Applications such as urban surveillance, search and rescue, agricultural applications, military applications, etc., require miniature air vehicles (MAVs) to fly for a long time. But they have restricted flight duration due to their dependence on battery life, which necessitates optimal path planning. The generated optimal path should obey the curvature limits prescribed by the minimum turn radius/ maximum turn rate of the MAV. Further, in a dynamically changing environment, the final configuration that the MAV has to achieve may change en route, which demands the path to be replanned by an airborne processor in real-time. As MAVs are small in size and light in weight, wind has a very significant effect on the flight of MAVs and the computation of the minimum-time path in the presence of wind plays an important role. The thesis develops feasible trajectory generation algorithms which are fast, efficient, optimal and implementable in an onboard computer for rectilinear and circular path convergence problems and waypoint following problems both in the absence and in the presence of wind. The first part of the thesis addresses the problem of computation of optimal trajectories when MAVs fly on a two-dimensional (2D) plane maintaining a constant altitude. The shortest path is computed for MAVs from a given initial position and orientation to a given final path with a specified direction as required for a given mission. Unlike the classical Dubins problem where the shortest path was computed between two given configurations (position and orientation), the final point in this case is not specified. However, the final path, which can either be a rectilinear path or a circular path, and the direction to which the MAV should converge, is specified. The time-optimal path of MAVs is developed in the presence of wind mainly using the geometric approach although a few important properties are also obtained using optimal control theory, specifically, Pontryagin’s minimum principle (which provides only the necessary condition for optimality) for control-constrained systems. The complete optima l solution to this problem in all its generality is a major contribution of this thesis as existing methods in the literature that address this problem are either not optimal or do not give a complete solution. Further, the time-optimal path for specified initial and final configurations is generated in reasonably short time without computing all the path lengths of possible candidate paths, which is the method that exists in the literature for similar problems. Simulation results illustrate path generation for various cases, including the presence of steady and time-varying wind. Another problem in MAV path planning in 2D addressed in this thesis computes an extremal path that transitions between two consecutive waypoint segments (obtained by joining two way points in sequence) in a time-optimal fashion. This designed trajectory, named as γ-trajectory, is also used to track the maximum portion of waypoint segments in minimum time and the shortest distance between this trajectory and the associated waypoint can be set to a desired value. Another optimal path, called the loop trajectory, that goes through the way points as well as through the entire waypoint segments, is also proposed. Subsequently, the thesis proposes algorithms to generate trajectories in the presence of steady wind and compares these with the optimal trajectory generated using nonlinear programming based multiple shooting method to show that the generated paths are optimal in most cases. In three-dimensional (3D) space, if the initial and final configurations – in terms of (X,Y,Z) position, heading angle and flight path angle- of the vehicle are specified then shortest path computation is an interesting problem in literature. The proposed method in this thesis is based on 3D geometry and, unlike the existing iterative methods which yield suboptimal paths and are computationally more intensive, this method generates the shortest path in much less time. Due to its simplicity and low computational requirements, this approach can be implemented on a MAV in real-time. But, If the path demands very high pitch angle (as in the case of steep climbs), the generated path may not be flyable for an aerial vehicle with limited range of flight path angles. In such cases numerical methods, such as multiple shooting, coupled with nonlinear programming, are used to obtain the optimal solution. The time-optimal 3D path is also developed in the presence of wind which has a magnitude comparable to the speed of MAVs. The simulation results show path generation for a few sample cases to show the efficacy of the proposed approach as compared to the available approach in the literature. Next, the path convergence problem is studied in 3D for MAVs. The shortest path is generated to converge to a rectilinear path and a circular path starting from a known initial position and orientation. The method is also extended to compute the time-optimal path in the presence of wind. In simulation, optimal paths are generated for a variety of cases to show the efficacy of the algorithm. The other problem discussed in this thesis considers curvature-constrained trajectory generation technique for following a series of way points in 3D space. Extending the idea used in 2D, a γ-trajectory in 3D is generated to track the maximum portion of waypoint segments with a desired shortest distance between the trajectory and the associated waypoint. Considering the flyability issue of the plane a loop-trajectory is generated which is flyable by a MAV with constrained flight path angle. Simulation results are given for illustrative purposes. The path generation algorithms are all based on a kinematic model, considering the vehicle as a point in space. Implementing these results in a real MAV will require the dynamics of the MAV to be considered. So, a 6-DOF SIMULINK model of a MAV is used to demonstrate the tracking of the computed paths both in 2D plane and in 3D space using autopilots consisting of proportional-integral-derivative (PID )controllers .Achieving terminal condition accurately in real-time, if there is noisy measurement of wind data, is also addressed.

