Variational Bayes Phase Tracking for Correlated Dual-Frequency Measurements with Slow Dynamics

We consider the problem of estimating the absolute phase of a noisy signal when this latter consists of correlated dual-frequency measurements. This scenario may arise in many application areas such as global navigation satellite system (GNSS). In this paper, we assume a slow varying phase and propose accordingly a Bayesian filtering technique that makes use of the frequency diversity. More specifically, the method results from a variational Bayes approximation and belongs to the class of nonlinear filters. Numerical simulations are performed to assess the performance of the tracking technique especially in terms of mean square error and cycle-slip rate. Comparison with a more conventional approach, namely a Gaussian sum estimator, shows substantial improvements when the signal-to-noise ratio and/or the correlation of the measurements are low

Machine learning algorithms for cognitive radio wireless networks

In this thesis new methods are presented for achieving spectrum sensing in cognitive radio wireless networks. In particular, supervised, semi-supervised and unsupervised machine learning based spectrum sensing algorithms are developed and various techniques to improve their performance are described. Spectrum sensing problem in multi-antenna cognitive radio networks is considered and a novel eigenvalue based feature is proposed which has the capability to enhance the performance of support vector machines algorithms for signal classification. Furthermore, spectrum sensing under multiple primary users condition is studied and a new re-formulation of the sensing task as a multiple class signal detection problem where each class embeds one or more states is presented. Moreover, the error correcting output codes based multi-class support vector machines algorithms is proposed and investigated for solving the multiple class signal detection problem using two different coding strategies. In addition, the performance of parametric classifiers for spectrum sensing under slow fading channel is studied. To address the attendant performance degradation problem, a Kalman filter based channel estimation technique is proposed for tracking the temporally correlated slow fading channel and updating the decision boundary of the classifiers in real time. Simulation studies are included to assess the performance of the proposed schemes. Finally, techniques for improving the quality of the learning features and improving the detection accuracy of sensing algorithms are studied and a novel beamforming based pre-processing technique is presented for feature realization in multi-antenna cognitive radio systems. Furthermore, using the beamformer derived features, new algorithms are developed for multiple hypothesis testing facilitating joint spatio-temporal spectrum sensing. The key performance metrics of the classifiers are evaluated to demonstrate the superiority of the proposed methods in comparison with previously proposed alternatives

Enabling Robust State Estimation through Covariance Adaptation

Several robust state estimation frameworks have been proposed over the previous decades. Underpinning all of these robust frameworks is one dubious assumption. Specifically, the assumption that an accurate a priori measurement uncertainty model can be provided. As systems become more autonomous, this assumption becomes less valid (i.e., as systems start operating in novel environments, there is no guarantee that the assumed a priori measurement uncertainty model characterizes the sensors current observation uncertainty). In an attempt to relax this assumption, a novel robust state estimation framework is proposed. The proposed framework enables robust state estimation through the iterative adaptation of the measurement uncertainty model. The adaptation of the measurement uncertainty model is granted through non-parametric clustering of the estimator\u27 s residuals, which enables the characterization of the measurement uncertainty via a Gaussian mixture model. This Gaussian mixture model based measurement uncertainty characterization can be incorporated into any non-linear least square optimization routine. Within this dissertation, the proposed framework is instantiated into three novel robust state estimation algorithms: batch covariance estimation (BCE), batch covariance estimation over an augmented data space (BCE-AD), and incremental covariance estimation (ICE). To verify the proposed framework, three global navigation satellite system (GNSS) data sets were collected. The collected data sets provide varying levels of observation degradation to enable the characterization of the proposed algorithm on a diverse data set. Utilizing these data sets, it is shown that the proposed framework exhibits improved state estimation accuracy when compared to other robust estimation techniques when confronted with degraded data quality

Recurrences reveal shared causal drivers of complex time series

Many experimental time series measurements share unobserved causal drivers. Examples include genes targeted by transcription factors, ocean flows influenced by large-scale atmospheric currents, and motor circuits steered by descending neurons. Reliably inferring this unseen driving force is necessary to understand the intermittent nature of top-down control schemes in diverse biological and engineered systems. Here, we introduce a new unsupervised learning algorithm that uses recurrences in time series measurements to gradually reconstruct an unobserved driving signal. Drawing on the mathematical theory of skew-product dynamical systems, we identify recurrence events shared across response time series, which implicitly define a recurrence graph with glass-like structure. As the amount or quality of observed data improves, this recurrence graph undergoes a percolation transition manifesting as weak ergodicity breaking for random walks on the induced landscape -- revealing the shared driver's dynamics, even in the presence of strongly corrupted or noisy measurements. Across several thousand random dynamical systems, we empirically quantify the dependence of reconstruction accuracy on the rate of information transfer from a chaotic driver to the response systems, and we find that effective reconstruction proceeds through gradual approximation of the driver's dominant orbit topology. Through extensive benchmarks against classical and neural-network-based signal processing techniques, we demonstrate our method's strong ability to extract causal driving signals from diverse real-world datasets spanning ecology, genomics, fluid dynamics, and physiology.Comment: 8 pages, 5 figure

