Methods for Direction of Arrival, DOA estimation of multiple objects based on phased arrayantenna technology have many advantages in for example electronic warfare and radarapplications. However, perfect calibration of an antenna array can seldom be achieved. Thepurpose of this report is to study different methods for DOA estimation and how calibration-/modelerrors affect the results. Possible methods for quantifying these kinds of errors using measurement data are suggested. This thesis consists of essentially five parts. The different studies have been carried out using MATLAB simulations as well as theoretical considerations, i.e., calculations. In the first study, examples of the possible performance of four DOA algorithms, MUSIC, TLS-ESPRIT, WSF, and DML are provided. Results are given both with and without applying spatial smoothing. The latter scheme is used for handling correlated, or even coherent, sources. The results show that, for the considered scenarios, MUSIC performs the most consistently well, while the performance of DML is inferior. ESPRIT is well-performing when spatial smoothing is applied and performs the best when the angles of two signals are very close. It has been observed that WSF with weighting matrices for optimal asymptotic performance as well as spatial smoothing applied doesn’t perform well. When applying model errors to the systemin the second study, the corresponding conclusions about the algorithms can be drawn. That separation distance between the angles and that higher SNR results in better estimates are also confirmed. Quantification of certain array errors is also considered using methods inspired by a scheme proposed in the context of nonlinear system identification. The results show that the DOA algorithms are very good at dealing with noise and that the attempted method works well when the model error is like the true signals, but different enough that it is not confused with a problem with more signals. The model error that results in the worst results is when it only affects some ofthe channels in the antenna array. The fourth study explores DOA estimation using extended Kalman filtering and concludes that it is a very good tracker of the angle over time for the considered scenarios. All of this is then applied to measured data, but due to either extensive model error, errors with processing the data, or both, the results are worse than expected. Simulations that try to replicate the measured data results in good angle estimation for the DOA algorithms. The Kalman filter also performs well in simulations.

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This research investigates signal processing involving a single electromagnetic vector-sensor, with an emphasis on the problem regarding signal-selective narrowband direction-of-arrival (DOA) estimation in the presence of interference. The approach in this thesis relies on a high-resolution ESPRIT-based algorithm. Unlike spatially displaced arrays, the sensor cannot estimate the DOA of sources using phase differences between the array elements, as the elements are spatially co-located. However, the sensor measures the full electromagnetic field vectors, so the DOA can be estimated through the Poynting vector. Limited information is available in the open literature regarding signal-selective DOA estimation for a single electromagnetic vector-sensor. In this thesis, it is shown how the Uni-Vector-Sensor-ESPRIT (UVS-ESPRIT) algorithm that relies on a time-series invariance and was originally devised for deterministic harmonic sources can be applied to non-deterministic sources. Additionally, two algorithms, one based on cyclostationarity and the other based on fourth-order cumulants, are formulated based on the UVS-ESPRIT algorithm and are capable of selectively estimating the source DOA in the presence of interference based on the statistical properties of the sources. The cyclostationarity-based UVS-ESPRIT algorithm is capable of selectively estimating the signal-of-interest DOA when the sources have the same carrier frequency, and thus overlap in frequency. The cumulant-based UVS-ESPRIT algorithm devised for this sensor relies on the independent component analysis algorithm JADE and is capable of selectively estimating the signal-of-interest DOA through the fourth-order cumulants only, is robust to spatially colored noise, and is capable of estimating the DOA of more sources than sensor elements. / Master of Science / Electromagnetic vector-sensors are specialized sensors capable of capturing the full electromagnetic field vectors at a single point in space. Direction-of-arrival (DOA) estimation is the problem of estimating the spatial-angular parameters of one or more wavefronts impinging on an array. For a single electromagnetic vector-sensor, the array elements are not spatially displaced, but it is still possible to estimate the direction-of-arrival through the Poynting vector, which relates the electric and magnetic field vectors to the direction of propagation of an electromagnetic wave. Although direction-of-arrival estimation is a well-established area of research, there is limited discussion in the open literature regarding signal-selective DOA estimation in the presence of interference for a single electromagnetic vector-sensor. This research investigates this problem and discusses how the high-resolution Uni-Vector-Sensor-ESPRIT (UVS-ESPRIT) algorithm may be applied to non-deterministic sources. ESPRIT based algorithms capable of selectively estimating the source DOA are formulated based on the cyclostationarity and higher-order statistics of the sources, which are approaches known to be robust to interference. The approach based on higher-order statistics is also robust to spatially colored noise and is capable of estimating the DOA of more sources than sensor elements. The formulation of the UVS-ESPRIT for higher-order statistics relies on the application of the independent component analysis algorithm JADE, an unsupervised learning technique. Overall, this research investigates signal-selective direction-of-arrival estimation using an ESPRIT-based algorithm for a single electromagnetic vector-sensor.

