Beyond Gaussian Statistical Modeling in Geophysical Data Assimilation

International audienceThis review discusses recent advances in geophysical data assimilation beyond Gaussian statistical modeling, in the fields of meteorology, oceanography, as well as atmospheric chemistry. The non-Gaussian features are stressed rather than the nonlinearity of the dynamical models, although both aspects are entangled. Ideas recently proposed to deal with these non-Gaussian issues, in order to improve the state or parameter estimation, are emphasized. The general Bayesian solution to the estimation problem and the techniques to solve it are first presented, as well as the obstacles that hinder their use in high-dimensional and complex systems. Approximations to the Bayesian solution relying on Gaussian, or on second-order moment closure, have been wholly adopted in geophysical data assimilation (e.g., Kalman filters and quadratic variational solutions). Yet, nonlinear and non-Gaussian effects remain. They essentially originate in the nonlinear models and in the non-Gaussian priors. How these effects are handled within algorithms based on Gaussian assumptions is then described. Statistical tools that can diagnose them and measure deviations from Gaussianity are recalled. The following advanced techniques that seek to handle the estimation problem beyond Gaussianity are reviewed: maximum entropy filter, Gaussian anamorphosis, non-Gaussian priors, particle filter with an ensemble Kalman filter as a proposal distribution, maximum entropy on the mean, or strictly Bayesian inferences for large linear models, etc. Several ideas are illustrated with recent or original examples that possess some features of high-dimensional systems. Many of the new approaches are well understood only in special cases and have difficulties that remain to be circumvented. Some of the suggested approaches are quite promising, and sometimes already successful for moderately large though specific geophysical applications. Hints are given as to where progress might come from

Dynamic Machine Learning with Least Square Objectives

As of the writing of this thesis, machine learning has become one of the most active research fields. The interest comes from a variety of disciplines which include computer science, statistics, engineering, and medicine. The main idea behind learning from data is that, when an analytical model explaining the observations is hard to find ---often in contrast to the models in physics such as Newton's laws--- a statistical approach can be taken where one or more candidate models are tuned using data. Since the early 2000's this challenge has grown in two ways: (i) The amount of collected data has seen a massive growth due to the proliferation of digital media, and (ii) the data has become more complex. One example for the latter is the high dimensional datasets, which can for example correspond to dyadic interactions between two large groups (such as customer and product information a retailer collects), or to high resolution image/video recordings. Another important issue is the study of dynamic data, which exhibits dependence on time. Virtually all datasets fall into this category as all data collection is performed over time, however I use the term dynamic to hint at a system with an explicit temporal dependence. A traditional example is target tracking from signal processing literature. Here the position of a target is modeled using Newton's laws of motion, which relates it to time via the target's velocity and acceleration. Dynamic data, as I defined above, poses two important challenges. Firstly, the learning setup is different from the standard theoretical learning setup, also known as Probably Approximately Correct (PAC) learning. To derive PAC learning bounds one assumes a collection of data points sampled independently and identically from a distribution which generates the data. On the other hand, dynamic systems produce correlated outputs. The learning systems we use should accordingly take this difference into consideration. Secondly, as the system is dynamic, it might be necessary to perform the learning online. In this case the learning has to be done in a single pass. Typical applications include target tracking and electricity usage forecasting. In this thesis I investigate several important dynamic and online learning problems, where I develop novel tools to address the shortcomings of the previous solutions in the literature. The work is divided into three parts for convenience. The first part is about matrix factorization for time series analysis which is further divided into two chapters. In the first chapter, matrix factorization is used within a Bayesian framework to model time-varying dyadic interactions, with examples in predicting user-movie ratings and stock prices. In the next chapter, a matrix factorization which uses autoregressive models to forecast future values of multivariate time series is proposed, with applications in predicting electricity usage and traffic conditions. Inspired by the machinery we use in the first part, the second part is about nonlinear Kalman filtering, where a hidden state is estimated over time given observations. The nonlinearity of the system generating the observations is the main challenge here, where a divergence minimization approach is used to unify the seemingly unrelated methods in the literature, and propose new ones. This has applications in target tracking and options pricing. The third and last part is about cost sensitive learning, where a novel method for maximizing area under receiver operating characteristics curve is proposed. Our method has theoretical guarantees and favorable sample complexity. The method is tested on a variety of benchmark datasets, and also has applications in online advertising

