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This dissertation consists of two parts. The first part deals with the performance appraisal of estimation algorithms. The second part focuses on the application of estimation algorithms to target tracking. Performance appraisal is crucial for understanding, developing and comparing various estimation algorithms. In particular, with the evolvement of estimation theory and the increase of problem complexity, performance appraisal is getting more and more challenging for engineers to make comprehensive conclusions. However, the existing theoretical results are inadequate for practical reference. The first part of this dissertation is dedicated to performance measures which include local performance measures, global performance measures and model distortion measure. The second part focuses on application of the recursive best linear unbiased estimation (BLUE) or lineae minimum mean square error (LMMSE) estimation to nonlinear measurement problem in target tracking. Kalman filter has been the dominant basis for dynamic state filtering for several decades. Beyond Kalman filter, a more fundamental basis for the recursive best linear unbiased filtering has been thoroughly investigated in a series of papers by Dr. X. Rong Li. Based on the so-called quasirecursive best linear unbiased filtering technique, the constraints of the Kalman filter Linear-Gaussian assumptions can be relaxed such that a general linear filtering technique for nonlinear systems can be achieved. An approximate optimal BLUE filter is implemented for nonlinear measurements in target tracking which outperforms the existing method significantly in terms of accuracy, credibility and robustness.

This dissertation mainly consists of three parts. The first part proposes generalized linear minimum mean-square error (GLMMSE) estimation for nonlinear point estimation. The second part proposes a recursive joint decision and estimation (RJDE) algorithm for joint decision and estimation (JDE). The third part analyzes the performance of sequential probability ratio test (SPRT) when the log-likelihood ratios (LLR) are independent but not identically distributed. The linear minimum mean-square error (LMMSE) estimation plays an important role in nonlinear estimation. It searches for the best estimator in the set of all estimators that are linear in the measurement. A GLMMSE estimation framework is proposed in this disser- tation. It employs a vector-valued measurement transform function (MTF) and finds the best estimator among all estimators that are linear in MTF. Several design guidelines for the MTF based on a numerical example were provided. A RJDE algorithm based on a generalized Bayes risk is proposed in this dissertation for dynamic JDE problems. It is computationally efficient for dynamic problems where data are made available sequentially. Further, since existing performance measures for estimation or decision are effective to evaluate JDE algorithms, a joint performance measure is proposed for JDE algorithms for dynamic problems. The RJDE algorithm is demonstrated by applications to joint tracking and classification as well as joint tracking and detection in target tracking. The characteristics and performance of SPRT are characterized by two important functions—operating characteristic (OC) and average sample number (ASN). These two functions have been studied extensively under the assumption of independent and identically distributed (i.i.d.) LLR, which is too stringent for many applications. This dissertation relaxes the requirement of identical distribution. Two inductive equations governing the OC and ASN are developed. Unfortunately, they have non-unique solutions in the general case. They do have unique solutions in two special cases: (a) the LLR sequence converges in distributions and (b) the LLR sequence has periodic distributions. Further, the analysis can be readily extended to evaluate the performance of the truncated SPRT and the cumulative sum test.

Introdução: O inquérito por telefone, quando comparado ao inquérito domiciliar possui vários atrativos, em especial baixo custo operacional e rapidez do processo de divulgação de resultados. No entanto, a exclusão de domicílios sem telefone fixo, pode representar série questão de validade nas estimativas obtidas. Objetivo: Avaliar vícios potenciais nos resultados divulgados no Sistema de Vigilância de Fatores de Risco para Doenças Crônicas por Inquérito Telefônico (VIGITEL) em município de baixa cobertura de domicílios com telefone fixo. Métodos: A partir de resultados levantados pelo Inquérito Domiciliar realizado no município de Rio Branco-AC, com cobertura de 41 por cento dos domicílios com telefone fixo, tentou-se localizar vícios introduzidos nos resultados do Vigitel. Foi usado método alternativo de ponderação para diminuir o vício da estimativa do Vigitel. Resultados: O Vigitel subestima a maioria das prevalências estimadas. Os pesos de pós-estratificação eliminam parcialmente o vício, cuja origem é proveniente de baixa taxa de cobertura de domicílios com telefone fixo. Por outro lado, o uso desses pesos, quando não necessário, potencializou o vício das variáveis não associadas à posse de telefone fixo. Conclusões: Em municípios de baixa taxa de cobertura de domicílios com telefone fixo, torna-se necessária a implementação de novo método de ponderação e estratégia de seleção de variáveis externas para construção dos pesos de pós estratificação, que minimizem o vício nas estimativas das variáveis levantadas / Introdução: O inquérito por telefone, quando comparado ao inquérito domiciliar possui vários atrativos, em especial baixo custo operacional e rapidez do processo de divulgação de resultados. No entanto, a exclusão de domicílios sem telefone fixo, pode representar série questão de validade nas estimativas obtidas. Objetivo: Avaliar vícios potenciais nos resultados divulgados no Sistema de Vigilância de Fatores de Risco para Doenças Crônicas por Inquérito Telefônico (VIGITEL) em município de baixa cobertura de domicílios com telefone fixo. Métodos: A partir de resultados levantados pelo Inquérito Domiciliar realizado no município de Rio Branco-AC, com cobertura de 41 por cento dos domicílios com telefone fixo, tentou-se localizar vícios introduzidos nos resultados do Vigitel. Foi usado método alternativo de ponderação para diminuir o vício da estimativa do Vigitel. Resultados: O Vigitel subestima a maioria das prevalências estimadas. Os pesos de pós-estratificação eliminam parcialmente o vício, cuja origem é proveniente de baixa taxa de cobertura de domicílios com telefone fixo. Por outro lado, o uso desses pesos, quando não necessário, potencializou o vício das variáveis não associadas à posse de telefone fixo. Conclusões: Em municípios de baixa taxa de cobertura de domicílios com telefone fixo, torna-se necessária a implementação de novo método de ponderação e estratégia de seleção de variáveis externas para construção dos pesos de pós estratificação, que minimizem o vício nas estimativas das variáveis levantadas

