Qubit state estimation and enhancement by quantum thermal noise

International audience

Nested Sampling and its Applications in Stable Compressive Covariance Estimation and Phase Retrieval with Near-Minimal Measurements

Compressed covariance sensing using quadratic samplers is gaining increasing interest in recent literature. Covariance matrix often plays the role of a sufficient statistic in many signal and information processing tasks. However, owing to the large dimension of the data, it may become necessary to obtain a compressed sketch of the high dimensional covariance matrix to reduce the associated storage and communication costs. Nested sampling has been proposed in the past as an efficient sub-Nyquist sampling strategy that enables perfect reconstruction of the autocorrelation sequence of Wide-Sense Stationary (WSS) signals, as though it was sampled at the Nyquist rate. The key idea behind nested sampling is to exploit properties of the difference set that naturally arises in quadratic measurement model associated with covariance compression. In this thesis, we will focus on developing novel versions of nested sampling for low rank Toeplitz covariance estimation, and phase retrieval, where the latter problem finds many applications in high resolution optical imaging, X-ray crystallography and molecular imaging. The problem of low rank compressive Toeplitz covariance estimation is first shown to be fundamentally related to that of line spectrum recovery. In absence if noise, this connection can be exploited to develop a particular kind of sampler called the Generalized Nested Sampler (GNS), that can achieve optimal compression rates. In presence of bounded noise, we develop a regularization-free algorithm that provably leads to stable recovery of the high dimensional Toeplitz matrix from its order-wise minimal sketch acquired using a GNS. Contrary to existing TV-norm and nuclear norm based reconstruction algorithms, our technique does not use any tuning parameters, which can be of great practical value. The idea of nested sampling idea also finds a surprising use in the problem of phase retrieval, which has been of great interest in recent times for its convex formulation via PhaseLift, By using another modified version of nested sampling, namely the Partial Nested Fourier Sampler (PNFS), we show that with probability one, it is possible to achieve a certain conjectured lower bound on the necessary measurement size. Moreover, for sparse data, an l1 minimization based algorithm is proposed that can lead to stable phase retrieval using order-wise minimal number of measurements.

POSE ESTIMATION AND 3D RECONSTRUCTION USING SENSOR FUSION

A camera maps 3-dimensional (3D) world space to a 2-dimensional (2D) image space. In the process it loses the depth information, i.e., the distance from the camera focal point to the imaged objects. It is impossible to recover this information from a single image. However, by using two or more images from different viewing angles this information can be recovered, which in turn can be used to obtain the pose (position and orientation) of the camera. Using this pose, a 3D reconstruction of imaged objects in the world can be computed. Numerous algorithms have been proposed and implemented to solve the above problem; these algorithms are commonly called Structure from Motion (SfM). State-of-the-art SfM techniques have been shown to give promising results. However, unlike a Global Positioning System (GPS) or an Inertial Measurement Unit (IMU) which directly give the position and orientation respectively, the camera system estimates it after implementing SfM as mentioned above. This makes the pose obtained from a camera highly sensitive to the images captured and other effects, such as low lighting conditions, poor focus or improper viewing angles. In some applications, for example, an Unmanned Aerial Vehicle (UAV) inspecting a bridge or a robot mapping an environment using Simultaneous Localization and Mapping (SLAM), it is often difficult to capture images with ideal conditions. This report examines the use of SfM methods in such applications and the role of combining multiple sensors, viz., sensor fusion, to achieve more accurate and usable position and reconstruction information. This project investigates the role of sensor fusion in accurately estimating the pose of a camera for the application of 3D reconstruction of a scene. The first set of experiments is conducted in a motion capture room. These results are assumed as ground truth in order to evaluate the strengths and weaknesses of each sensor and to map their coordinate systems. Then a number of scenarios are targeted where SfM fails. The pose estimates obtained from SfM are replaced by those obtained from other sensors and the 3D reconstruction is completed. Quantitative and qualitative comparisons are made between the 3D reconstruction obtained by using only a camera versus that obtained by using the camera along with a LIDAR and/or an IMU. Additionally, the project also works towards the performance issue faced while handling large data sets of high-resolution images by implementing the system on the Superior high performance computing cluster at Michigan Technological University.

