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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Este trabalho trata da proposiÃÃo de algoritmos para equalizaÃÃo cega de canais lineares e nÃao-lineares inspirados no Algoritmo do MÃdulo Constante (CMA). O CMA funciona de maneira bastante eficiente com constelaÃÃes nas quais todos os pontos possuem a mesma amplitude, como em modulaÃÃes do tipo Phase Shift Keying (PSK). Entretanto, quando os pontos da constelaÃÃo podem assumir diferentes valores de amplitudes, como em modulaÃÃes do tipo Quadrature Amplitude Modulation (QAM), o CMA e seus derivados muitas vezes nÃo funcionam de forma satisfatÃria. Desta forma, as tÃcnicas aqui propostas sÃo projetadas para melhorar a performance do CMA em termos de velocidade de convergÃncia e precisÃo, quando operando em sinais transmitidos com diversos mÃdulos, em particular para a modulaÃÃo QAM. Assim como o CMA, para possuir um bom apelo prÃtico, essas tÃcnicas devem apresentar bom compromisso entre complexidade, robustez e desempenho. Para tanto, as tÃcnicas propostas utilizam o Ãltimo sÃmbolo decidido para definir uma estimaÃÃo de raio de referÃncia para a saÃda do equalizador. De fato, esses algoritmos podem ser vistos como generalizaÃÃes do CMA e de alguns derivados do CMA para constelaÃÃes com mÃltiplos raios. A proposiÃÃo de algoritmos do tipo gradiente estocÃstico à concluÃda com o desenvolvimento de tÃcnicas originais, baseadas no CMA, para equalizaÃÃo de canais do tipo Wiener, que consiste em um filtro linear com memÃria, seguido por um filtro nÃo-linear sem memÃria. As expressÃes para a adaptaÃÃo do equalizador sÃo encontradas com o auxÃlio de uma notaÃÃo unificada para trÃs diferentes estruturas: i) um filtro de Hammerstein; ii) um filtro de Volterra diagonal; e iii) um filtro de Volterra completo. Um estudo teÃrico acerca do comportamento do principal algoritmo proposto, o Decision Directed Modulus Algorithm (DDMA) à realizado. SÃo analisadas a convergÃncia e a estabilidade do algoritmo atravÃs de uma anÃlise dos pontos de mÃnimo de sua funÃÃo custo. Outro objetivo à encontrar o valor teÃrico do Erro MÃdio QuadrÃtico MÃdio em Excesso - Excess Mean Square Error (EMSE) fornecido pelo DDMA considerando-se o caso sem ruÃdo. Ao final, à feito um estudo em que se constata que o algoritmo DDMA possui fortes ligaÃÃes com a soluÃÃo de Wiener e com o CMA. VersÃes normalizadas, bem como versÃes do tipo Recursive Least Squares (RLS), dos algoritmos do tipo gradiente estocÃstico estudados sÃo tambÃm desenvolvidas. Cada famÃlia de algoritmos estudada fie composta por quatro algoritmos com algumas propriedades interessantes e vantagens sobre as tÃcnicas clÃssicas, especialmente quando operando em sinais QAM de ordem elevada. TambÃm sÃo desenvolvidas versÃes normalizadas e do tipo RLS dos algoritmos do tipo CMA estudados para equalizaÃÃo de canais nÃo-lineares. O comportamento de todas as famÃlias de algoritmos desenvolvidos à testado atravÃs de simulaÃÃes computacionais, em que à verificado que as tÃcnicas propostas fornecem ganhos significativos em desempenho, em termos de velocidade de convergÃncia e erro residual, em relaÃÃo Ãs tÃcnicas clÃssicas. / This work studies and proposes algorithms to perform blind equalization of linear and nonlinear channels inspired on the Constant Modulus Algorithm (CMA). The CMA works very well for modulations in which all points of the signal constellation have the same radius, like in Phase Shift Keying (PSK) modulations. However, when the constellation points are characterized by multiple radii, like in Quadrature Amplitude Modulation (QAM) signals, the CMA does not work properly in many situations. Thus, the techniques proposed here are designed to improve the performance of the CMA, in terms of speed of convergence and residual error, when working with signals transmitted with multiple magnitude, in particular with QAM signals. As well as for the CMA, these techniques should have a good compromise among performance, complexity and robustness. To do so, the techniques use the last decided symbol to estimate reference radius to the output of the equalizer. In fact, they can be seen as modifications of the CMA and of some of its derivatives for constellations with multiple radii. The proposition of stochastic gradient algorithms is concluded with the development of new adaptive blind techniques to equalize channels with a Wiener structure. A Wiener filter consists of a linear block with memory followed by a memoryless nonlinearity, by using the CMA. We develop expressions for the adaptation of the equalizer using a unified notation for three different equalizer filter structures: i) a Hammerstein filter, ii) a diagonal Volterra filter and iii) a Volterra filter. A theoretical analysis of the main proposed technique, the Decision Directed Modulus Algorithm (DDMA), is also done. We study the convergence and the stability of the DDMA by means of an analysis of the minima of the DDM cost function. We also develop an analytic expression for the Excess Mean Square Error (EMSE) provided by the DDMA in the noiseless case. Then, we nd some interesting relationships among the DDM, the CM and the Wiener cost functions. We also develop a class of normalized algorithms and a class of Recursive Least Squares (RLS)-type algorithms for blind equalization inspired on the CMA-based techniques studied. Each family is composed of four algorithms with desirable properties and advantages over the original CM algorithms, specially when working with high-level QAM signals. Normalized and RLS techniques for equalization of Wiener channels are also developed. The behavior of the proposed classes of algorithms discussed is tested by computational simulations. We verify that the proposed techniques provide significative gains in performance, in terms of speed of convergence and residual error, when compared to the classical algorithms.