The trend seasonal demand pattern is encountered when both trend and seasonal influences are interactive. The problem of this research is to project the seasonal market sales using ice cream and fresh milk in Taiwan as examples. In order to improve the accuracy of forecast, two different methods are validated and the best forecasting method is selected based on the minimum Mean Square Error. In this study, we present two forecasting models used for evaluation to predict seasonal market sales of ice cream, fresh milk, and air conditioner in Taiwan. It includes Winters multiplicative seasonal trend model and the Decomposition method. Two different methods are validated and the best forecasting method is selected based on the minimum Mean Square Error. After the validation process, Winters multiplicative seasonal trend model is selected based on the minimum MSE, and the monthly sales forecast for the year of 2011 is conducted using the data(60 months). Number Cruncher Statistical System (NCSS) is used for analyzing the data which proves useful and powerful. In summary, the results demonstrate that Winters multiplicative seasonal trend model has the smallest mean square error in this case. Therefore, we conclude that both Winters multiplicative seasonal trend model and the Decomposition model are well fitted for forecasting the seasonal market sales. Yet, Winters multiplicative seasonal trend model is the better method to be used in this study since it generates the smallest mean square error (MSE) during the period of validation.

The efficiency of direct sequence spread spectrum (DS/SS) receiver is highly dependent on the accurate and fast synchronization between the incoming and locally generated PN (pseudo-noise) codes. The code synchronization is processed in two steps, acquisition (coarse alignment) and tracking (fine alignment), to estimate the delay offset between the two codes. In general, the schemes for code acquisition and tracking processes are performed, separately, and implemented with different structure. Recently, an alternative approach, with the adaptive LMS filtering scheme, has been proposed for performing both code acquisition and tracking with the identical structure, where the coherent receiver was employed. With this approach, dramatically, hardware complexity reduction could be achieved, especially, when long PN code is considered. In this thesis, a new differentially coherent code synchronization scheme, based on a differential detector followed by an adaptive constrained LMS (CLMS) filtering algorithm with maximum tap weight (MTW) test scheme, is devised for performing both code acquisition and tracking with the identical structure. With a differential detector for code synchronization, the prior knowledge of the carrier phase is not required as the non-coherent techniques. Numerical analyses and simulation results verify that the proposed scheme has better acquisition performance, in terms of mean acquisition time, than the conventional LMS filtering algorithm with MTW test and mean square error (MSE) test schemes for the integer and non-integer time delay environments. At the same time, the proposed scheme has better tracking capability, in terms of mean hold-in time and mean penalty time, over the conventional LMS filtering schemes, for the variation of signal-to-noise ratio (SNR) and delay offset (delay difference).