An Islanding Detection Method based on Impedance Estimation and Grid Identification for Grid-Tie Distributed Power Generation Systems

Power system policies are broadly on track to escalate the use of renewable energy resources in electric power generation. Integration of dispersed generation to the utility network not only intensifies the benefits of renewable generation but also introduces further advantages such as power quality enhancement and freedom of power generation for the consumers. However, issues arise from the integration of distributed generators to the existing utility grid are as significant as its benefits. The issues are aggravated as the number of grid-connected distributed generators increases. Therefore, power quality demands become stricter to ensure a safe and proper advancement towards the emerging smart grid. In this regard, system protection is the area that is highly affected as the grid-connected distributed generation share in electricity generation increases. Islanding detection, amongst all protection issues, is the most important concern for a power system with high penetration of distributed sources. Islanding occurs when a portion of the distribution network which includes one or more distributed generation units and local loads is disconnected from the remaining portion of the grid. Upon formation of a power island, it remains energized due to the presence of one or more distributed sources. This thesis introduces a new islanding detection technique based on an enhanced multi-layer scheme that shows superior performance over the existing techniques. It provides improved solutions for safety and protection of power systems and distributed sources that are capable of operating in grid-connected mode. The proposed active method offers negligible non-detection zone. It is applicable to micro-grids with a number of distributed generation sources without sacrificing the dynamic response of the system. In addition, the information obtained from the proposed scheme allows for smooth transition to stand-alone operation if required. The proposed technique paves the path towards a comprehensive protection solution for future power networks. The proposed method is converter-resident and all power conversion systems that are operating based on power electronics converters can benefit from this method. The theoretical analysis is presented, and extensive simulation results confirm the validity of the analytical work.

Comprehensive characterization of snowfall in terms of microphysical features, quantitative precipitation estimation and scavenging properties by in situ and remote sensing observations at an Antarctic coastal site

Snow plays a crucial role in the Earth's hydrological cycle and energy budget, making its monitoring necessary. In this context, ground-based radars and in situ instruments are essential thanks to their spatial coverage, resolution, and temporal sampling. Deep understanding and reliable measurements of snow properties are crucial over Antarctica to assess potential future changes of the surface mass balance (SMB) and define the contribution of the Antarctic ice sheet on sea-level rise. However, despite its key role, Antarctic precipitation is poorly investigated due to the continent's inaccessibility and extreme environment. In this framework, this Thesis aims to contribute to filling this gap by in-depth characterization of Antarctic precipitation at the Mario Zucchelli station from different points of view: microphysical features, quantitative precipitation estimation (QPE), vertical structure of precipitation, and scavenging properties. For this purpose, a K-band vertically pointing radar collocated with a laser disdrometer and an optical particle counter (OPC) were used. The radar probed the lowest atmospheric layers with high vertical resolution, allowing the first trusted measurement at only 105 m height. Disdrometer and OPC provided information on the particle size distribution and aerosol concentrations. An innovative snow classification methodology was designed by comparing the radar reflectivity (Ze) and disdrometer-derived reflectivity by means of DDA simulations. Results of classification were exploited in QPE through appropriate Ze-snow rate relationships. The accuracy of the resulting QPE was benchmarked against a collocated weighing gauge. Vertical radar profiles were also investigated to highlight hydrometeors' sublimation and growth processes. Finally, OPC and disdrometer data allowed providing the first-ever estimates of scavenging properties of Antarctic snowfall. Results presented in this Thesis give rise to advances in knowledge of the characteristics of snowfall in Antarctica, contributing to a better assessment of the SMB of the Antarctic ice sheet, the major player in the global sea-level rise.

