MATLAB-based general approach for square-root extended-unscented and fifth-degree cubature Kalman filtering methods

A stable square-root approach has been recently proposed for the unscented Kalman filter (UKF) and fifth-degree cubature Kalman filter (5D-CKF) as well as for the mixed-type methods consisting of the extended Kalman filter (EKF) time update and the UKF/5D-CKF measurement update steps. The mixed-type estimators provide a good balance in trading between estimation accuracy and computational demand because of the EKF moment differential equations involved. The key benefit is a consolidation of reliable state mean and error covariance propagation by using delicate discretization error control while solving the EKF moment differential equations and an accurate measurement update according to the advanced UKF and/or 5D-CKF filtering strategies. Meanwhile the drawback of the previously proposed estimators is an utilization of sophisticated numerical integration scheme with the built-in discretization error control that is, in fact, a complicated and computationally costly tool. In contrast, we design here the mixed-type methods that keep the same estimation quality but reduce a computational time significantly. The novel estimators elegantly utilize any MATLAB-based numerical integration scheme developed for solving ordinary differential equations (ODEs) with the required accuracy tolerance pre-defined by users. In summary, a simplicity of the suggested estimators, their numerical robustness with respect to roundoff due to the square-root form utilized as well as their estimation accuracy due to the MATLAB ODEs solvers with discretization error control involved are the attractive features of the novel estimators. The numerical experiments are provided for illustrating a performance of the suggested methods in comparison with the existing ones

Kalman Filtering and its Application to On-Line State Estimation of a Once-Through Boiler

This thesis contributes to non-linear continuous-discrete Kalman filtering of multiplex systems through the development of two main ideas, namely, integration of the unscented transforms with linearly implicit methods and incorporation of simulation errors in the state estimation problem. The newly developed techniques are then applied to the technically relevant problem of state estimation on the main components of a utility boiler. State estimators in industrial systems are used as soft-sensors in monitoring and control applications as the most cost effective and practical alternative to telemetering all variables of interest. One such example is in utility boilers where reliable and real-time data characterising its behaviour is used to detect faults and optimise performance. With respect to the state-of-the-art, state estimators display limitations in real-time applications to large-scale systems. This motivates theoretical developments in state estimation as a first part in this thesis. These developments are aimed at producing more practical and efficient algorithms in non-linear continuous discrete Kalman filtering for stiff large-scale industrial systems. This is achieved using two novel ideas. The first is to exploit the similarities between the extended and unscented Kalman filter in order to estimate the Jacobian required for linearly implicit schemes, thereby tightly coupling state propagation and continuous-time simulation. The second is to account for numerical integration error by appending a stochastic local error model to the system's stochastic differential equation. This allows for coarser integration time steps in systems that are otherwise only suited to relatively small step sizes, making the filter more computationally efficient without lowering its potential to construct accurate estimates. The second part of this thesis uses these algorithms to demonstrate the feasibility of on-line state estimation on the main components of a once-through utility power boiler that require in excess of a hundred state variables to capture its behaviour with adequate fidelity. Two separate models of the boiler are developed, a MATLAB® and a Flownex® model, comprising the economiser, evaporators, reheaters, superheaters and furnace. The mathematical MATLAB® model is better suited to real-time execution and is used in the filter. The more sophisticated model is based on a commercial thermal-hydraulic simulation environment, Flownex® , and is used to validate the mathematical modelling philosophies and construct filter observation data. After validating the performance of the filter against ground-truth data provided by the Flownex® model, the filter is demonstrated on historical plant data to illustrate its utility

Nonlinear State Estimation Using Optimal Gaussian Sampling with Applications to Tracking

This thesis is concerned with the ubiquitous problem of estimating the hidden state of a discrete-time stochastic nonlinear dynamic system. The focus is on the derivation of new Gaussian state estimators and the improvement of existing approaches. Also the challenging task of distributed state estimation is addressed by proposing a sample-based fusion of local state estimates. The proposed estimation techniques are applied to extended object tracking

Multitarget tracking and terrain-aided navigation using square-root consider filters

Filtering is a term used to describe methods that estimate the values of partially observed states, such as the position, velocity, and attitude of a vehicle, using current observations that are corrupted due to various sources, such as measurement noise, transmission dropouts, and spurious information. The study of filtering has been an active focus of research for decades, and the resulting filters have been the cornerstone of many of humankind\u27s greatest technological achievements. However, these achievements are enabled principally by the use of specialized techniques that seek to, in some way, combat the negative impacts that processor roundoff and truncation error have on filtering. Two of these specialized techniques are known as square-root filters and consider filters. The former alleviates the fragility induced from estimating error covariance matrices by, instead, managing a factorized representation of that matrix, known as a square-root factor. The latter chooses to account for the statistical impacts a troublesome system parameter has on the overall state estimate without directly estimating it, and the result is a substantial reduction in numerical sensitivity to errors in that parameter. While both of these techniques have found widespread use in practical application, they have never been unified in a common square-root consider framework. Furthermore, consider filters are historically rooted to standard, vector-valued estimation techniques, and they have yet to be generalized to the emerging, set-valued estimation tools for multitarget tracking. In this dissertation, formulae for the square-root consider filter are derived, and the result is extended to finite set statistics-based multitarget tracking tools. These results are used to propose a terrain-aided navigation concept wherein data regarding a vehicle\u27s environment is used to improve its state estimate, and square-root consider techniques provide the numerical stability necessary for an onboard navigation application. The newly developed square-root consider techniques are shown to be much more stable than standard formulations, and the terrain-aided navigation concept is applied to a lunar landing scenario to illustrate its applicability to navigating in challenging environments --Abstract, page iii