Single-molecule tracking and its application in biomolecular binding detection

In the past two decades significant advances have been made in single-molecule detection, which enables the direct observation of single biomolecules at work in real time under physiological conditions. In particular, the development of single-molecule tracking (SMT) microscopy allows us to monitor the motion paths of individual biomolecules in living systems, unveiling the localization dynamics and transport modalities of the biomolecules that support the development of life. While 3D-SMT is probably the most suitable method for determining whether tracked molecules (can be any biomolecule such as DNA, membrane receptors, and transcription factors) form dimers or complexes with other molecules, great technical challenges remain to be overcome before the potential of 3D-SMT in biomolecular binding detection can be realized. This dissertation describes my work on recent methodology development to overcome these challenges, and new applications of the 3D-SMT technology in rare molecular species quantification. First, we provide an overview of current SMT technologies, with an emphasis on three-dimensional feedback controlled SMT. Advantages and drawbacks of each SMT method are outlined. Second, we describe the theoretical modeling and instrumentation of our confocal tracking microscope. Its multi-dimensional sensing capability (3D position, diffusion coefficient, fluorescence lifetime) is experimentally characterized. In order to maximize the tracking duration, we have also developed strategies to effectively slow-down fast diffusing molecule, and optimized the buffer conditions. Third, we show that our 3D-SMT microscope can detect biomolecular association/disassociated by two types of contrast mechanisms: diffusion rate and lifetime FRET signal. DNA transient binding is used as a model system because of ease of fluorescent labeling and tunable binding kinetics. Both of the two mechanisms involve tracking a fluorescent-labeled single-stranded DNA (ssDNA), but the second approach also requires its complementary strand to be labeled by a dark quencher. A combined analysis of multiple single-molecule trajectories allow us to measure the kinetics that is even beyond the physical bandwidth of the tracking system. In the end, we introduce the application of SMT in rare single-molecule species quantification. The theory for predicting the sensitivity and fidelity is established. Our work highlights the fundamental limitations that we are facing in precise single-molecule identification and quantification without amplification.Biomedical Engineerin

Robust Filtering Techniques for RTK Positioning in Harsh Propagation Environments

Global navigation satellite systems (GNSSs) play a key role in intelligent transportation systems such as autonomous driving or unmanned systems navigation. In such applications, it is fundamental to ensure a reliable precise positioning solution able to operate in harsh propagation conditions such as urban environments and under multipath and other disturbances. Exploiting carrier phase observations allows for precise positioning solutions at the complexity cost of resolving integer phase ambiguities, a procedure that is particularly affected by non-nominal conditions. This limits the applicability of conventional filtering techniques in challenging scenarios, and new robust solutions must be accounted for. This contribution deals with real-time kinematic (RTK) positioning and the design of robust filtering solutions for the associated mixed integer- and real-valued estimation problem. Families of Kalman filter (KF) approaches based on robust statistics and variational inference are explored, such as the generalized M-based KF or the variational-based KF, aiming to mitigate the impact of outliers or non-nominal measurement behaviors. The performance assessment under harsh propagation conditions is realized using a simulated scenario and real data from a measurement campaign. The proposed robust filtering solutions are shown to offer excellent resilience against outlying observations, with the variational-based KF showcasing the overall best performance in terms of Gaussian efficiency and robustness