Novel methods of state estimation and parameter identification for high-performance motorcycles

This research activity aims at providing a reliable estimation of particular state variables or parameters concerning the dynamics and performance optimization of a MotoGP-class motorcycle, integrating the classical model-based approach with new methodologies involving artificial intelligence. The first topic of the research focuses on the estimation of the thermal behavior of the MotoGP carbon braking system. Numerical tools are developed to assess the instantaneous surface temperature distribution in the motorcycle's front brake discs. Within this application other important brake parameters are identified using Kalman filters, such as the disc convection coefficient and the power distribution in the disc-pads contact region. Subsequently, a physical model of the brake is built to estimate the instantaneous braking torque. However, the results obtained with this approach are highly limited by the knowledge of the friction coefficient (μ) between the disc rotor and the pads. Since the value of μ is a highly nonlinear function of many variables (namely temperature, pressure and angular velocity of the disc), an analytical model for the friction coefficient estimation appears impractical to establish. To overcome this challenge, an innovative hybrid solution is implemented, combining the benefit of artificial intelligence (AI) with classical model-based approach. Indeed, the disc temperature estimated through the thermal model previously implemented is processed by a machine learning algorithm that outputs the actual value of the friction coefficient thus improving the braking torque computation performed by the physical model of the brake. Finally, the last topic of this research activity regards the development of an AI algorithm to estimate the current sideslip angle of the motorcycle's front tire. While a single-track motorcycle kinematic model and IMU accelerometer signals theoretically enable sideslip calculation, the presence of accelerometer noise leads to a significant drift over time. To address this issue, a long short-term memory (LSTM) network is implemented.

Neural Network Based UAV Fault Tolerant Control with Aerodynamic Disturbance Estimation and Compensation

In this thesis, the problem of controlling a quadrotor UAV is considered. It is done by presenting an original control system, designed as a combination of Neural Networks and Disturbance Observer, using a composite learning approach for a system of the second order, which is a novel methodology in literature. After a brief introduction about the quadrotors, the concepts needed to understand the controller are presented, such as the main notions of advanced control, the basic structure and design of a Neural Network, the modeling of a quadrotor and its dynamics. The full simulator, developed on the MATLAB Simulink environment, used throughout the whole thesis, is also shown. For the guidance and control purposes, a Sliding Mode Controller, used as a reference, it is firstly introduced, and its theory and implementation on the simulator are illustrated. Finally the original controller is introduced, through its novel formulation, and implementation on the model. The effectiveness and robustness of the two controllers are then proven by extensive simulations in all different conditions of external disturbance and faults.

Bayesian methods for estimation, optimization and experimental design

Mathematical models often contain parameters that need to be calibrated from measured data. The emergence of efficient Markov Chain Monte Carlo (MCMC) methods has made the Bayesian approach a standard tool in quantifying the uncertainty in the parameters. With MCMC, the parameter estimation problem can be solved in a fully statistical manner, and the whole distribution of the parameters can be explored, instead of obtaining point estimates and using, e.g., Gaussian approximations. In this thesis, MCMC methods are applied to parameter estimation problems in chemical reaction engineering, population ecology, and climate modeling. Motivated by the climate model experiments, the methods are developed further to make them more suitable for problems where the model is computationally intensive. After the parameters are estimated, one can start to use the model for various tasks. Two such tasks are studied in this thesis: optimal design of experiments, where the task is to design the next measurements so that the parameter uncertainty is minimized, and model-based optimization, where a model-based quantity, such as the product yield in a chemical reaction model, is optimized. In this thesis, novel ways to perform these tasks are developed, based on the output of MCMC parameter estimation. A separate topic is dynamical state estimation, where the task is to estimate the dynamically changing model state, instead of static parameters. For example, in numerical weather prediction, an estimate of the state of the atmosphere must constantly be updated based on the recently obtained measurements. In this thesis, a novel hybrid state estimation method is developed, which combines elements from deterministic and random sampling methods.

