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Detecting and preventing the electronic transmission of illicit imagesIbrahim, Amin Abdurahman 01 April 2009 (has links)
The sexual exploitation of children remains a very serious problem and is rapidly increasing globally through the use of the Internet. This work focuses on the current methods employed by criminals to generate and distribute child pornography, the methods used by law enforcement agencies to deter them, and the drawbacks of currently used methods, as well as the surrounding legal and privacy issues. A proven method to detect the transmission of illicit images at the network layer is presented within this paper. With this research, it is now possible to actively filter illicit pornographic images as they are transmitted over the network layer in real-time. It is shown that a Stochastic Learning Weak Estimator learning algorithm and a Maximum Likelihood Estimator learning algorithm can be applied against Linear Classifiers to identify and filter illicit pornographic images. In this thesis, these two learning algorithms were combined with algorithms such as the Non-negative Vector Similarity Coefficient-based Distance algorithm, Euclidian Distance, and Weighted Euclidian Distance. Based upon this research, a prototype was developed using the abovementioned system, capable of performing classification on both compressed and uncompressed images. Experimental results showed that classification accuracies and the overhead of network-based approaches did have a significant effect on routing devices. All images used in our experiments were legal. No actual child pornography images were ever collected, seen, sought, or used.
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Likelihood ratio tests of separable or double separable covariance structure, and the empirical null distributionGottfridsson, Anneli January 2011 (has links)
The focus in this thesis is on the calculations of an empirical null distributionfor likelihood ratio tests testing either separable or double separable covariancematrix structures versus an unstructured covariance matrix. These calculationshave been performed for various dimensions and sample sizes, and are comparedwith the asymptotic χ2-distribution that is commonly used as an approximative distribution. Tests of separable structures are of particular interest in cases when data iscollected such that more than one relation between the components of the observationis suspected. For instance, if there are both a spatial and a temporalaspect, a hypothesis of two covariance matrices, one for each aspect, is reasonable.
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Matriz de covariâncias do estimador de máxima verossimilhança corrigido pelo viés em modelos lineares generalizados com parâmetro de dispersão desconhecido. / Matrix of covariates of the bias-corrected maximum likelihood estimator in generalized linear models with unknown dispersion parameter.BARROS, Fabiana Uchôa. 27 July 2018 (has links)
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Previous issue date: 2011-12 / Capes / Com base na expressão de Pace e Salvan (1997 pág. 30), obtivemos a matriz de
covariâncias de segunda ordem dos estimadores de máxima verossimilhança corrigidos
pelo viés de ordem n−1 em modelos lineares generalizados, considerando o parâmetro
de dispersão desconhecido, porém o mesmo para todas as observações. A partir dessa
matriz, realizamos modi cações no teste de Wald. Os resultados obtidos foram avaliados
através de estudos de simulação de Monte Carlo. / Based on the expression of Pace and Salvan (1997 pág. 30), we obtained the
second order covariance matrix of the of the maximum likelihood estimators corrected
for bias of order n−1in generalized linear models, considering that the dispersion parameter is the same although unknown for all observations. From this matrix, we made
modi cations to the Wald test. The results were evaluated through simulation studies
of Monte Carlo.