Effort to estimate unknown time-varying channels as a part of high-speed mobile communication systems is of interest especially for next-generation wireless systems. The high computational complexity of the optimal Wiener estimator usually makes its use impractical in fast time-varying channels. As a powerful candidate, the adaptive least mean squares (LMS) algorithm offers a computationally efficient solution with its simple first-order weight-vector update equation. However, the performance of the LMS algorithm deteriorates in time-varying channels as a result of the eigenvalue disparity, i.e., spread, of the input correlation matrix in such chan nels. In this work, we incorporate the L MS algorithm into the well-known bidirectional processing idea to produce an extension called the bidirectional LMS. This algorithm is shown to be robust to the adverse effects of time-varying channels such as large eigenvalue spread. The associated tracking performance is observed to be very close to that of the optimal Wiener filter in many cases and the bidirectional LMS algorithm is therefore referred to as near-optimal. The computational complexity is observed to increase by the bidirectional employment of the LMS algorithm, but nevertheless is significantly lower than that of the optimal Wiener filter. The tracking behavior of the bidirectional LMS algorithm is also analyzed and eventually a steady-state step-size dependent mean square error (MSE) expression is derived for single antenna flat-fading channels with various correlation properties. The aforementioned analysis is then generalized to include single-antenna frequency-selective channels where the so-called ind ependence assumption is no more applicable due to the channel memory at hand, and then to multi-antenna flat-fading channels. The optimal selection of the step-size values is also presented using the results of the MSE analysis. The numerical evaluations show a very good match between the theoretical and the experimental results under various scenarios. The tracking analysis of the bidirectional LMS algorithm is believed to be novel in the sense that although there are several works in the literature on the bidirectional estimation, none of them provides a theoretical analysis on the underlying estimators. An iterative channel estimation scheme is also presented as a more realistic application for each of the estimation algorithms and the channel models under consideration. As a result, the bidirectional LMS algorithm is observed to be very successful for this real-life application with its increased but still practical level of complexity, the near-optimal tracking performa nce and robustness to the imperfect initialization.

This manuscript concerns the performance analysis in signal processing and consists into two parts : First, we study the lower bounds in characterizing and predicting the estimation performance in terms of mean square error (MSE). The lower bounds on the MSE give the minimum variance that an estimator can expect to achieve and it can be divided into two categories depending on the parameter assumption: the so-called deterministic bounds dealing with the deterministic unknown parameters, and the so-called Bayesian bounds dealing with the random unknown parameter. Particularly, we derive the closed-form expressions of the lower bounds for two applications in two different fields: (i) The first one is the target localization using the multiple-input multiple-output (MIMO) radar in which we derive the lower bounds in the contexts with and without modeling errors, respectively. (ii) The other one is the pulse phase estimation of X-ray pulsars which is a potential solution for autonomous deep space navigation. In this application, we show the potential universality of lower bounds to tackle problems with parameterized probability density function (pdf) different from classical Gaussian pdf since in X-ray pulse phase estimation, observations are modeled with a Poisson distribution. Second, we study the statistical resolution limit (SRL) which is the minimal distance in terms of the parameter of interest between two signals allowing to correctly separate/estimate the parameters of interest. More precisely, we derive the SRL in two contexts: array processing and MIMO radar by using two approaches based on the estimation theory and information theory. We also present in this thesis the usefulness of SRL in optimizing the array system.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Este trabalho apresenta estudos sobre sistemas de comunicaÃÃo cujos sinais utilizados para a transmissÃo das informaÃÃes sÃo nÃo-ortogonais, superpostos em frequÃncia, e com espaÃamento entre portadoras menor do que a taxa de sÃmbolo. As pesquisas estÃo direcionadas na obtenÃÃo de estruturas de transmissor e receptor Ãtimos e sub-Ãtimos, na modelagem e anÃlise matemÃtica dos sistemas incluindo o canal, em propostas de estratÃgias para detecÃÃo de sÃmbolo, e na avaliaÃÃo de desempenho. SÃo propostas sete estratÃgias de recepÃÃo de N sinais m-QAM nÃo-ortogonais atravÃs do canal AWGN. Dentre as estratÃgias de detecÃÃo duas sÃo Ãtimas e as outras cinco sÃo subÃtimas. As duas estruturas de receptores Ãtimos apresentados neste trabalho sÃo: o receptor de mÃxima verossimilhanÃa (ML) clÃssico e o receptor de mÃxima verossimilhanÃa com base na decomposiÃÃo de Gram-Schmidt. Os receptores sub-Ãtimos desenvolvidos neste trabalho sÃo de dois tipos: receptores com equalizaÃÃo linear e receptores com equalizaÃÃo nÃo-linear. O primeiro tipo de receptor à desenvolvido com base nos critÃrios de erro quadrÃtico mÃdio mÃnimo (MMSE) e o de forÃagem a zero (ZF). à apresentado o desenvolvimento analÃtico do projeto de cada uma das arquiteturas de receptores lineares, assim como à determinado o erro dos estimadores. Os receptores com equalizaÃÃo nÃo-linear sÃo baseados no cancelamento de interferÃncia sucessiva (SIC). Neste trabalho, à proposta uma modificaÃÃo no algoritmo do SIC original, resultando em uma nova arquitetura de equalizaÃÃo. O desempenho dos receptores propostos à avaliado em diferentes condiÃÃes de nÃmero de portadoras e de grau de superposiÃÃo espectral atravÃs de simulaÃÃo computacional. Por fim, sÃo apresentados as conlusÃes e as perspectivas futuras de pesquisa. / This work presents studies on communication systems, whose signals used for transmission of information are non-orthogonal, overlapping in frequency and carrier spacing less than the rate of symbols. The research is aimed to obtain structures of transmitter, optimal and sub-optimal receivers using modeling and mathematical analysis of systems including the channel. Furthermore, propose strategies for symbol detection and performance evaluation. Seven strategies of reception to N signals m-QAM non-orthogonal through the AWGN channel. Among the strategies of detection two are optimal and the others five are suboptimal. The two optimal receivers structures presented in this paper are: the classical receiver maximum likelihood (ML) receiver and maximum likelihood based on the Gram-Schmidt decomposition. The suboptimal receivers in this work are of two types: receivers with linear and nonlinear equalization. The first type of receiver is developed based on the criteria of minimum mean square error (MMSE) and the zero forcing (ZF). It is presented the development of analytical design of each linear receiver architectures, as well as determined the error of the estimators. The receivers with nonlinear equalization are based on successive interference cancellation (SIC). In this paper, we propose a modification to the original algorithm of SIC, resulting in a new architecture of equalization. The performance of the proposed receivers is evaluated under different number of carriers and the degree of spectral overlap using computer simulation. Finally, we present the conclusions of this work and future prospects of the research.