Neural-Kalman Schemes for Non-Stationary Channel Tracking and Learning

This Thesis focuses on channel tracking in Orthogonal Frequency-Division Multiplexing (OFDM), a widely-used method of data transmission in wireless communications, when abrupt changes occur in the channel. In highly mobile applications, new dynamics appear that might make channel tracking non-stationary, e.g. channels might vary with location, and location rapidly varies with time. Simple examples might be the di erent channel dynamics a train receiver faces when it is close to a station vs. crossing a bridge vs. entering a tunnel, or a car receiver in a route that grows more tra c-dense. Some of these dynamics can be modelled as channel taps dying or being reborn, and so tap birth-death detection is of the essence. In order to improve the quality of communications, we delved into mathematical methods to detect such abrupt changes in the channel, such as the mathematical areas of Sequential Analysis/ Abrupt Change Detection and Random Set Theory (RST), as well as the engineering advances in Neural Network schemes. This knowledge helped us nd a solution to the problem of abrupt change detection by informing and inspiring the creation of low-complexity implementations for real-world channel tracking. In particular, two such novel trackers were created: the Simpli- ed Maximum A Posteriori (SMAP) and the Neural-Network-switched Kalman Filtering (NNKF) schemes. The SMAP is a computationally inexpensive, threshold-based abrupt-change detector. It applies the three following heuristics for tap birth-death detection: a) detect death if the tap gain jumps into approximately zero (memoryless detection); b) detect death if the tap gain has slowly converged into approximately zero (memory detection); c) detect birth if the tap gain is far from zero. The precise parameters for these three simple rules can be approximated with simple theoretical derivations and then ne-tuned through extensive simulations. The status detector for each tap using only these three computationally inexpensive threshold comparisons achieves an error reduction matching that of a close-to-perfect path death/birth detection, as shown in simulations. This estimator was shown to greatly reduce channel tracking error in the target Signal-to-Noise Ratio (SNR) range at a very small computational cost, thus outperforming previously known systems. The underlying RST framework for the SMAP was then extended to combined death/birth and SNR detection when SNR is dynamical and may drift. We analyzed how di erent quasi-ideal SNR detectors a ect the SMAP-enhanced Kalman tracker's performance. Simulations showed SMAP is robust to SNR drift in simulations, although it was also shown to bene t from an accurate SNR detection. The core idea behind the second novel tracker, NNKFs, is similar to the SMAP, but now the tap birth/death detection will be performed via an arti cial neuronal network (NN). Simulations show that the proposed NNKF estimator provides extremely good performance, practically identical to a detector with 100% accuracy. These proposed Neural-Kalman schemes can work as novel trackers for multipath channels, since they are robust to wide variations in the probabilities of tap birth and death. Such robustness suggests a single, low-complexity NNKF could be reusable over di erent tap indices and communication environments. Furthermore, a di erent kind of abrupt change was proposed and analyzed: energy shifts from one channel tap to adjacent taps (partial tap lateral hops). This Thesis also discusses how to model, detect and track such changes, providing a geometric justi cation for this and additional non-stationary dynamics in vehicular situations, such as road scenarios where re ections on trucks and vans are involved, or the visual appearance/disappearance of drone swarms. An extensive literature review of empirically-backed abrupt-change dynamics in channel modelling/measuring campaigns is included. For this generalized framework of abrupt channel changes that includes partial tap lateral hopping, a neural detector for lateral hops with large energy transfers is introduced. Simulation results suggest the proposed NN architecture might be a feasible lateral hop detector, suitable for integration in NNKF schemes. Finally, the newly found understanding of abrupt changes and the interactions between Kalman lters and neural networks is leveraged to analyze the neural consequences of abrupt changes and brie y sketch a novel, abrupt-change-derived stochastic model for neural intelligence, extract some neuro nancial consequences of unstereotyped abrupt dynamics, and propose a new portfolio-building mechanism in nance: Highly Leveraged Abrupt Bets Against Failing Experts (HLABAFEOs). Some communication-engineering-relevant topics, such as a Bayesian stochastic stereotyper for hopping Linear Gauss-Markov (LGM) models, are discussed in the process. The forecasting problem in the presence of expert disagreements is illustrated with a hopping LGM model and a novel structure for a Bayesian stereotyper is introduced that might eventually solve such problems through bio-inspired, neuroscienti cally-backed mechanisms, like dreaming and surprise (biological Neural-Kalman). A generalized framework for abrupt changes and expert disagreements was introduced with the novel concept of Neural-Kalman Phenomena. This Thesis suggests mathematical (Neural-Kalman Problem Category Conjecture), neuro-evolutionary and social reasons why Neural-Kalman Phenomena might exist and found signi cant evidence for their existence in the areas of neuroscience and nance. Apart from providing speci c examples, practical guidelines and historical (out)performance for some HLABAFEO investing portfolios, this multidisciplinary research suggests that a Neural- Kalman architecture for ever granular stereotyping providing a practical solution for continual learning in the presence of unstereotyped abrupt dynamics would be extremely useful in communications and other continual learning tasks.Programa de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Luis Castedo Ribas.- Secretaria: Ana García Armada.- Vocal: José Antonio Portilla Figuera