On state and parameter estimation in chaotic systems

State-of-the-art predictions of atmospheric states rely on large-scale numerical models of chaotic systems. This dissertation studies numerical methods for state and parameter estimation in such systems. The motivation comes from weather and climate models and a methodological perspective is adopted. The dissertation comprises three sections: state estimation, parameter estimation and chemical data assimilation with real atmospheric satellite data. In the state estimation part of this dissertation, a new filtering technique based on a combination of ensemble and variational Kalman filtering approaches, is presented, experimented and discussed. This new filter is developed for large-scale Kalman filtering applications. In the parameter estimation part, three different techniques for parameter estimation in chaotic systems are considered. The methods are studied using the parameterized Lorenz 95 system, which is a benchmark model for data assimilation. In addition, a dilemma related to the uniqueness of weather and climate model closure parameters is discussed. In the data-oriented part of this dissertation, data from the Global Ozone Monitoring by Occultation of Stars (GOMOS) satellite instrument are considered and an alternative algorithm to retrieve atmospheric parameters from the measurements is presented. The validation study presents first global comparisons between two unique satellite-borne datasets of vertical profiles of nitrogen trioxide (NO3), retrieved using GOMOS and Stratospheric Aerosol and Gas Experiment III (SAGE III) satellite instruments. The GOMOS NO3 observations are also considered in a chemical state estimation study in order to retrieve stratospheric temperature profiles. The main result of this dissertation is the consideration of likelihood calculations via Kalman filtering outputs. The concept has previously been used together with stochastic differential equations and in time series analysis. In this work, the concept is applied to chaotic dynamical systems and used together with Markov chain Monte Carlo (MCMC) methods for statistical analysis. In particular, this methodology is advocated for use in numerical weather prediction (NWP) and climate model applications. In addition, the concept is shown to be useful in estimating the filter-specific parameters related, e.g., to model error covariance matrix parameters.

Automatic front-crawl temporal phase detection using adaptive filtering of inertial signals

This study introduces a novel approach for automatic temporal phase detection and inter-arm coordination estimation in front-crawl swimming using inertial measurement units (IMUs). We examined the validity of our method by comparison against a video-based system. Three waterproofed IMUs (composed of 3D accelerometer, 3D gyroscope) were placed on both forearms and the sacrum of the swimmer. We used two underwater video cameras in side and frontal views as our reference system. Two independent operators performed the video analysis. To test our methodology, seven well-trained swimmers performed three 300 m trials in a 50 m indoor pool. Each trial was in a different coordination mode quantified by the index of coordination. We detected different phases of the arm stroke by employing orientation estimation techniques and a new adaptive change detection algorithm on inertial signals. The difference of 0.2 +/- 3.9% between our estimation and video-based system in assessment of the index of coordination was comparable to experienced operators' difference (1.1 +/- 3.6%). The 95% limits of agreement of the difference between the two systems in estimation of the temporal phases were always less than 7.9% of the cycle duration. The inertial system offers an automatic easy-to-use system with timely feedback for the study of swimming.

Methods for testing association between uncertain genotypes and quantitative traits.

Interpretability and power of genome-wide association studies can be increased by imputing unobserved genotypes, using a reference panel of individuals genotyped at higher marker density. For many markers, genotypes cannot be imputed with complete certainty, and the uncertainty needs to be taken into account when testing for association with a given phenotype. In this paper, we compare currently available methods for testing association between uncertain genotypes and quantitative traits. We show that some previously described methods offer poor control of the false-positive rate (FPR), and that satisfactory performance of these methods is obtained only by using ad hoc filtering rules or by using a harsh transformation of the trait under study. We propose new methods that are based on exact maximum likelihood estimation and use a mixture model to accommodate nonnormal trait distributions when necessary. The new methods adequately control the FPR and also have equal or better power compared to all previously described methods. We provide a fast software implementation of all the methods studied here; our new method requires computation time of less than one computer-day for a typical genome-wide scan, with 2.5 M single nucleotide polymorphisms and 5000 individuals.

