Bayesian Framework for Sparse Vector Recovery and Parameter Bounds with Application to Compressive Sensing

abstract: Signal compressed using classical compression methods can be acquired using brute force (i.e. searching for non-zero entries in component-wise). However, sparse solutions require combinatorial searches of high computations. In this thesis, instead, two Bayesian approaches are considered to recover a sparse vector from underdetermined noisy measurements. The first is constructed using a Bernoulli-Gaussian (BG) prior distribution and is assumed to be the true generative model. The second is constructed using a Gamma-Normal (GN) prior distribution and is, therefore, a different (i.e. misspecified) model. To estimate the posterior distribution for the correctly specified scenario, an algorithm based on generalized approximated message passing (GAMP) is constructed, while an algorithm based on sparse Bayesian learning (SBL) is used for the misspecified scenario. Recovering sparse signal using Bayesian framework is one class of algorithms to solve the sparse problem. All classes of algorithms aim to get around the high computations associated with the combinatorial searches. Compressive sensing (CS) is a widely-used terminology attributed to optimize the sparse problem and its applications. Applications such as magnetic resonance imaging (MRI), image acquisition in radar imaging, and facial recognition. In CS literature, the target vector can be recovered either by optimizing an objective function using point estimation, or recovering a distribution of the sparse vector using Bayesian estimation. Although Bayesian framework provides an extra degree of freedom to assume a distribution that is directly applicable to the problem of interest, it is hard to find a theoretical guarantee of convergence. This limitation has shifted some of researches to use a non-Bayesian framework. This thesis tries to close this gab by proposing a Bayesian framework with a suggested theoretical bound for the assumed, not necessarily correct, distribution. In the simulation study, a general lower Bayesian Cram\'er-Rao bound (BCRB) bound is extracted along with misspecified Bayesian Cram\'er-Rao bound (MBCRB) for GN model. Both bounds are validated using mean square error (MSE) performances of the aforementioned algorithms. Also, a quantification of the performance in terms of gains versus losses is introduced as one main finding of this report.Dissertation/ThesisMasters Thesis Computer Engineering 201

Weiss-Weinstein bound of frequency estimation error for very weak GNSS signals

Tightness remains the center quest in all modern estimation bounds. For very weak signals, this is made possible with judicial choices of prior probability distribution and bound family. While current bounds in GNSS assess performance of carrier frequency estimators under Gaussian or uniform assumptions, the circular nature of frequency is overlooked. In addition, of all bounds in Bayesian framework, Weiss-Weinstein bound (WWB) stands out since it is free from regularity conditions or requirements on the prior distribution. Therefore, WWB is extended for the current frequency estimation problem. A divide-and-conquer type of hyperparameter tuning method is developed to level off the curse of computational complexity for the WWB family while enhancing tightness. Synthetic results show that with von Mises as prior probability distribution, WWB provides a bound up to 22.5% tighter than Ziv-Zaka\"i bound (ZZB) when SNR varies between -3.5 dB and -20 dB, where GNSS signal is deemed extremely weak.Comment: 35 pages, 13 figures, submitted to NAVIGATION, Journal of the Institute of Navigatio

Lipid-lipid interactions in bilayers containing polar sphingolipids, ceramide and cholesterol.

265 p.La presente tesis se ha centrado el estudio de las interacciones lípido-lípido asociadas a la segregación lateral de esfingolipidos y colesterol. Estos estudios se han llevado a cabo utilizando sistemas de membranas modelo compuestos por tres o cuatro componentes, y utilizando diferentes técnicas biofísicas, principalmente calorimetría diferencial de barrido, espectroscopia y microscopía de fluorescencia y microscopía de fuerza atómica, con los siguientes objetivos:- Caracterizar la estructura de las fases de la eSM y la pSM por debajo de su temperatura de transición principal de fase.- Analizar el comportamiento de la ceramida y el colesterol con un fosfolípido saturado en un sistema modelo de tres componentes.- Estudiar el efecto de la incorporación de esfingolipidos insaturados en membranas fosfolipídicas modelo.¿Describir la interacción de glicoesfingolipidos naturales (cerebrósidos) en sistemas binarios con esfingolípidos, glicerolípidos o colesterol

Cooperative Position and Orientation Estimation with Multi-Mode Antennas

Robotic multi-agent systems are envisioned for planetary exploration and terrestrial applications. Autonomous operation of robots requires estimations of their positions and orientations, which are obtained from the direction-of-arrival (DoA) and the time-of-arrival (ToA) of radio signals exchanged among the agents. In this thesis, we estimate the signal DoA and ToA using a multi-mode antenna (MMA). An MMA is a single antenna element, where multiple orthogonal current modes are excited by different antenna ports. We provide a first study on the use of MMAs for cooperative position and orientation estimation, specifically exploring their DoA estimation capabilities. Assuming the agents of a cooperative network are equipped with MMAs, lower bounds on the achievable position and orientation accuracy are derived. We realize a gap between the theoretical lower bounds and real-world performance of a cooperative radio localization system, which is caused by imperfect antenna and transceiver calibration. Consequentially, we theoretically analyze in-situ antenna calibration, introduce an algorithm for the calibration of arbitrary multiport antennas and show its effectiveness by simulation. To also improve calibration during operation, we propose cooperative simultaneous localization and calibration (SLAC). We show that cooperative SLAC is able to estimate antenna responses and ranging biases of the agents together with their positions and orientations, leading to considerably better position and orientation accuracy. Finally, we validate the results from theory and simulation by experiments with robotic rovers equipped with software-defined radios (SDRs). In conclusion, we show that DoA estimation with an MMA is feasible, and accuracy can be improved by in-situ calibration and SLAC

Performance assessment of a low-complexity autoregressive Kalman filter for GNSS carrier tracking using real scintillation time series

Altres ajuts: Acord transformatiu CRUE-CSICIonospheric scintillation is one of the most challenging sources of errors in global navigation satellite systems (GNSS). It is an effect of space weather that introduces rapid amplitude and phase fluctuations to transionospheric signals and, as a result, it severely degrades the tracking performance of receivers, particularly carrier tracking. It can occur anywhere on the earth during intense solar activity, but the problem aggravates in equatorial and high-latitude regions, thus posing serious concerns to the widespread deployment of GNSS in those areas. One of the most promising approaches to address this problem is the use of Kalman filter-based techniques at the carrier tracking level, incorporating some a priori knowledge about the statistics of the scintillation to be dealt with. These techniques aim at dissociating the carrier phase dynamics of interest from phase scintillation by modeling the latter through some correlated Gaussian function, such as the case of autoregressive processes. However, besides the fact that the optimality of these techniques is still to be reached, their applicability for dealing with scintillation in real-world environments also remains to be confirmed. We carry out an extensive analysis and experimentation campaign on the suitability of these techniques by processing real data captures of scintillation at low and high latitudes. We first evaluate how well phase scintillation can be modeled through an autoregressive process. Then, we propose a novel adaptive, low-complexity autoregressive Kalman filter intended to facilitate the implementation of the approach in practice. Last, we provide an analysis of the operational region of the proposed technique and the limits at which a performance gain over conventional tracking architectures is obtained. The results validate the excellence of the proposed approach for GNSS carrier tracking under scintillation conditions