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Aplicação de computação natural ao problema de estimação de direção de chegada / Application of natural computing to the problem of estimating the direction of arrivalBoccato, Levy, 1986- 07 December 2010 (has links)
Orientadores: Romis Ribeiro de Faissol Attux, Amauri Lopes / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-16T06:42:29Z (GMT). No. of bitstreams: 1
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Previous issue date: 2010 / Resumo: O problema de estimação de direção de chegada (DOA, em inglês direction of arrival ) de ondas planas que incidem sobre um arranjo linear uniforme de sensores, através do critério da máxima verossimilhança (ML, em inglês maximum likelihood), requer a minimização de uma função custo não-linear, não-quadrática, multimodal e variante com a relação sinal-ruído (SNR, em inglês signal-to-noise ratio). Esta dissertação trata da aplicação de algoritmos de computação natural como alternativa ao uso de métodos clássicos, como o MODE e o MODEX, os quais não são capazes de alcançar o desempenho do estimador ML em uma ampla faixa de valores de SNR. As simulações realizadas em diferentes cenários indicam que alguns dos algoritmos analisados conseguem estimar os ângulos de chegada adequadamente. Por fim, inspirados em uma proposta de filtragem de ruído dos dados recebidos, elaboramos uma maneira de realizar a amostragem no espaço de soluções candidatas: a resposta em frequência do filtro que produz a maior atenuação de ruído é empregada como função densidade de probabilidade no processo de amostragem. Os resultados obtidos atestam que este procedimento tende a aumentar a eficiência dos algoritmos estudados na estimação DOA / Abstract: The problem of estimating the direction of arrival (DOA) of plane waves impinging on a uniform linear array of sensors, through the maximum likelihood (ML) criterion, requires the minimization of a cost function that is non-linear, non-quadratic, multimodal and variant with the signal-to-noise ratio (SNR). This work deals with the application of natural computing algorithms as an alternative to the use of classical methods, such as MODE and MODEX, which are not capable of achieving the performance of the ML estimator in a wide range of SNR values. The simulations performed in different scenarios indicate that some of the studied algorithms can adequately estimate the angles of arrival. Finally, inspired by a proposal of noise filtering of the received data, we designed a procedure of sampling the search space: the frequency response of the filter which produces the maximal noise reduction is employed as the probability density function during the sampling process. The obtained results attest that this procedure tends to increase the efficiency of the considered algorithms in DOA estimation / Mestrado / Engenharia de Computação / Mestre em Engenharia Elétrica
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Contribuições à caracterização estatística do canal de rádio móvel e estimação de parâmetros por máxima verossimilhança / Contributions to the statistical characterization of mobile radio channel and parameter estimation by maximum likelihoodRibeiro, Antonio Marcelo Oliveira, 1970- 23 August 2018 (has links)
Orientador: Evandro Conforti / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-23T23:28:57Z (GMT). No. of bitstreams: 1
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Previous issue date: 2013 / Resumo: Os efeitos provocados pelo ambiente de propagação sobre o sinal transmitido, assim como as condições impostas pela mobilidade do receptor, afetam diretamente a qualidade de serviço em sistemas de comunicação sem fios. Portanto, é necessário compreender e analisar os efeitos de degradação que o canal terá sobre um dado sistema de comunicação de dados e, dessa forma, avaliar a necessidade de medidas para mitigar os eventuais efeitos prejudiciais do canal. Neste trabalho, apresenta-se uma caracterização estatística do canal de rádio móvel, a partir de medições em campo nas bandas de 1800, 2500 e 3500 MHz, através de uma técnica simples de aquisição da envoltória do sinal. Em particular, são calculadas, para a envoltória, funções de distribuição de probabilidade, taxas de cruzamentos, duração de desvanecimento e sua distribuição, funções de correlação espacial e em frequência, tempo de coerência e largura de banda de coerência. Realiza-se, igualmente, uma análise comparativa destes resultados com os seguintes modelos estatísticos: Rayleigh, Nakagami, Rice, Weibull, Hoyt (Nakagami-q) e ?-?. Além disso, é dada ênfase à estimação de parâmetros dos modelos de canal de rádio, através de dois métodos: momentos (MoM) e máxima verossimilhança (ML). Neste contexto, obtém-se expressões para a variância e o intervalo de confiança, assintóticos, de estimadores ML, baseadas na informação de Fisher que uma amostra aleatória contém a respeito do parâmetro a ser estimado. De forma geral, foi observado um bom ajuste entre as medidas em campo e correspondentes curvas teóricas, para estatísticas de primeira e segunda ordem da envoltória. As medições em campo deste trabalho mostraram que os estimadores ML agruparam mais as curvas teóricas, em torno da curva experimental, quando comparados aos estimadores MoM. Adicionalmente, a matriz de covariância dos estimadores ML para ? e ?, obtida a partir das medições em campo, mostrou que a variância do estimador de ? é, pelo menos, dez vezes maior que aquela do estimador de ?. Igualmente, valores medidos de correlação espacial apresentaram bom ajuste aos modelos teóricos, em termos de uma