.In this study,we apply an interpolation technique for arbitrary array geometries in an attempt to extend root-MUSIC algorithm to arbitrary array geometries.Another issue of array interpolation related to direction finding is spatial smoothing in the presence of multipath sources.It is shown that due to the Vandermonde structure of virtual array manifold vector obtained from the proposed interpolation method, it is possible to use spatial smoothing algorithms for the case of multipath sources.

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[pt] Esta tese desenvolve técnicas avançadas de processamento de sinais com arranjos de sensores, tanto para arranjos completamente calibrados quanto parcialmente calibrados. São propostas novas geometrias de arranjos esparsos baseadas em subarranjos lineares esparsos, bem como são desenvolvidos novos algoritmos de estimativa de direção de chegada (DOA) para sinais eletromagnéticos de banda estreita, utilizando-se a teoria de processamento estatístico. Os algoritmos propostos, denominados Generalized Coarray MUSIC (GCA-MUSIC) e Generalized Coarray Root MUSIC (GCA-rMUSIC), expandem a técnica clássica denominada Multiple Signal Classification (MUSIC) para configurações de subarranjos esparsos. Técnicas de projeto de subarranjos lineares esparsos foram propostas, assim como uma análise dos graus de liberdade dos subarranjos (sDoF) em função dos graus de liberdade do arranjo completo (DoF). Além disso, desenvolvem-se versões com tamanho de Janela Variável (VWS) desses algoritmos, que incorporam técnicas de suavização espacial com abertura variável. Esses métodos proporcionam estimativas de direção de alta precisão e conseguem estimar um número maior de fontes do que o número de sensores físicos em cada subarranjo, explorando estruturas de coarranjo específicas. A análise de desempenho demonstra que o GCA-MUSIC e o GCA-rMUSIC, juntamente com suas variantes VWS, melhoram a precisão no contexto de arranjos parcialmente calibrados, onde podem existir incertezas de calibração. Além disso, são apresentadas variantes VWS do algoritmo Coarray MUSIC (CA-MUSIC) para arranjos totalmente calibrados (coerentes), permitindo estratégias de suavização adaptáveis para um desempenho aprimorado. Além do desenvolvimento algorítmico, foram derivadas as Matrizes de Informação de Fisher (FIMs) para o conjunto completo de parâmetros deste modelo de dados generalizado, incluindo tanto as relações de parâmetros consigo próprios quanto cruzados. Essas matrizes levam em consideração as direções das fontes, potências das fontes, potência do ruído e as componentes reais e imaginárias de todos os parâmetros de calibração, representando cenários com fontes correlacionadas e descorrelacionadas. Este trabalho avança significativamente a compreensão teórica dos limites de desempenho da estimativa de direções, fornecendo uma quantificação mais rigorosa dos limitantes de Cramér-Rao. Esses limitantes são particularmente relevantes em cenários com arranjos parcialmente calibrados e fontes descorrelacionadas, conforme demonstrado utilizando-se modelos de dados baseados no produto de Khatri-Rao. / [en] This thesis explores advanced array signal processing techniques for both fully and partially calibrated arrays. We introduce novel sparse array geometries based on sparse linear subarrays and develop new direction-of-arrival (DOA) estimation algorithms for narrowband electromagnetic signals, framed within statistical signal processing principles. The proposed algorithms, named Generalized Coarray MUSIC (GCA-MUSIC) and Generalized Coarray Root MUSIC (GCA-rMUSIC), extend the classical Multiple Signal Classification (MUSIC) framework to sparse subarrays configurations. Sparse linear subarray design techniques were proposed, as well as an analysis of the degrees of freedom of subarrays (sDoF) as a function of degrees of freedom of the whole array (DoF). Additionally, we develop Variable Window Size (VWS) versions of these algorithms, which incorporate flexible spatial smoothing apertures. These methods provide high-accuracy DoA estimates and offer the key advantage of resolving more sources than the number of physical sensors in each subarray by exploiting coarray structures. Performance analysis demonstrates that GCA-MUSIC and GCA-rMUSIC, along with its VWS variants, improve accuracy in the context of partially-calibrated arrays, where calibration uncertainties may exist. Furthermore, VWS variants of the Coarray MUSIC (CA-MUSIC) algorithm are presented for fully calibrated (coherent) arrays, enabling adaptable smoothing strategies for enhanced performance. In addition to algorithmic development, we compute the Fisher Information Matrices (FIMs) for the complete set of parameters in this generalized data model, including both self and cross-coupled parameter relationships. These matrices account for source directions, source powers, noise power, and the real and imaginary components of all calibration parameters, representing both correlated and uncorrelated source scenarios. This work significantly advances the theoretical understanding of DoA estimation performance limits by providing a more rigorous quantification of the Cramér-Rao bounds. These bounds are particularly relevant in scenarios with partially calibrated arrays and uncorrelated sources, as demonstrated using the Khatri-Rao product-based data model.