A Compact Formulation for the ℓ2,1\ell_{2,1} Mixed-Norm Minimization Problem

Parameter estimation from multiple measurement vectors (MMVs) is a fundamental problem in many signal processing applications, e.g., spectral analysis and direction-of- arrival estimation. Recently, this problem has been address using prior information in form of a jointly sparse signal structure. A prominent approach for exploiting joint sparsity considers mixed-norm minimization in which, however, the problem size grows with the number of measurements and the desired resolution, respectively. In this work we derive an equivalent, compact reformulation of the $\ell_{2,1}$ mixed-norm minimization problem which provides new insights on the relation between different existing approaches for jointly sparse signal reconstruction. The reformulation builds upon a compact parameterization, which models the row-norms of the sparse signal representation as parameters of interest, resulting in a significant reduction of the MMV problem size. Given the sparse vector of row-norms, the jointly sparse signal can be computed from the MMVs in closed form. For the special case of uniform linear sampling, we present an extension of the compact formulation for gridless parameter estimation by means of semidefinite programming. Furthermore, we derive in this case from our compact problem formulation the exact equivalence between the $\ell_{2,1}$ mixed-norm minimization and the atomic-norm minimization. Additionally, for the case of irregular sampling or a large number of samples, we present a low complexity, grid-based implementation based on the coordinate descent method

Performance Comparison Of Weak And Strong Learners In Detecting GPS Spoofing Attacks On Unmanned Aerial Vehicles (uavs)

Unmanned Aerial Vehicle systems (UAVs) are widely used in civil and military applications. These systems rely on trustworthy connections with various nodes in their network to conduct their safe operations and return-to-home. These entities consist of other aircrafts, ground control facilities, air traffic control facilities, and satellite navigation systems. Global positioning systems (GPS) play a significant role in UAV\u27s communication with different nodes, navigation, and positioning tasks. However, due to the unencrypted nature of the GPS signals, these vehicles are prone to several cyberattacks, including GPS meaconing, GPS spoofing, and jamming. Therefore, this thesis aims at conducting a detailed comparison of two widely used machine learning techniques, namely weak and strong learners, to investigate their performance in detecting GPS spoofing attacks that target UAVs. Real data are used to generate training datasets and test the effectiveness of machine learning techniques. Various features are derived from this data. To evaluate the performance of the models, seven different evaluation metrics, including accuracy, probabilities of detection and misdetection, probability of false alarm, processing time, prediction time per sample, and memory size, are implemented. The results show that both types of machine learning algorithms provide high detection and low false alarm probabilities. In addition, despite being structurally weaker than strong learners, weak learner classifiers also, achieve a good detection rate. However, the strong learners slightly outperform the weak learner classifiers in terms of multiple evaluation metrics, including accuracy, probabilities of misdetection and false alarm, while weak learner classifiers outperform in terms of time performance metrics

Maximum Likelihood-based Gridless DoA Estimation Using Structured Covariance Matrix Recovery and SBL with Grid Refinement

We consider the parametric data model employed in applications such as line spectral estimation and direction-of-arrival estimation. We focus on the stochastic maximum likelihood estimation (MLE) framework and offer approaches to estimate the parameter of interest in a gridless manner, overcoming the model complexities of the past. This progress is enabled by the modern trend of reparameterization of the objective and exploiting the sparse Bayesian learning (SBL) approach. The latter is shown to be a correlation-aware method, and for the underlying problem it is identified as a grid-based technique for recovering a structured covariance matrix of the measurements. For the case when the structured matrix is expressible as a sampled Toeplitz matrix, such as when measurements are sampled in time or space at regular intervals, additional constraints and reparameterization of the SBL objective leads to the proposed structured matrix recovery technique based on MLE. The proposed optimization problem is non-convex, and we propose a majorization-minimization based iterative procedure to estimate the structured matrix; each iteration solves a semidefinite program. We recover the parameter of interest in a gridless manner by appealing to the Caratheodory-Fejer result on decomposition of PSD Toeplitz matrices. For the general case of irregularly spaced time or spatial samples, we propose an iterative SBL procedure that refines grid points to increase resolution near potential source locations, while maintaining a low per iteration complexity. We provide numerical results to evaluate and compare the performance of the proposed techniques with other gridless techniques, and the CRB. The proposed correlation-aware approach is more robust to environmental/system effects such as low number of snapshots, correlated sources, small separation between source locations and improves sources identifiability.Comment: Submitted to the IEEE Transactions on Signal Processing (Previous submission date: 29-Oct-2021

Acoustic localization of people in reverberant environments using deep learning techniques