tendência geral de variação. Em particular, curvas de distribuição cumulativa do tempo de coerência, , para medidas em campo em 3500MHz, mostraram que é maior que 1,7 ms, para 90% do tempo, quando o receptor se move a 30 km/h. Por fim, medidas em campo da largura de banda de coerência, em 1800MHz, revelaram que um valor de ?f < 60 kHz irá garantir um nível de correlação da envoltória maior que 0,9, para 90% do tempo / Abstract: The propagation environment effects on the transmitted signal as well as the conditions imposed by the receiver mobility directly affect the quality of service (QoS) in wireless communication systems. Therefore, it is necessary to understand and analyze the degradation effects inflicted by the channel on a given data communication system, in order to evaluate the measures to mitigate these deleterious effects. In this thesis, we present a statistical characterization of the mobile radio channel based on field measurements performed over the 1800, 2500, and 3500 MHz bands, using a simple technique for acquiring the signal envelope. In particular, envelope statistics for probability distribution functions were calculated, as well as the crossing rates, duration of fading and its distribution, spatial and frequency correlation functions, coherence time, and coherence bandwidth. A comparative analysis of these results was also carried out against the following statistical models: Rayleigh, Nakagami, Rice, Weibull, Hoyt (Nakagami-q), and ?-?. Also, emphasis is given to the parameter estimation of radio channel models using two methods: moments (MoM) and maximum likelihood (ML). In this context, expressions for the asymptotic variance and confidence interval of ML estimators were obtained, based on the Fisher information a random sample contains over the parameter to be estimated. In general, there was a good fit between the field measurements and corresponding theoretical curves for envelope statistics of first and second order. Field measurements of this work have shown that ML estimators grouped more the theoretical curves around the experimental one, when compared to MoM estimators. Additionally, the covariance matrix of ML estimators for ? and ?, obtained from field measurements, showed that the variance of ? estimator is at least ten times greater than the one of ? estimator. Moreover, measured values of spatial correlation showed a good .t to the theoretical models, in terms of a general tendency of variation. Particularly, cumulative distribution curves of the coherence time , for field measurements at 3500MHz, showed that is greater than 1,7 ms for 90% of time when the receiver is moving at 30 km/h. Finally, 1800- MHz field measurements of coherence bandwidth revealed that a value of ?f < 60 kHz will ensure a level of envelope correlation greater than 0.9 for 90% of time / Doutorado / Telecomunicações e Telemática / Doutor em Engenharia Elétrica
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Estimation statistique des paramètres pour les processus de Cox-Ingersoll-Ross et de Heston / Statistical inference for the parameters of the Cox-Ingersoll-Ross process and the Heston processDu Roy de Chaumaray, Marie 02 December 2016 (has links)
Les processus de Cox-Ingersoll-Ross et de Heston jouent un rôle prépondérant dans la modélisation mathématique des cours d’actifs financiers ou des taux d’intérêts. Dans cette thèse, on s’intéresse à l’estimation de leurs paramètres à partir de l’observation en temps continu d’une de leurs trajectoires. Dans un premier temps, on se place dans le cas où le processus CIR est géométriquement ergodique et ne s’annule pas. On établit alors un principe de grandes déviationspour l’estimateur du maximum de vraisemblance du couple des paramètres de dimension et de dérive d’un processus CIR. On établit ensuite un principe de déviations modérées pour l’estimateur du maximum de vraisemblance des quatre paramètres d’un processus de Heston, ainsi que pour l’estimateur du maximum de vraisemblance du couple des paramètres d’un processus CIR. Contrairement à ce qui a été fait jusqu’ici dans la littérature,les paramètres sont estimés simultanément. Dans un second temps, on ne se restreint plus au cas où le processus CIR n’atteint jamais zéro et on propose un nouvel estimateur des moindres carrés pondérés pour le quadruplet des paramètres d’un processus de Heston.On établit sa consistance forte et sa normalité asymptotique, et on illustre numériquement ses bonnes performances. / The Cox-Ingersoll-Ross process and the Heston process are widely used in financial mathematics for pricing and hedging or to model interest rates. In this thesis, we focus on estimating their parameters using continuous-time observations. Firstly, we restrict ourselves to the most tractable situation where the CIR processis geometrically ergodic and does not vanish. We establish a large deviations principle for the maximum likelihood estimator of the couple of dimensionnal and drift parameters of a CIR process. Then we establish a moderate deviations principle for the maximum likelihood estimator of the four parameters of an Heston process, as well as for the maximum likelihood estimator of the couple of parameters of a CIR process. In contrast to the previous literature, parameters are estimated simultaneously. Secondly, we do not restrict ourselves anymore to the case where the CIR process never reaches zero and we introduce a new weighted least squares estimator for the quadruplet of parameters of an Heston process. We establish its strong consitency and asymptotic normality, and we illustrate numerically its good performances.