Radar (RAdio Detection And Ranging) uses radio waves to detect the presence of a target and measure its position and other properties. This sensor has found many civilian and military applications due to advantages such as possible large surveillance areas and operation day and night and in all weather. The contributions of this thesis are within applied signal processing for radar in two somewhat separate research areas: 1) radar with array antennas and 2) radar with micro-Doppler measurements. Radar with array antennas: An array antenna consists of several small antennas in the same space as a single large antenna. Compared to a traditional single-antenna radar, an array antenna radar gives higher flexibility, higher capacity, several radar functions simultaneously and increased reliability, and makes new types of signal processing possible which give new functions and higher performance. The contributions on array antenna radar in this thesis are in three different problem areas. The first is High Resolution DOA (Direction Of Arrival) Estimation (HRDE) as applied to radar and using real measurement data. HRDE is useful in several applications, including radar applications, to give new functions and improve the performance. The second problem area is suppression of interference (clutter, direct path jamming and scattered jamming) which often is necessary in order to detect and localize the target. The thesis presents various results on interference signal properties, antenna geometry and subarray design, and on interference suppression methods. The third problem area is measurement techniques for which the thesis suggests two measurement designs, one for radar-like measurements and one for scattered signal measurements. Radar with micro-Doppler measurements: There is an increasing interest and need for safety, security and military surveillance at short distances. Tasks include detecting targets, such as humans, animals, cars, boats, small aircraft and consumer drones; classifying the target type and target activity; distinguishing between target individuals; and also predicting target intention. An approach is to employ micro-Doppler radar to perform these tasks. Micro-Doppler is created by the movement of internal parts of the target, like arms and legs of humans and animals, wheels of cars and rotors of drones. Using micro-Doppler, this thesis presents results on feature extraction for classification; on classification of targets types (humans, animals and man-made objects) and human gaits; and on information in micro-Doppler signatures for re-identification of the same human individual. It also demonstrates the ability to use different kinds of radars for micro-Doppler measurements. The main conclusion about micro-Doppler radar is that it should be possible to use for safety, security and military surveillance applications.

National security needs dictate the development of new radar systems capable of identifying and tracking exoatmospheric threats to aid our defense. These new radar systems feature reduced noise floors, electronic beam steering, and ultra-wide bandwidths, all of which facilitate threat discrimination. However, in order to identify missile attributes such as RF reflectivity, distance, and velocity, many existing processing algorithms rely upon narrow bandwidth assumptions that break down with increased signal bandwidth. We present a fresh investigation into these algorithms for removing bandwidth limitations and propose novel state-space and direct-data factoring formulations such as * the multidimensional extension to the Eigensystem Realization Algorithm, * employing state-space models in place of interpolation to obtain a form which admits a separation and isolation of solution components, * and side-stepping the joint diagonalization of state transition matrices, which commonly plagues methods like multidimensional ESPRIT. We then benchmark our approaches and relate the outcomes to the Cramer-Rao bound for the case of one and two adjacent reflectors to validate their conceptual design and identify those techniques that compare favorably to or improve upon existing practices.