La localización de las personas a partir de información acústica es cada vez más importante en aplicaciones del mundo real como la seguridad, la vigilancia y la interacción entre personas y robots. En muchos casos, es necesario localizar con precisión personas u objetos en función del sonido que generan, especialmente en entornos ruidosos y reverberantes en los que los métodos de localización tradicionales pueden fallar, o en escenarios en los que los métodos basados en análisis de vídeo no son factibles por no disponer de ese tipo de sensores o por la existencia de oclusiones relevantes. Por ejemplo, en seguridad y vigilancia, la capacidad de localizar con precisión una fuente de sonido puede ayudar a identificar posibles amenazas o intrusos. En entornos sanitarios, la localización acústica puede utilizarse para controlar los movimientos y actividades de los pacientes, especialmente los que tienen problemas de movilidad. En la interacción entre personas y robots, los robots equipados con capacidades de localización acústica pueden percibir y responder mejor a su entorno, lo que permite interacciones más naturales e intuitivas con los humanos. Por lo tanto, el desarrollo de sistemas de localización acústica precisos y robustos utilizando técnicas avanzadas como el aprendizaje profundo es de gran importancia práctica. Es por esto que en esta tesis doctoral se aborda dicho problema en tres líneas de investigación fundamentales: (i) El diseño de un sistema extremo a extremo (end-to-end) basado en redes neuronales capaz de mejorar las tasas de localización de sistemas ya existentes en el estado del arte. (ii) El diseño de un sistema capaz de localizar a uno o varios hablantes simultáneos en entornos con características y con geometrías de arrays de sensores diferentes sin necesidad de re-entrenar. (iii) El diseño de sistemas capaces de refinar los mapas de potencia acústica necesarios para localizar a las fuentes acústicas para conseguir una mejor localización posterior. A la hora de evaluar la consecución de dichos objetivos se han utilizado diversas bases de datos realistas con características diferentes, donde las personas involucradas en las escenas pueden actuar sin ningún tipo de restricción. Todos los sistemas propuestos han sido evaluados bajo las mismas condiciones consiguiendo superar en términos de error de localización a los sistemas actuales del estado del arte

Sparse Bases and Bayesian Inference of Electromagnetic Scattering

Many approaches in CEM rely on the decomposition of complex radiation and scattering behavior with a set of basis vectors. Accurate estimation of the quantities of interest can be synthesized through a weighted sum of these vectors. In addition to basis decompositions, sparse signal processing techniques developed in the CS community can be leveraged when only a small subset of the basis vectors are required to sufficiently represent the quantity of interest. We investigate several concepts in which novel bases are applied to common electromagnetic problems and leverage the sparsity property to improve performance and/or reduce computational burden. The first concept explores the use of multiple types of scattering primitives to reconstruct scattering patterns of electrically large targets. Using a combination of isotropic point scatterers and wedge diffraction primitives as our bases, a 40% reduction in reconstruction error can be achieved. Next, a sparse basis is used to improve DOA estimation. We implement the BSBL technique to determine the angle of arrival of multiple incident signals with only a single snapshot of data from an arbitrary arrangement of non-isotropic antennas. This is an improvement over the current state-of-the-art, where restrictions on the antenna type, configuration, and a priori knowledge of the number of signals are often assumed. Lastly, we investigate the feasibility of a basis set to reconstruct the scattering patterns of electrically small targets. The basis is derived from the TCM and can capture non-localized scattering behavior. Preliminary results indicate that this basis may be used in an interpolation and extrapolation scheme to generate scattering patterns over multiple frequencies

Too Brittle To Touch: Comparing the Stability of Quantization and Distillation Towards Developing Lightweight Low-Resource MT Models

Leveraging shared learning through Massively Multilingual Models, state-of-the-art machine translation models are often able to adapt to the paucity of data for low-resource languages. However, this performance comes at the cost of significantly bloated models which are not practically deployable. Knowledge Distillation is one popular technique to develop competitive, lightweight models: In this work, we first evaluate its use to compress MT models focusing on languages with extremely limited training data. Through our analysis across 8 languages, we find that the variance in the performance of the distilled models due to their dependence on priors including the amount of synthetic data used for distillation, the student architecture, training hyperparameters and confidence of the teacher models, makes distillation a brittle compression mechanism. To mitigate this, we explore the use of post-training quantization for the compression of these models. Here, we find that while distillation provides gains across some low-resource languages, quantization provides more consistent performance trends for the entire range of languages, especially the lowest-resource languages in our target set.Comment: 16 Pages, 7 Figures, Accepted to WMT 2022 (Research Track