With the expected growth of Unmanned Aerial Vehicle (UAV) traffic in the coming years, the demand for UAV tracking solutions in the Air Traffic Control (ATC) industry has been incentivized. To ensure the safe integration of UAVs into airspace, Air Traffic Management (ATM) systems will need to provide a number of services such as UAV tracking. The Interacting Multiple Model Extended Kalman Filter (IMM-EKF) is an industry standard for aircraft tracking, but no such algorithm has been tried and tested for UAV tracking. This thesis aims to determine a suitable tracking algorithm for the specific case of non-cooperative tracking of UAVs from radar data. In non-cooperative tracking scenarios, we do not have any information regarding the UAV other than radar measurements indicating the target’s position. We investigate an Adaptive Interacting Multiple Model Unscented Kalman Filter (IMM-UKF) method with three different motion model combinations in addition to comparing a Cartesian vs. Spherical measurement model. A comparison of motion models shows that using a Constant Jerk (CJ) model to model target maneuvers in the IMM structure reduces the risk of filter divergence as compared to using a turn model, such as Constant Turn (CT) or Constant Angular Velocity (CAV). The CJ model is thus a suitable choice to have as one of the motion models in an IMM structure and works well in conjunction with two Constant Velocity (CV) models. We were not able to determine if the Spherical measurement model is better than the Cartesian measurement model in general. However, the Spherical measurement model improves the accuracy of the state estimate in some cases. Adaptive tuning of the system noise covariance Q and measurement noise covariance R does not improve the accuracy of the state estimate but it improves the filter robustness and consistency when the filter is incorrectly tuned. Based on our results, we believe that the adaptive IMM-UKF shows promise but that there is still room for improvement with regards to both the accuracy and consistency. However, we will need to perform extensive tests with real UAV radar data to draw concrete conclusions. / Med den förväntade tillväxten av trafik med obemannade flygfordon (UAV) under de kommande åren kommer efterfrågan för spårningslösningar för UAV inom flygövervakning. För att säkerställa en säker integration av UAV:er i luftrummet, kommer Air Traffic Management (ATM)-system att behöva tillhandahålla tjänster för UAV-spårning. Det så kallade Interacting Multiple Model Extended Kalman Filter (IMM-EKF) filtret är en industristandard spårning av flygplan, men ingen sådan algoritm har prövats och testats för UAV-spårning. Denna avhandling syftar till att fastställa en lämplig spårningsalgoritm för det specifika fallet med icke samarbetande spårning av UAV från radardata. I icke samarbetande spårningsscenarier har vi ingen information om UAV:n utöver radarmätningar. Vi presenterar en adaptiv metod baserad på IMM-UKF, där vi ersätter EKF i industristandarden IMM-EKF med ett filter av typen UKF. Vi undersöker tre olika kombinationer av rörelsemodeller och jämför också en kartesisk med en sfärisk mätmodell. Vår jämförelse av rörelsemodeller visar om man använder en Constant Jerk (CJ) modell för manövrar i IMM-strukturen minskar risken för divergens jämfört med att använda en svängmodell, såsom Constant Turn (CT) eller Constant Angular Velocity (CAV). CJ-modellen är alltså ett lämpligt val att ha som en av rörelsemodellerna i en IMM-struktur och fungerar bra i kombination med två Constant Velocity (CV) modeller. Vi kunde inte avgöra om den sfäriska modellen var bättre än den kartesiska modellen. Adaptiv inställning av systembrusets kovarians Q och mätbrus kovarians R förbättrar inte tillståndsuppskattningens noggrannhet men den förbättrar filtrets robusthet och konsistens när filtret är felaktigt inställt. Baserat på våra resultat tror vi att den adaptiva IMM-UKF metoden är lovande men att det fortfarande finns utrymme för förbättringar när det gäller både noggrannhet och konsistens i spårningen. Vi kommer dock att behöva utföra omfattande tester med riktiga UAV-radardata för att dra konkreta slutsatser.