In this thesis a new approach is proposed for non-uniform linear arrays (NLA) which employs conventional subspace methods to improve the direction of arrival (DOA) estimation performance. Uniform linear arrays (ULA) are composed of evenly spaced sensor elements located on a straight line. ULA&#039 / s covariance matrix have a Vandermonde matrix structure, which is required by fast subspace DOA estimation algorithms. NLA differ from ULA only by some missing sensor elements. These missing elements cause some gaps in covariance matrix and Vandermonde structure is lost. Therefore fast subspace DOA algorithms can not be applied in this case. Linear programming methods and array interpolation methods can be used to solve this problem. However linear programming is computationally expensive and array interpolation is angular sector dependent and requires the same number of sensor in the virtual array. In this thesis, a covariance matrix augmentation method is developed by using the array interpolation technique and initial DOA estimates. An initial DOA estimate is obtained by Toeplitz completion of the covariance matrix. This initial DOA estimates eliminates the sector dependency and reduces the least square mapping error of array interpolation. A Wiener formulation is developed which allows more sensors in the virtual array than the real array. In addition, it leads to better estimates at low SNR. The new covariance matrix is used in the root-MUSIC algorithm to obtain a better DOA estimate. Several computer simulations are done and it is shown that the proposed approach improves the DOA estimation accuracy significantly compared to the same number of sensor ULA. This approach also increases the number of sources that can be identifed.

In this thesis, a Neural Network (NN) based beamforming algorithm is proposed for real time target tracking problem. The algorithm is performed for two applications, linear and cylindrical arrays. The linear array application is implemented with equispaced omnidirectional sources. The influence of the number of antenna elements and the angular seperation between the incoming signals on the performance of the beamformer in the linear array beamformer is studied, and it is observed that the algorithm improves its performance by increasing both two parameters in linear array beamformer. The cylindrical array application is implemented with twelve microstrip patch antenna (MPA) elements. The angular range of interest is divided into twelve sectors. Since three MPA elements are used to form the beam in each sector, the input size of the neural network (NN) is reduced in cylindrical array. According to the reduced size of NN, the training time of the beamformer is decreased. The reduced size of the NN has no degradation in forming the beams to the desired directions. The angular separation between the targets is an important parameter in cylindrical array beamformer.

An antenna array is an indispensable portion of a direction-of-arrival (DOA) estimation operation. A number of error sources in the arrays degrade the DOA estimation accuracy. Mutual coupling effect is one of the main error sources and should be corrected for any antenna array. In this thesis, a system theoretic approach is presented for mutual coupling characterization of antenna arrays. In this approach, the idea is to model the mutual coupling effect through a simple linear transformation between the measured and the ideal array data. In this context, a measurement reduction method (MRM) is proposed to decrease the number of calibration measurements. This new method dramatically reduces the number of calibration measurements for omnidirectional antennas. It is shown that a single calibration measurement is sufficient for uniform circular arrays when MRM is used. The method is extended for the arrays composed of non-omnidirectional (NOD) antennas. It is shown that a single calibration matrix can not properly model the mutual coupling effect in an NOD antenna array. Therefore, a sectorized calibration approach is proposed for NOD antenna arrays where the mutual coupling calibration is done in angular sectors. Furthermore, mutual coupling problem is also investigated for antenna arrays over a perfect electric conductor plate. In this case, reflections from the plate lead to gain/phase mismatches in the antenna elements. In this context, a composite matrix approach is proposed where mutual coupling and gain/phase mismatch are jointly modelled by using a single composite calibration matrix. The proposed methods are evaluated over DOA estimation accuracies using Multiple Signal Classification (MUSIC) algorithm. The calibration measurements are obtained using the numerical electromagnetic simulation tool FEKO. The evaluation results show that the proposed methods effectively realize the mutual coupling calibration of antenna arrays.