Enhanced particle PHD filtering for multiple human tracking

PhD ThesisVideo-based single human tracking has found wide application but multiple human tracking is more challenging and enhanced processing techniques are required to estimate the positions and number of targets in each frame. In this thesis, the particle probability hypothesis density (PHD) lter is therefore the focus due to its ability to estimate both localization and cardinality information related to multiple human targets. To improve the tracking performance of the particle PHD lter, a number of enhancements are proposed. The Student's-t distribution is employed within the state and measurement models of the PHD lter to replace the Gaussian distribution because of its heavier tails, and thereby better predict particles with larger amplitudes. Moreover, the variational Bayesian approach is utilized to estimate the relationship between the measurement noise covariance matrix and the state model, and a joint multi-dimensioned Student's-t distribution is exploited. In order to obtain more observable measurements, a backward retrodiction step is employed to increase the measurement set, building upon the concept of a smoothing algorithm. To make further improvement, an adaptive step is used to combine the forward ltering and backward retrodiction ltering operations through the similarities of measurements achieved over discrete time. As such, the errors in the delayed measurements generated by false alarms and environment noise are avoided. In the nal work, information describing human behaviour is employed iv Abstract v to aid particle sampling in the prediction step of the particle PHD lter, which is captured in a social force model. A novel social force model is proposed based on the exponential function. Furthermore, a Markov Chain Monte Carlo (MCMC) step is utilized to resample the predicted particles, and the acceptance ratio is calculated by the results from the social force model to achieve more robust prediction. Then, a one class support vector machine (OCSVM) is applied in the measurement model of the PHD lter, trained on human features, to mitigate noise from the environment and to achieve better tracking performance. The proposed improvements of the particle PHD lters are evaluated with benchmark datasets such as the CAVIAR, PETS2009 and TUD datasets and assessed with quantitative and global evaluation measures, and are compared with state-of-the-art techniques to con rm the improvement of multiple human tracking performance

Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age

Simultaneous Localization and Mapping (SLAM)consists in the concurrent construction of a model of the environment (the map), and the estimation of the state of the robot moving within it. The SLAM community has made astonishing progress over the last 30 years, enabling large-scale real-world applications, and witnessing a steady transition of this technology to industry. We survey the current state of SLAM. We start by presenting what is now the de-facto standard formulation for SLAM. We then review related work, covering a broad set of topics including robustness and scalability in long-term mapping, metric and semantic representations for mapping, theoretical performance guarantees, active SLAM and exploration, and other new frontiers. This paper simultaneously serves as a position paper and tutorial to those who are users of SLAM. By looking at the published research with a critical eye, we delineate open challenges and new research issues, that still deserve careful scientific investigation. The paper also contains the authors' take on two questions that often animate discussions during robotics conferences: Do robots need SLAM? and Is SLAM solved

Gossip Algorithms for Distributed Signal Processing

Gossip algorithms are attractive for in-network processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This article presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmitted messages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page

Nonlinear Gaussian Filtering : Theory, Algorithms, and Applications

By restricting to Gaussian distributions, the optimal Bayesian filtering problem can be transformed into an algebraically simple form, which allows for computationally efficient algorithms. Three problem settings are discussed in this thesis: (1) filtering with Gaussians only, (2) Gaussian mixture filtering for strong nonlinearities, (3) Gaussian process filtering for purely data-driven scenarios. For each setting, efficient algorithms are derived and applied to real-world problems

Modelling and estimation in lithium-ion batteries: a literature review

Lithium-ion batteries are widely recognised as the leading technology for electrochemical energy storage. Their applications in the automotive industry and integration with renewable energy grids highlight their current significance and anticipate their substantial future impact. However, battery management systems, which are in charge of the monitoring and control of batteries, need to consider several states, like the state of charge and the state of health, which cannot be directly measured. To estimate these indicators, algorithms utilising mathematical models of the battery and basic measurements like voltage, current or temperature are employed. This review focuses on a comprehensive examination of various models, from complex but close to the physicochemical phenomena to computationally simpler but ignorant of the physics; the estimation problem and a formal basis for the development of algorithms; and algorithms used in Li-ion battery monitoring. The objective is to provide a practical guide that elucidates the different models and helps to navigate the different existing estimation techniques, simplifying the process for the development of new Li-ion battery applications.This research received support from the Spanish Ministry of Science and Innovation under projects MAFALDA (PID2021-126001OB-C31 funded by MCIN/AEI/10.13039/501100011033/ ERDF,EU) and MASHED (TED2021-129927B-I00), and by FI Joan Oró grant (code 2023 FI-1 00827), cofinanced by the European Union.Peer ReviewedPostprint (published version