Systems and control : 21th Benelux meeting, 2002, March 19-21, Veldhoven, The Netherlands

Book of abstract

Innovative Methods and Materials in Structural Health Monitoring of Civil Infrastructures

In the past, when elements in sructures were composed of perishable materials, such as wood, the maintenance of houses, bridges, etc., was considered of vital importance for their safe use and to preserve their efficiency. With the advent of materials such as reinforced concrete and steel, given their relatively long useful life, periodic and constant maintenance has often been considered a secondary concern. When it was realized that even for structures fabricated with these materials that the useful life has an end and that it was being approached, planning maintenance became an important and non-negligible aspect. Thus, the concept of structural health monitoring (SHM) was introduced, designed, and implemented as a multidisciplinary method. Computational mechanics, static and dynamic analysis of structures, electronics, sensors, and, recently, the Internet of Things (IoT) and artificial intelligence (AI) are required, but it is also important to consider new materials, especially those with intrinsic self-diagnosis characteristics, and to use measurement and survey methods typical of modern geomatics, such as satellite surveys and highly sophisticated laser tools

Hidden states, hidden structures: Bayesian learning in time series models

This thesis presents methods for the inference of system state and the learning of model structure for a number of hidden-state time series models, within a Bayesian probabilistic framework. Motivating examples are taken from application areas including finance, physical object tracking and audio restoration. The work in this thesis can be broadly divided into three themes: system and parameter estimation in linear jump-diffusion systems, non-parametric model (system) estimation and batch audio restoration. For linear jump-diffusion systems, efficient state estimation methods based on the variable rate particle filter are presented for the general linear case (chapter 3) and a new method of parameter estimation based on Particle MCMC methods is introduced and tested against an alternative method using reversible-jump MCMC (chapter 4). Non-parametric model estimation is examined in two settings: the estimation of non-parametric environment models in a SLAM-style problem, and the estimation of the network structure and forms of linkage between multiple objects. In the former case, a non-parametric Gaussian process prior model is used to learn a potential field model of the environment in which a target moves. Efficient solution methods based on Rao-Blackwellized particle filters are given (chapter 5). In the latter case, a new way of learning non-linear inter-object relationships in multi-object systems is developed, allowing complicated inter-object dynamics to be learnt and causality between objects to be inferred. Again based on Gaussian process prior assumptions, the method allows the identification of a wide range of relationships between objects with minimal assumptions and admits efficient solution, albeit in batch form at present (chapter 6). Finally, the thesis presents some new results in the restoration of audio signals, in particular the removal of impulse noise (pops and clicks) from audio recordings (chapter 7)This work was supported by the Engineering and Physical Sciences Research Council (EPSRC

Design and implementation of a mobile sensor system for human posture tracking

De reconstructie van menselijke houding en het traceren van bewegingen kan in vele toepassingen worden gebruikt. Van animatie waar de bewegingen van acteurs kunnen gekoppeld worden aan een digitaal personage, tot revalidatie waar artsen na biomechanische analyse snel accurate diagnoses kunnen stellen. De snelle evolutie in de ontwikkeling van microsensoren en de opkomst van draadloze sensornetwerken hebben ertoe geleid dat draadloze nodes met verschillende sensoren hiervoor kunnen worden gebruikt. Door de informatie van deze sensoren te combineren is het immers mogelijk om absolute oriëntatie te berekenen. Eens deze informatie van elk lichaamsdeel bekend is, kan de volledige houding gereconstrueerd worden. In dit onderzoek werd een inertieel traceringssysteem ontwikkeld waarbij, in tegenstelling tot commerciële oplossingen, geen gyroscopen werden gebruikt. De sensor nodes worden enkel voorzien van accelerometers en magnetometers. Computer software implementeert het traceringssalgoritme en visualiseert de gereconstrueerde menselijke houding. Ingebedde software bepaalt dan weer de werking van de nodes en implementeert een draadloos protocol op maat dat toelaat om de informatie van verschillende nodes te ontvangen. De werking van het volledige systeem werd gevalideerd aan de hand van experimenten waarbij de houding van een persoon werd gevolgd.Human posture reconstruction and motion tracking is of interest for many different applications. From animation where captured motion sequences from actors can be mapped to a digital character in order to obtain a realistic visualization, to revalidation, where biomechanical analysis enables physicians to determine which exercises should be executed for a better and faster recovery. The combination of the increasingly fast evolution in the development of micromachined and the rise of wireless sensor networks as a distributed solution has allowed inertial sensors to become a fast emerging technology for orientation tracking. Sensor nodes equipped with accelerometers, magnetometers and gyroscopes supply three dimensional readings that can be used to determine driftfree absolute orientation. By approximating the human body by a set of rigid structures interconnected by joints, posture reconstruction is made possible when each of the individual bodyparts is equipped with a sensor node. In this work, an inertial tracking system was developed where, contrast to commercial applications, no gyroscopes were included. The sensor nodes were only equipped with accelerometers and magnetometers. Computer software implements the tracking algorithm and visualizes the reconstructed human posture. Embedded software determines the functionality of the nodes and implements a fully custom wireless protocol that allows to receive information from several nodes. The functionality of the entire system was validated by conducting full body tracking experiments