A mathematical model of a discrete sequential search for a target moving in discrete space is given. The model is based on a Bayesian updating algorithm giving successive probability distributions of target position at intervals throughout the search. Updating allows for target movement and for negative information gained from unsuccessful search. The search is conducted by taking a sequence of discrete, instantaneous looks at chosen points, or nodes, of the search area. The sequence of chosen nodes is termed a strategy. The successive target position distributions allow the probability of detecting the target to be found for any strategy. The model is an improvement over previous discrete sequential search models with respect to the following points. Target movement between nodes of the search area is formulated in terms of statistical information of target speed and direction, which are likely to be known. The time interval between looks, and target movement during this time, are related to the distance travelled by the searcher between search nodes. Also, with each look, the searcher has a view of surrounding nodes as well as the chosen search node. Implementation of these refinements is aided by considering the search area to consist of a finite, isometric pattern of nodes. Optimisation of strategies with respect to both detection probability and detection probability per unit cost is considered, and a criterion given in each case to assist optimisation. However, in practice, these criteria are of limited use, and full optimisation can only be carried out in a limited range of cases. Restricting both the planning horizon of the optimisation process, and searcher travel distance, allows sub-optimal strategies to be found in a wider range of cases. Results suggest that the detection probability of strategies found under these restrictions is normally close to optimal.

Various unmanned missions deploy vehicles such as missiles, torpedoes, ground robots, and unmanned aerial vehicles. Guidance strategies for these vehicles aim to intercept a target point and satisfy additional objectives such as specifications on impact angle and interception time. Certain impact angles are crucial for a greater warhead effectiveness, and minimizing the interception time is important for vehicles with limited endurance time and for reducing the probability of detection. This thesis considers the time-optimal impact angle constrained guidance problem for interception of moving targets. In the first part of the thesis, a Dubins paths–based guidance methodology for minimum-time lateral interception of a moving and non-maneuvering target is designed. The existence and the time-optimality of the paths are established for impact angle constrained interception of moving targets. The capture regions are analyzed and a classification of the initial geometries is developed for deducing the time-optimal path type. The corresponding guidance command for optimal interception can be generated from the information of initial engagement geometry and target’s speed. In the next part of the thesis, the concept of equivalent virtual target is introduced to address the problem of impact along a general direction. An algorithm is developed to obtain the optimal interception point for generalized interception scenarios. A proof of convergence is presented for the proposed algorithm. Achieving different impact angles, the interceptor often takes sharp turns. Following such curved trajectories, the interceptor may fail to keep the target inside the seeker field-of-view. In the next part of the thesis, the field-of-view characteristics of the proposed optimal guidance strategies are analyzed. Closed-form expressions are derived for the interceptor’s look-angle to the target. Satisfying field-of-view condition at endpoints of the path segments that constitute the optimal path is proven to guarantee target motion inside the field-of-view throughout the engagement. The stationary target case is also analyzed as a specific scenario. The last part of the thesis presents a method to extend the proposed guidance strategies to maneuvering target scenarios.

Στην εργασία αυτή, μελετάται το πρόβλημα της ανίχνευσης κινούμενων στόχων και της εκτίμησης της θέσης και της ταχύτητάς τους από ένα σύστημα ραντάρ. Η κίνηση των στόχων ως προς το ραντάρ έχει σαν αποτέλεσμα τη μετατόπιση Doppler της συχνότητας της επιστρεφόμενης ακτινοβολίας ως προς τη συχνότητα εκπομπής του ραντάρ. Εκτιμώντας αυτή τη μετατόπιση στη συχνότητα μπορούμε να ανιχνεύσουμε το στόχο καθώς και να εκτιμήσουμε τη θέση και την ταχύτητά του. Διερευνάται η δυνατότητα βελτίωσης της πιθανότητας ανίχνευσης των στόχων καθώς και του μέσου τετραγωνικού σφάλματος των εκτιμήσεων θέσης και ταχύτητας, με χρήση μοντέρνων εκτιμητών συχνοτήτων, αντί των κλασσικών εκτιμητών που βασίζονται στο Μετασχηματισμό Fourrier. Αναλύονται θεωρητικά και μέσω προσομοιώσεων οι δυνατότητες των μοντέρνων εκτιμητών συχνοτήτων, δίνοντας ιδιαίτερη έμφαση στους εκτιμητές Υποχώρου (MUSIC, ESPRIT). Ακολουθεί, η παρουσίαση μιας γενίκευσης της χρήσης των εκτιμητών συχνοτήτων στην περίπτωση διανυσματικών σημάτων. Ο αλγόριθμος που προτείνεται για την ανίχνευση στόχων από ένα σύστημα ραντάρ, επεξεργάζεται τα δείγματα της ληφθείσας ακτινοβολίας κατά μπλοκ οπότε προκύπτει η ανάγκη χρήσης αυτής της διανυσματικής μορφής των εκτιμητών συχνοτήτων. Παρουσιάζονται, τέλος, αποτελέσματα προσομοιώσεων, για διάφορα σενάρια, που επιβεβαιώνουν την αποτελεσματικότητα του αλγορίθμου και φανερώνουν τα πλεονεκτήματα της χρήσης των μοντέρνων τεχνικών εκτίμησης συχνοτήτων. / This report focuses on the problem of detection of moving targets and estimation of their positions and velocities using a radar system. By estimating the targets' Doppler frequencies it is possible to detect the targets and estimate both their position and velocity. It is shown how the use of modern frequency estimators results in higher values of the probability of detection compared to the Fourrier-based methods. Modern estimators are analyzed, with emphasis shown on the subspace-based estimators (MUSIC, ESPRIT) and their use is generalized for the case of estimating frequencies in vector signals. This generalized form of frequency estimators is used by our proposed algorithm for target detection. Simulation results are presented that prove the superiority of modern techniques.

Le Synthetic Aperture Radar (SAR) aéroporté permet d’obtenir des images hautes résolutions, en compensant un déphasage lié au déplacement de l’avion. Il n’est cependant pas adapté à l’imagerie des cibles mobiles, celles-ci introduisant un déphasage supplémentaire, dépendant de leur vitesse et de leur accélération. En utilisant un système SAR multivoies, il est cependant possible de réaliser des traitements adaptés aux cibles mobiles, dont les principes sont proches du Space-Time Adaptive Processing (STAP). Le Synthetic Aperture Radar (SAR) aéroporté permet d’obtenir des images hautes résolutions, en compensant un déphasage lié au déplacement de l’avion. Il n’est cependant pas adapté à l’imagerie des cibles mobiles, celles-ci introduisant un déphasage supplémentaire, dépendant de leur vitesse et de leur accélération. En utilisant un système SAR multivoies, il est cependant possible de réaliser des traitements adaptés aux cibles mobiles, dont les principes sont proches du Space-Time Adaptive Processing (STAP). / Airborne Synthetic Aperture Radar (SAR) provides high-resolution images, by compensating a phase shift linked to the platform movement. However, this processing is not suited for imaging moving target, for they introduce an additional phase shift, depending on their velocity and acceleration. By using a multichannel SAR system, it is possible to correctly process moving targets. Such a processing is closely related to Space-Time Adaptive Processing (STAP) principles. Airborne Synthetic Aperture Radar (SAR) provides high-resolution images, by compensating a phase shift linked to the platform movement. However, this processing is not suited for imaging moving target, for they introduce an additional phase shift, depending on their velocity and acceleration. By using a multichannel SAR system, it is possible to correctly process moving targets. Such a processing is closely related to Space-Time Adaptive Processing (STAP) principles.