L’estimation et la localisation de sources sont des problèmes centraux en traitement d’antenne, en particulier en télécommunication, sismologie, acoustique, ingénierie médicale ou astronomie. Une antenne de capteurs est un système d’acquisition composé par de multiples capteurs qui reçoivent des ondes en provenance de sources de directions différentes: elle échantillonne les champs incidents en espace et en temps.Pour cette raison, des techniques haute résolution comme MUSIC utilisent ces deux éléments de diversité, l’espace et le temps, afin d’estimer l’espace signal engendré par les sources incidentes, ainsi que leur direction d’arrivée. Ceci est généralement atteint par une estimation préalable de statistiques de deuxième ordre ou d’ordre supérieur, comme la covariance spatiale de l’antenne, qui nécessitent donc de temps d’observation suffisamment longs.Seulement récemment, l’analyse tensorielle a été appliquée au traitement d’antenne, grâce à l’introduction, comme troisième modalité (ou diversité), de la translation en espace d’une sous-antenne de référence, sans faire appel à l’estimation préalable de quantités statistiques.Les décompositions tensorielles consistent en l’analyse de cubes de données multidimensionnelles, au travers de leur décomposition en somme d’éléments constitutifs plus simples, grâce à la multilinéarité et à la structure de rang faible du modèle sous-jacent.Ainsi, les mêmes techniques tensorielles nous fournissent une estimée des signaux eux-mêmes, ainsi que de leur direction d’arrivée, de façon déterministe. Ceci peut se faire en vertu du modèle séparable et de rang faible vérifié par des sources en bande étroite et en champs lointain.Cette thèse étudie l’estimation et la localisation de sources par des méthodes tensorielles de traitement d’antenne.Le premier chapitre présente le modèle physique de source en bande étroite et en champs lointain, ainsi que les définitions et hypothèses fondamentales. Le deuxième chapitre passe en revue l’état de l’art sur l’estimation des directions d’arrivée, en mettant l’accent sur les méthodes haute résolution à sous-espace. Le troisième chapitre introduit la notation tensorielle, à savoir la définition des tableaux de coordonnées multidimensionnels, les opérations et décompositions principales. Le quatrième chapitre présente le sujet du traitement tensoriel d’antenne au moyen de l’invariance par translation.Le cinquième chapitre introduit un modèle tensoriel général pour traiter de multiples diversités à la fois, comme l’espace, le temps, la translation en espace, les profils de gain spatial et la polarisation des ondes élastiques en bande étroite.Par la suite, les sixième et huitième chapitres établissent un modèle tensoriel pour un traitement d’antenne bande large cohérent. Nous proposons une opération de focalisation cohérente et séparable par une transformée bilinéaire et par un ré-échantillonnage spatial, respectivement, afin d’assurer la multilinéarité des données interpolées.Nous montrons par des simulations numériques que l’estimation proposée des paramètres des signaux s’améliore considérablement, par rapport au traitement tensoriel classique en bande étroite, ainsi qu’à MUSIC cohérent bande large.Egalement, tout au long de la thèse, nous comparons les performances de l’estimation tensorielle avec la borne de Cramér-Rao du modèle multilinéaire associé, que nous développons, dans sa forme la plus générale, dans le septième chapitre. En outre, dans le neuvième chapitre nous illustrons une application à des données sismiques réelles issues d’une campagne de mesure sur un glacier alpin, grâce à la diversité de vitesse de propagation.Enfin, le dixième et dernier chapitre de cette thèse traite le sujet parallèle de la factorisation spectrale multidimensionnelle d’ondes sismiques, et présente une application à l’estimation de la réponse impulsionnelle du soleil pour l’héliosismologie. / Source estimation and localization are a central problem in array signal processing, and in particular in telecommunications, seismology, acoustics, biomedical engineering, and astronomy. Sensor arrays, i.e. acquisition systems composed of multiple sensors that receive source signals from different directions, sample the impinging wavefields in space and time. Hence, high resolution techniques such as MUSIC make use of these two elements of diversities: space and time, in order to estimate the signal subspace generated by impinging sources, as well as their directions of arrival. This is generally done through the estimation of second or higher orders statistics, such as the array spatial