Introdução: O inquérito por telefone, quando comparado ao inquérito domiciliar possui vários atrativos, em especial baixo custo operacional e rapidez do processo de divulgação de resultados. No entanto, a exclusão de domicílios sem telefone fixo, pode representar série questão de validade nas estimativas obtidas. Objetivo: Avaliar vícios potenciais nos resultados divulgados no Sistema de Vigilância de Fatores de Risco para Doenças Crônicas por Inquérito Telefônico (VIGITEL) em município de baixa cobertura de domicílios com telefone fixo. Métodos: A partir de resultados levantados pelo Inquérito Domiciliar realizado no município de Rio Branco-AC, com cobertura de 41 por cento dos domicílios com telefone fixo, tentou-se localizar vícios introduzidos nos resultados do Vigitel. Foi usado método alternativo de ponderação para diminuir o vício da estimativa do Vigitel. Resultados: O Vigitel subestima a maioria das prevalências estimadas. Os pesos de pós-estratificação eliminam parcialmente o vício, cuja origem é proveniente de baixa taxa de cobertura de domicílios com telefone fixo. Por outro lado, o uso desses pesos, quando não necessário, potencializou o vício das variáveis não associadas à posse de telefone fixo. Conclusões: Em municípios de baixa taxa de cobertura de domicílios com telefone fixo, torna-se necessária a implementação de novo método de ponderação e estratégia de seleção de variáveis externas para construção dos pesos de pós estratificação, que minimizem o vício nas estimativas das variáveis levantadas / Introdução: O inquérito por telefone, quando comparado ao inquérito domiciliar possui vários atrativos, em especial baixo custo operacional e rapidez do processo de divulgação de resultados. No entanto, a exclusão de domicílios sem telefone fixo, pode representar série questão de validade nas estimativas obtidas. Objetivo: Avaliar vícios potenciais nos resultados divulgados no Sistema de Vigilância de Fatores de Risco para Doenças Crônicas por Inquérito Telefônico (VIGITEL) em município de baixa cobertura de domicílios com telefone fixo. Métodos: A partir de resultados levantados pelo Inquérito Domiciliar realizado no município de Rio Branco-AC, com cobertura de 41 por cento dos domicílios com telefone fixo, tentou-se localizar vícios introduzidos nos resultados do Vigitel. Foi usado método alternativo de ponderação para diminuir o vício da estimativa do Vigitel. Resultados: O Vigitel subestima a maioria das prevalências estimadas. Os pesos de pós-estratificação eliminam parcialmente o vício, cuja origem é proveniente de baixa taxa de cobertura de domicílios com telefone fixo. Por outro lado, o uso desses pesos, quando não necessário, potencializou o vício das variáveis não associadas à posse de telefone fixo. Conclusões: Em municípios de baixa taxa de cobertura de domicílios com telefone fixo, torna-se necessária a implementação de novo método de ponderação e estratégia de seleção de variáveis externas para construção dos pesos de pós estratificação, que minimizem o vício nas estimativas das variáveis levantadas