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Analyse statistique de quelques modèles de processus de type fractionnaire / Statistical analysis of some models of fractional type processCai, Chunhao 18 April 2014 (has links)
Cette thèse porte sur l’analyse statistique de quelques modèles de processus stochastiques gouvernés par des bruits de type fractionnaire, en temps discret ou continu.Dans le Chapitre 1, nous étudions le problème d’estimation par maximum de vraisemblance (EMV) des paramètres d’un processus autorégressif d’ordre p (AR(p)) dirigé par un bruit gaussien stationnaire, qui peut être à longue mémoire commele bruit gaussien fractionnaire. Nous donnons une formule explicite pour l’EMV et nous analysons ses propriétés asymptotiques. En fait, dans notre modèle la fonction de covariance du bruit est supposée connue, mais le comportement asymptotique de l’estimateur (vitesse de convergence, information de Fisher) n’en dépend pas.Le Chapitre 2 est consacré à la détermination de l’entrée optimale (d’un point de vue asymptotique) pour l’estimation du paramètre de dérive dans un processus d’Ornstein-Uhlenbeck fractionnaire partiellement observé mais contrôlé. Nous exposons un principe de séparation qui nous permet d’atteindre cet objectif. Les propriétés asymptotiques de l’EMV sont démontrées en utilisant le programme d’Ibragimov-Khasminskii et le calcul de transformées de Laplace d’une fonctionnellequadratique du processus.Dans le Chapitre 3, nous présentons une nouvelle approche pour étudier les propriétés du mouvement brownien fractionnaire mélangé et de modèles connexes, basée sur la théorie du filtrage des processus gaussiens. Les résultats mettent en lumière la structure de semimartingale et mènent à un certain nombre de propriétés d’absolue continuité utiles. Nous établissons l’équivalence des mesures induites par le mouvement brownien fractionnaire mélangé avec une dérive stochastique, et en déduisons l’expression correspondante de la dérivée de Radon-Nikodym. Pour un indice de Hurst H > 3=4, nous obtenons une représentation du mouvement brownien fractionnaire mélangé comme processus de type diffusion dans sa filtration naturelle et en déduisons une formule de la dérivée de Radon-Nikodym par rapport à la mesurede Wiener. Pour H < 1=4, nous montrons l’équivalence de la mesure avec celle la composante fractionnaire et obtenons une formule pour la densité correspondante. Un domaine d’application potentielle est l’analyse statistique des modèles gouvernés par des bruits fractionnaires mélangés. A titre d’exemple, nous considérons le modèle de régression linéaire de base et montrons comment définir l’EMV et étudié son comportement asymptotique. / This thesis focuses on the statistical analysis of some models of stochastic processes generated by fractional noise in discrete or continuous time.In Chapter 1, we study the problem of parameter estimation by maximum likelihood (MLE) for an autoregressive process of order p (AR (p)) generated by a stationary Gaussian noise, which can have long memory as the fractional Gaussiannoise. We exhibit an explicit formula for the MLE and we analyze its asymptotic properties. Actually in our model the covariance function of the noise is assumed to be known but the asymptotic behavior of the estimator ( rate of convergence, Fisher information) does not depend on it.Chapter 2 is devoted to the determination of the asymptotical optimal input for the estimation of the drift parameter in a partially observed but controlled fractional Ornstein-Uhlenbeck process. We expose a separation principle that allows us toreach this goal. Large sample asymptotical properties of the MLE are deduced using the Ibragimov-Khasminskii program and Laplace transform computations for quadratic functionals of the process.In Chapter 3, we present a new approach to study the properties of mixed fractional Brownian motion (fBm) and related models, based on the filtering theory of Gaussian processes. The results shed light on the semimartingale structure andproperties lead to a number of useful absolute continuity relations. We establish equivalence of the measures, induced by the mixed fBm with stochastic drifts, and derive the corresponding expression for the Radon-Nikodym derivative. For theHurst index H > 3=4 we obtain a representation of the mixed fBm as a diffusion type process in its own filtration and derive a formula for the Radon-Nikodym derivative with respect to the Wiener measure. For H < 1=4, we prove equivalenceto the fractional component and obtain a formula for the corresponding derivative. An area of potential applications is statistical analysis of models, driven by mixed fractional noises. As an example we consider only the basic linear regression setting and show how the MLE can be defined and studied in the large sample asymptotic regime.