covariance matrix, thus requiring sufficiently large data samples. Only recently, tensor analysis has been applied to array processing using as a third mode (or diversity), the space shift translation of a reference subarray, with no need for the estimation of statistical quantities. Tensor decompositions consist in the analysis of multidimensional data cubes of at least three dimensions through their decomposition into a sum of simpler constituents, thanks to the multilinearity and low rank structure of the underlying model. Thus, tensor methods provide us with an estimate of source signatures, together with directions of arrival, in a deterministic way. This can be achieved by virtue of the separable and low rank model followed by narrowband sources in the far field. This thesis deals with source estimation and localization of multiple sources via these tensor methods for array processing. Chapter 1 presents the physical model of narrowband elastic sources in the far field, as well as the main definitions and assumptions. Chapter 2 reviews the state of the art on direction of arrival estimation, with a particular emphasis on high resolution signal subspace methods. Chapter 3 introduces the tensor formalism, namely the definition of multi-way arrays of coordinates, the main operations and multilinear decompositions. Chapter 4 presents the subject of tensor array processing via rotational invariance. Chapter 5 introduces a general tensor model to deal with multiple physical diversities, such as space, time, space shift, polarization, and gain patterns of narrowband elastic waves. Subsequently, Chapter 6 and Chapter 8 establish a tensor model for wideband coherent array processing. We propose a separable coherent focusing operation through bilinear transform and through a spatial resampling, respectively, in order to ensure the multilinearity of the interpolated data. We show via computer simulations that the proposed estimation of signal parameters considerably improves, compared to existing narrowband tensor processing and wideband MUSIC. Throughout the chapters we also compare the performance of tensor estimation to the Cramér-Rao bounds of the multilinear model, which we derive in its general formulation in Chapter 7. Moreover, in Chapter 9 we propose a tensor model via the diversity of propagation speed for seismic waves and illustrate an application to real seismic data from an Alpine glacier. Finally, the last part of this thesis in Chapter 10 moves to the parallel subject of multidimensional spectral factorization of seismic ways, and illustrates an application to the estimation of the impulse response of the Sun for helioseismology.

This work deals with the further development of a method for Direction of Arrival (DOA) estimation based on the Discrete Fourier Transform (DFT) of the sensor array output. In the existing DFT-based algorithm, relatively high SNR is considered, and it is assumed that a large number of sensors are available. In this study an overview of some of the most commonly used DOA estimation techniques will be presented. Then the performance of the DFT method will be analyzed and compared with the performance of existing techniques. Two main objectives will be studied, firstly the reduction of the number of sensors and secondly the performance of the DFT based technique in the presence of noise. Experimental simulations will be presented to illustrate that in absence of noise, the proposed method is very fast and using just one snapshot is sufficient to accurately estimate DOAs. Also, in presence of noise, the method is still relatively fast and using a small number of snapshots, it can accurately estimate DOAs. The above mentioned properties are the result of taking an average of the peaks of the DFTs, X_n (k), obtained from a sequence of N_s snapshots. With N_s sufficiently large, the average over N_s snapshots approaches expected value. Also, the conditions that should be satisfied to avoid overlapping of main-lobes, and thus loosing the DOA of some signals, in the DFT spectrum are examined. This study further analyzes the performance of the proposed method as well as two other commonly used algorithms, MUSIC and conventional beamformer. An extensive simulation was conducted and different features of the spatial DFT technique, such as accuracy, resolution, sensitivity to noise, effect of multiple snapshots and the number of sensors were evaluated and compared with those of existing techniques. The simulations indicate that in most aspects the proposed spatial DFT algorithm outperforms the other techniques. / Graduate