Le récepteur SAIC/MAIC introduit récemment est capable de séparer jusqu'à 2N utilisateurs synchronisés avec N antennes pour les réseaux de radiocommunications utilisant des modulations rectilignes ou quasi-rectilignes. Un tel récepteur, opérationnel dans les téléphones GSM depuis 2006, exploite la non-circularité du second ordre des signaux et met en œuvre un filtre optimal linéaire au sens large (widely linéaire WL). Il s'est montré performant pour les utilisateurs synchrones en absence de résidu de porteuse (l'effet doppler par exemple), mais son comportement en présence d'utilisateurs asynchrones ayant des résidus de porteuse potentiellement non nuls, omniprésents dans de nombreuses applications radio, n'a pas encore fait l'objet d'études théoriques, ce qui ne permet pas d'en connaître les dégradations. Le but de la 1e partie de ce travail consiste à présenter une analyse des performances du SAIC/MAIC, implanté via une approche MMSE avec séquence d'apprentissage, en présence de deux utilisateurs non nécessairement synchronisés et ayant des dérives de fréquence. Pour simplifier, nous avons limité l'analyse théorique à quelques cas particuliers avec des modulations rectilignes. Ainsi des expressions analytiques simples et interprétables ont été données et analysées. Nous avons prouvé que les performances sont moins dégradées dans le cas d'une dérive sur l'utile qu'en présence d'une dérive sur le brouilleur. En outre, la dégradation augmente avec la désynchronisation des deux signaux. Afin de préciser le domaine de validité des approximations analytiques, des illustrations numériques ont été réalisées en prenant comme paramètres ceux du standard GSM dans le but d'appliquer cette étude à ce standard et aux réseaux cellulaires. L'extension de l'analyse aux modulations quasi-rectilignes a nécessité la mise en œuvre d'un filtrage spatio-temporel. Nous avons ainsi étudié l'impact de la taille du filtre spatio-temporel sur les performances du MMSE SAIC/MAIC pour des modulations quasi-rectilignes (MSK et GMSK) en présence de résidus de porteuse. L'étude révèle qu'avec des résidus de porteuse standards, ce récepteur reste relativement robuste et ne nécessite pas de compensation. La 2e partie de ce travail considère des canaux sélectifs en fréquence et consiste à développer un SIMO MLSE pour un signal utile à modulation linéaire quelconque en présence de bruit additif gaussien centré stationnaire coloré temporellement et spatialement et potentiellement non circulaire, en partant d'un problème général de détection d'une forme d'onde. Nous avons démontré que le SIMO MLSE est constitué d'un filtre WL, d'un échantillonneur au rythme symbole et d'une minimisation récursive d'une métrique qui peut se mettre en oeuvre par l'algorithme de Viterbi. Le cas des modulations quasi rectilignes a aussi été considéré. Dans ce cadre, nous avons démontré que le SIMO MLSE a la même structure moyennant un prétraitement de dérotation. Tous ces filtres WL sont interprétés comme des filtres WL adaptés multidimensionnels (WL MMF) au sens où ils maximisent le rapport SNR sur le symbole courant en sortie. Nous avons ensuite étendu la structure du MLSE développée au cas d'un bruit gaussien non circulaire mais cyclostationnaire, de manière à se rapprocher des applications cellulaires. Nous appelons ce nouveau récepteur "pseudo-MLSE" car sa structure a été imposée. En conjecturant que les performances en probabilité d'erreur par symbole sont directement reliées au SNR sur le symbole courant, des expressions générales de celui-ci ont été données pour des MLSE et pseudo-MLSE dans le cadre d'interférences stationnaires et cyclostationnaires potentiellement non circulaires. Des formules interprétables de ces SNR ont été données dans des cas particuliers et des simulations numériques ont été présentées pour montrer les gains en performance des récepteurs introduits par rapport aux MLSE classiques dérivés sous hypothèse de bruit stationnaire circulaire / The SAIC/MAIC (Single/Multiple Antenna Interference Cancellation) receiver, recently introduced, is able to separate up to 2N synchronous users with N antennas for the radiocommunications networks using rectilinear or quasi-rectilinear modulations. A such receiver, operational in GSM handsets since 2006, exploits the second order non-circularity of signals and gives rise to an optimal widely linear (WL) filter. This receiver has been shown to be powerful for synchronous users without any frequency offsets (for example Doppler shift), but its behaviour in the presence of asynchronous users having potentially non zero carrier residues, omnipresent in many radio applications, has not yet been the subject of theoretical studies, which doesn't allow us to know their damage. For this reason, the purpose of the first part of this work is to present an analysis of SAIC/MAIC receiver performances, implemented via an MMSE approach with training sequence, with two users not necessarily synchronized with frequency shifts. To simplify the analytical developments, we limited the theoretical analysis to some particular cases with rectilinear modulations. Hence, simple and interpretable analytical expressions were given and analyzed. We proved in particular that the performance is less degraded in the case of a shift on the useful than in the presence of a drift on the jammer. Furthermore, the degradation increases with desynchronization of the two signals. To precise the range of validity of analytical approximations, numerical illustrations were made using as parameters those of the GSM standard in order to apply this study to this standard in particular and cellular networks in general. Extending the analysis to quasi-rectilinear modulations had required the implementation of a spatio-temporal filtering. We have studied the impact of the size of the spatio-temporal filter on the performance of MMSE SAIC/MAIC receiver for quasi-rectilinear modulations (GMSK and MSK) in the presence of residual frequencies. The study reveals that with standard carrier residues, this receiver remains relatively robust and doesn't require a compensation. The second part of this work considers frequency-selective channels and is developing a SIMO MLSE receiver for a useful signal with any linear modulation in the presence of an additive Gaussian centered stationary temporally and spatially colored and potentially non-circular noise, starting from a general problem of detection of a waveform. We have shown that SIMO MLSE receiver consists of a WL filter, a sampler at the symbol rate and a recursive minimization of a metric that can be solved by the Viterbi algorithm. The case of quasi-rectilinear modulations is also considered. Within this framework, we had proved that the SIMO MLSE receiver has the same structure through a postreatment derotation. All these filters are interpreted as WL multidimensional matched filters (WL MMF) in the sense that they maximize the SNR of the current symbol at output. Then, we extended the MLSE receiver structure developed in case of a noncircular gaussian noise but this time cyclostationary, so as to approximate radio cellular applications. We call this new receiver "pseudo-MLSE" because its structure was imposed. By conjecturing that the performances by per symbol error probability are directly related to the SNR of the current symbol, general expressions of this SNR are given for MLSE and pseudo MLSE receivers with stationary and cyclostationary potentially noncircular interferences. Interpretable formulas of these SNR were given in special cases and numerical simulations were presented to show performance gains of the receivers we have introduced relative to conventional MLSE receivers derived under the assumption of circular stationary noise