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Modelos de regressão beta inflacionados truncados / The truncated inflated beta regressionPereira, Gustavo Henrique de Araujo 24 May 2012 (has links)
Os modelos de regressão beta e beta inflacionados conseguem ajustar adequadamente grande parte das variáveis do tipo proporção. No entanto, esses modelos não são úteis quando a variável resposta não pode assumir valores no intervalo (0,c) e assume o valor c com probabilidade positiva. Variáveis relacionadas a algum tipo de pagamento limitado entre dois valores, quando estudadas em relação ao seu valor máximo, possuem essas características. Para ajustar essas variáveis, introduzimos a distribuição beta inflacionada truncada (BIZUT), que é uma mistura de uma distribuição beta com suporte no intervalo (c,1) e uma distribuição trinomial que assume os valores zero, um e c. Propomos ainda um modelo de regressão para as situações em que a variável resposta tem distribuição BIZUT. Admitimos que todos os parâmetros da distribuição podem variar em função de variáveis preditoras. Além disso, o modelo permite que o parâmetro conhecido c varie entre as unidades populacionais. Para esse modelo são desenvolvidos diversos aspectos inferenciais, são obtidos resultados para as situações em que c é variável e são conduzidos estudos de simulação de Monte Carlo. Além disso, discutimos análise de resíduos, desenvolvemos análise de influência local e realizamos uma aplicação a dados reais de cartão de crédito. / The beta regression model or the inflated beta regression model may be a reasonable choice to fit a proportion in most situations. However, they do not fit well variables that do not assume values in the open interval (0,c), 0 < c < 1 and assume the c value with positive probability. Variables related to a kind of double bounded payment amount when studied as a proportion of the maximum payment amount have this feature. For these variables, we introduce the truncated inflated beta distribution (TBEINF). This proposed distribution is a mixture of the beta distribution bounded in the open interval (c,1) and a trinomial distribution that assumes the values zero, one and c. This work also proposes a regression model where the response variable is TBEINF distributed. The model allows all the unknown parameters of the conditional distribution of the response variable to be modeled as functions of explanatory variables. Moreover, the model allows nonconstant known parameter c across population units. For this model, some inferential aspects are developed, some results when c is not constant are obtained and Monte Carlo simulation studies are performed. In addition, residual and local influence analysis are discussed and an application to credit card data is presented.
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Modelos de regressão beta inflacionados truncados / The truncated inflated beta regressionGustavo Henrique de Araujo Pereira 24 May 2012 (has links)
Os modelos de regressão beta e beta inflacionados conseguem ajustar adequadamente grande parte das variáveis do tipo proporção. No entanto, esses modelos não são úteis quando a variável resposta não pode assumir valores no intervalo (0,c) e assume o valor c com probabilidade positiva. Variáveis relacionadas a algum tipo de pagamento limitado entre dois valores, quando estudadas em relação ao seu valor máximo, possuem essas características. Para ajustar essas variáveis, introduzimos a distribuição beta inflacionada truncada (BIZUT), que é uma mistura de uma distribuição beta com suporte no intervalo (c,1) e uma distribuição trinomial que assume os valores zero, um e c. Propomos ainda um modelo de regressão para as situações em que a variável resposta tem distribuição BIZUT. Admitimos que todos os parâmetros da distribuição podem variar em função de variáveis preditoras. Além disso, o modelo permite que o parâmetro conhecido c varie entre as unidades populacionais. Para esse modelo são desenvolvidos diversos aspectos inferenciais, são obtidos resultados para as situações em que c é variável e são conduzidos estudos de simulação de Monte Carlo. Além disso, discutimos análise de resíduos, desenvolvemos análise de influência local e realizamos uma aplicação a dados reais de cartão de crédito. / The beta regression model or the inflated beta regression model may be a reasonable choice to fit a proportion in most situations. However, they do not fit well variables that do not assume values in the open interval (0,c), 0 < c < 1 and assume the c value with positive probability. Variables related to a kind of double bounded payment amount when studied as a proportion of the maximum payment amount have this feature. For these variables, we introduce the truncated inflated beta distribution (TBEINF). This proposed distribution is a mixture of the beta distribution bounded in the open interval (c,1) and a trinomial distribution that assumes the values zero, one and c. This work also proposes a regression model where the response variable is TBEINF distributed. The model allows all the unknown parameters of the conditional distribution of the response variable to be modeled as functions of explanatory variables. Moreover, the model allows nonconstant known parameter c across population units. For this model, some inferential aspects are developed, some results when c is not constant are obtained and Monte Carlo simulation studies are performed. In addition, residual and local influence analysis are discussed and an application to credit card data is presented.