Model selection and error estimation

We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be converted into a data-based penalty function and the performance of the estimate is governed by the quality of the error estimate. We consider several penalty functions, involving error estimates on independent test data, empirical {\sc vc} dimension, empirical {\sc vc} entropy, andmargin-based quantities. We also consider the maximal difference between the error on the first half of the training data and the second half, and the expected maximal discrepancy, a closely related capacity estimate that can be calculated by Monte Carlo integration. Maximal discrepancy penalty functions are appealing for pattern classification problems, since their computation is equivalent to empirical risk minimization over the training data with some labels flipped.

Estimation of State Space Models and Stochastic Volatility

Ma thèse est composée de trois chapitres reliés à l'estimation des modèles espace-état et volatilité stochastique. Dans le première article, nous développons une procédure de lissage de l'état, avec efficacité computationnelle, dans un modèle espace-état linéaire et gaussien. Nous montrons comment exploiter la structure particulière des modèles espace-état pour tirer les états latents efficacement. Nous analysons l'efficacité computationnelle des méthodes basées sur le filtre de Kalman, l'algorithme facteur de Cholesky et notre nouvelle méthode utilisant le compte d'opérations et d'expériences de calcul. Nous montrons que pour de nombreux cas importants, notre méthode est plus efficace. Les gains sont particulièrement grands pour les cas où la dimension des variables observées est grande ou dans les cas où il faut faire des tirages répétés des états pour les mêmes valeurs de paramètres. Comme application, on considère un modèle multivarié de Poisson avec le temps des intensités variables, lequel est utilisé pour analyser le compte de données des transactions sur les marchés financières. Dans le deuxième chapitre, nous proposons une nouvelle technique pour analyser des modèles multivariés à volatilité stochastique. La méthode proposée est basée sur le tirage efficace de la volatilité de son densité conditionnelle sachant les paramètres et les données. Notre méthodologie s'applique aux modèles avec plusieurs types de dépendance dans la coupe transversale. Nous pouvons modeler des matrices de corrélation conditionnelles variant dans le temps en incorporant des facteurs dans l'équation de rendements, où les facteurs sont des processus de volatilité stochastique indépendants. Nous pouvons incorporer des copules pour permettre la dépendance conditionnelle des rendements sachant la volatilité, permettant avoir différent lois marginaux de Student avec des degrés de liberté spécifiques pour capturer l'hétérogénéité des rendements. On tire la volatilité comme un bloc dans la dimension du temps et un à la fois dans la dimension de la coupe transversale. Nous appliquons la méthode introduite par McCausland (2012) pour obtenir une bonne approximation de la distribution conditionnelle à posteriori de la volatilité d'un rendement sachant les volatilités d'autres rendements, les paramètres et les corrélations dynamiques. Le modèle est évalué en utilisant des données réelles pour dix taux de change. Nous rapportons des résultats pour des modèles univariés de volatilité stochastique et deux modèles multivariés. Dans le troisième chapitre, nous évaluons l'information contribuée par des variations de volatilite réalisée à l'évaluation et prévision de la volatilité quand des prix sont mesurés avec et sans erreur. Nous utilisons de modèles de volatilité stochastique. Nous considérons le point de vue d'un investisseur pour qui la volatilité est une variable latent inconnu et la volatilité réalisée est une quantité d'échantillon qui contient des informations sur lui. Nous employons des méthodes bayésiennes de Monte Carlo par chaîne de Markov pour estimer les modèles, qui permettent la formulation, non seulement des densités a posteriori de la volatilité, mais aussi les densités prédictives de la volatilité future. Nous comparons les prévisions de volatilité et les taux de succès des prévisions qui emploient et n'emploient pas l'information contenue dans la volatilité réalisée. Cette approche se distingue de celles existantes dans la littérature empirique en ce sens que ces dernières se limitent le plus souvent à documenter la capacité de la volatilité réalisée à se prévoir à elle-même. Nous présentons des applications empiriques en utilisant les rendements journaliers des indices et de taux de change. Les différents modèles concurrents sont appliqués à la seconde moitié de 2008, une période marquante dans la récente crise financière.