Adaptive Algorithms for Intelligent Acoustic Interfaces

Modern speech communications are evolving towards a new direction which involves users in a more perceptive way. That is the immersive experience, which may be considered as the “last-mile” problem of telecommunications. One of the main feature of immersive communications is the distant-talking, i.e. the hands-free (in the broad sense) speech communications without bodyworn or tethered microphones that takes place in a multisource environment where interfering signals may degrade the communication quality and the intelligibility of the desired speech source. In order to preserve speech quality intelligent acoustic interfaces may be used. An intelligent acoustic interface may comprise multiple microphones and loudspeakers and its peculiarity is to model the acoustic channel in order to adapt to user requirements and to environment conditions. This is the reason why intelligent acoustic interfaces are based on adaptive filtering algorithms. The acoustic path modelling entails a set of problems which have to be taken into account in designing an adaptive filtering algorithm. Such problems may be basically generated by a linear or a nonlinear process and can be tackled respectively by linear or nonlinear adaptive algorithms. In this work we consider such modelling problems and we propose novel effective adaptive algorithms that allow acoustic interfaces to be robust against any interfering signals, thus preserving the perceived quality of desired speech signals. As regards linear adaptive algorithms, a class of adaptive filters based on the sparse nature of the acoustic impulse response has been recently proposed. We adopt such class of adaptive filters, named proportionate adaptive filters, and derive a general framework from which it is possible to derive any linear adaptive algorithm. Using such framework we also propose some efficient proportionate adaptive algorithms, expressly designed to tackle problems of a linear nature. On the other side, in order to address problems deriving from a nonlinear process, we propose a novel filtering model which performs a nonlinear transformations by means of functional links. Using such nonlinear model, we propose functional link adaptive filters which provide an efficient solution to the modelling of a nonlinear acoustic channel. Finally, we introduce robust filtering architectures based on adaptive combinations of filters that allow acoustic interfaces to more effectively adapt to environment conditions, thus providing a powerful mean to immersive speech communications

Adaptive Algorithms for Intelligent Acoustic Interfaces

Modern speech communications are evolving towards a new direction which involves users in a more perceptive way. That is the immersive experience, which may be considered as the “last-mile” problem of telecommunications. One of the main feature of immersive communications is the distant-talking, i.e. the hands-free (in the broad sense) speech communications without bodyworn or tethered microphones that takes place in a multisource environment where interfering signals may degrade the communication quality and the intelligibility of the desired speech source. In order to preserve speech quality intelligent acoustic interfaces may be used. An intelligent acoustic interface may comprise multiple microphones and loudspeakers and its peculiarity is to model the acoustic channel in order to adapt to user requirements and to environment conditions. This is the reason why intelligent acoustic interfaces are based on adaptive filtering algorithms. The acoustic path modelling entails a set of problems which have to be taken into account in designing an adaptive filtering algorithm. Such problems may be basically generated by a linear or a nonlinear process and can be tackled respectively by linear or nonlinear adaptive algorithms. In this work we consider such modelling problems and we propose novel effective adaptive algorithms that allow acoustic interfaces to be robust against any interfering signals, thus preserving the perceived quality of desired speech signals. As regards linear adaptive algorithms, a class of adaptive filters based on the sparse nature of the acoustic impulse response has been recently proposed. We adopt such class of adaptive filters, named proportionate adaptive filters, and derive a general framework from which it is possible to derive any linear adaptive algorithm. Using such framework we also propose some efficient proportionate adaptive algorithms, expressly designed to tackle problems of a linear nature. On the other side, in order to address problems deriving from a nonlinear process, we propose a novel filtering model which performs a nonlinear transformations by means of functional links. Using such nonlinear model, we propose functional link adaptive filters which provide an efficient solution to the modelling of a nonlinear acoustic channel. Finally, we introduce robust filtering architectures based on adaptive combinations of filters that allow acoustic interfaces to more effectively adapt to environment conditions, thus providing a powerful mean to immersive speech communications