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3D conformal antennas for radar applications / Antennes 3D et conformes pour des applications radarsFourtinon, Luc 15 December 2017 (has links)
Embarqué sous le radôme du missile, les autodirecteurs existants utilisent une rotation mécanique du plan d’antenne pour balayer le faisceau en direction d’une cible. Les recherches actuelles examinent le remplacement des composantes mécaniques de rotation de l’antenne par un nouveau réseau d’antennes 3D conformes à balayage électronique. Les antennes 3D conformes pourraient offrir des avantages significatifs, tels qu’un balayage plus rapide et une meilleure couverture angulaire mais qui pourraient aussi offrir de nouveaux challenges résultant d’un diagramme de rayonnement plus complexes en 3D qu’en 2D. Le nouvel autodirecteur s’affranchit du système mécanique de rotation ce qui libère de l’espace pour le design d’une nouvelle antenne 3D conforme. Pour tirer le meilleur parti de cet espace, différentes formes de réseaux sont étudiées, ainsi l’impact de la position, de l’orientation et de la conformation des éléments est établi sur les performances de l’antenne, en termes de directivité, ellipticité et de polarisation. Pour faciliter cette étude de réseaux 3D conformes, un programme Matlab a été développé, il permet de générer rapidement le diagramme de rayonnement en polarisation d’un réseau donné dans toutes les directions. L’une des tâches de l’autodirecteur consiste à estimer la position d’une cible donnée afin de corriger la trajectoire du missile. Ainsi, l’impact de la forme du réseau sur l’erreur entre la direction d’arrivée mesurée de l’écho de la cible et sa vraie valeur est analysé. La borne inférieure de Cramer-Rao est utilisée pour calculer l’erreur minimum théorique. Ce modèle suppose que chaque élément est alimenté séparément et permet ainsi d’évaluer le potentiel des réseaux 3D conformes actifs.Finalement, l’estimateur du monopulse en phase est étudié pour des réseaux 3D conformes dont les quadrants n’auraient pas les mêmes caractéristiques. Un nouvel estimateur, plus adapté à des quadrants non identiques, est aussi proposé. / Embedded below the radome of a missile, existing RF-seekers use a mechanical rotating antenna to steer the radiating beam in the direction of a target. Latest research is looking at replacing the mechanical antenna components of the RF-seeker with a novel 3D conformal antenna array that can steer the beam electronically. 3D antennas may offer significant advantages, such as faster beam steering and better coverage but, at the same time, introduce new challenges resulting from a much more complex radiation pattern than that of 2D antennas. Thanks to the mechanical system removal, the new RF-seeker has a wider available space for the design of a new 3D conformal antenna. To take best benefits of this space, different array shapes are studied, hence the impact of the position, orientation and conformation of the elements is assessed on the antenna performance in terms of directivity, ellipticity and polarisation. To facilitate this study of 3D conformal arrays, a Matlab program has been developed to compute the polarisation pattern of a given array in all directions. One of the task of the RF-seeker consists in estimating the position of a given target to correct the missile trajectory accordingly. Thus, the impact of the array shape on the error between the measured direction of arrival of the target echo and its true value is addressed. The Cramer-Rao lower bound is used to evaluate the theoretical minimum error. The model assumes that each element receives independently and allows therefore to analyse the potential of active 3D conformal arrays. Finally, the phase monopulse estimator is studied for 3Dconformal arrays whose quadrants do not have the same characteristics. A new estimator more adapted to non-identical quadrants is also proposed.
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