Modeling and Analysis of Some Heavy Tailed Time Series

The thesis has covered various aspects of modeling and analysis of finite mean time series with symmetric stable distributed innovations. Time series analysis based on Box and Jenkins methods are the most popular approaches where the models are linear and errors are Gaussian. We highlighted the limitations of classical time series analysis tools and explored some generalized tools and organized the approach parallel to the classical set up. In the present thesis we mainly studied the estimation and prediction of signal plus noise model. Here we assumed the signal and noise follow some models with symmetric stable innovations.We start the thesis with some motivating examples and application areas of alpha stable time series models. Classical time series analysis and corresponding theories based on finite variance models are extensively discussed in second chapter. We also surveyed the existing theories and methods correspond to infinite variance models in the same chapter. We present a linear filtering method for computing the filter weights assigned to the observation for estimating unobserved signal under general noisy environment in third chapter. Here we consider both the signal and the noise as stationary processes with infinite variance innovations. We derived semi infinite, double infinite and asymmetric signal extraction filters based on minimum dispersion criteria. Finite length filters based on Kalman-Levy filters are developed and identified the pattern of the filter weights. Simulation studies show that the proposed methods are competent enough in signal extraction for processes with infinite variance.Parameter estimation of autoregressive signals observed in a symmetric stable noise environment is discussed in fourth chapter. Here we used higher order Yule-Walker type estimation using auto-covariation function and exemplify the methods by simulation and application to Sea surface temperature data. We increased the number of Yule-Walker equations and proposed a ordinary least square estimate to the autoregressive parameters. Singularity problem of the auto-covariation matrix is addressed and derived a modified version of the Generalized Yule-Walker method using singular value decomposition.In fifth chapter of the thesis we introduced partial covariation function as a tool for stable time series analysis where covariance or partial covariance is ill defined. Asymptotic results of the partial auto-covariation is studied and its application in model identification of stable auto-regressive models are discussed. We generalize the Durbin-Levinson algorithm to include infinite variance models in terms of partial auto-covariation function and introduce a new information criteria for consistent order estimation of stable autoregressive model.In chapter six we explore the application of the techniques discussed in the previous chapter in signal processing. Frequency estimation of sinusoidal signal observed in symmetric stable noisy environment is discussed in this context. Here we introduced a parametric spectrum analysis and frequency estimate using power transfer function. Estimate of the power transfer function is obtained using the modified generalized Yule-Walker approach. Another important problem in statistical signal processing is to identify the number of sinusoidal components in an observed signal. We used a modified version of the proposed information criteria for this purpose.

Data assimilation for state and parameter estimation: application to morphodynamic modelling

Data assimilation is predominantly used for state estimation; combining observational data with model predictions to produce an updated model state that most accurately approximates the true system state whilst keeping the model parameters fixed. This updated model state is then used to initiate the next model forecast. Even with perfect initial data, inaccurate model parameters will lead to the growth of prediction errors. To generate reliable forecasts we need good estimates of both the current system state and the model parameters. This paper presents research into data assimilation methods for morphodynamic model state and parameter estimation. First, we focus on state estimation and describe implementation of a three dimensional variational(3D-Var) data assimilation scheme in a simple 2D morphodynamic model of Morecambe Bay, UK. The assimilation of observations of bathymetry derived from SAR satellite imagery and a ship-borne survey is shown to significantly improve the predictive capability of the model over a 2 year run. Here, the model parameters are set by manual calibration; this is laborious and is found to produce different parameter values depending on the type and coverage of the validation dataset. The second part of this paper considers the problem of model parameter estimation in more detail. We explain how, by employing the technique of state augmentation, it is possible to use data assimilation to estimate uncertain model parameters concurrently with the model state. This approach removes inefficiencies associated with manual calibration and enables more effective use of observational data. We outline the development of a novel hybrid sequential 3D-Var data assimilation algorithm for joint state-parameter estimation and demonstrate its efficacy using an idealised 1D sediment transport model. The results of this study are extremely positive and suggest that there is great potential for the use of data assimilation-based state-parameter estimation in coastal morphodynamic modelling.