The objective of the research is to formulate and demonstrate protection schemes for radial and loop systems, an active distribution system, and a microgrid. The schemes are composed of a) A new loop scheme by utilizing voltage, current, and time (VIT) reclosers and sectionalizers and b) A new protection scheme, the dynamic state estimation-based protection, for active distribution systems and microgrids. The first part of the research explores the closing onto a fault during the conventional loop sectionalizing scheme and provides a VIT scheme that can solve the problem. The immediate benefit of the VIT schemes is a reduction of the nuisance trips because of the fault closing onto a fault. Moreover, the number of protection zones is increased by the application of the VIT sectionalizers. This thesis demonstrates the VIT protection scheme for a traditional distribution system and presents numerical experiments using various test scenarios with various fault locations. The simulation results verify that the protection scheme successfully performs the automatic load transfer scheme for a loop system. The second part of the research identifies the increased number of protection issues according to the installation of distributed generations (DGs) and provides solution to the problem. To solve the issue, a new fault detection scheme, dynamic state estimation-based protection scheme, is illustrated in this thesis based on synchronized measurements. The method uses dynamic state estimation, based on the dynamic model of the component that accurately reflects the nonlinear characteristics of the component. Numerical experiments show that the protection of active distribution systems and microgrids is feasible in real time.

Transformers are very important parts of any electrical network, and their size increase so does their price. Protecting these important devices is a daunting task due to the wide variety of operating conditions. This thesis develops a new protection scheme based on state estimation.The foundation upon which our protection scheme is built is the modeling of the single phase transformer system of equations. The transformer equations are composed of polynomial and differential equations and this system of equations involving the transformer's electrical quantities are modeled into a system of equations such that highest degree of each of the system's equations is quadratic―in a process named Quadratization and then integrated using a technique called Quadratic integration to give a set of algebraic companion equations that can be solved numerically to determine the health of the transformer.

The contributions of the research are (a) an infrastructure of data acquisition systems that provides the necessary information for an automated EMS system enabling autonomous distributed state estimation, model validation, simplified protection, and seamless integration of other EMS applications, (b) an object-oriented, interoperable, and unified component model that can be seamlessly integrated with a variety of applications of the EMS, (c) a distributed dynamic state estimator (DDSE) based on the proposed data acquisition system and the object-oriented, interoperable, and unified component model, (d) a physically-based synchronous machine model, which is expressed in terms of the actual self and mutual inductances of the synchronous machine windings as a function of rotor position, for the purpose of synchronous machine parameters identification, and (e) a robust and highly efficient algorithm for the optimal power flow (OPF) problem, one of the most important applications of the EMS, based on the validated states and models of the power system provided by the proposed DDSE.

The enhancement of the reliability, security, and resiliency of electric power systems depends on the availability of fast, accurate, and robust dynamic state estimators. These estimators should be robust to gross errors on the measurements and the model parameter values while providing good state estimates even in the presence of large dynamical system model uncertainties and non-Gaussian thick-tailed process and observation noises. It turns out that the current Kalman filter-based dynamic state estimators given in the literature suffer from several important shortcomings, precluding them from being adopted by power utilities for practical applications. To be specific, they cannot handle (i) dynamic model uncertainty and parameter errors; (ii) non-Gaussian process and observation noise of the system nonlinear dynamic models; (iii) three types of outliers; and (iv) all types of cyber attacks. The three types of outliers, including observation, innovation, and structural outliers are caused by either an unreliable dynamical model or real-time synchrophasor measurements with data quality issues, which are commonly seen in the power system. To address these challenges, we have pioneered a general theoretical framework that advances both robust statistics and robust control theory for robust dynamic state and parameter estimation of a cyber-physical system. Specifically, the generalized maximum-likelihood-type (GM)-estimator, the unscented Kalman filter (UKF), and the H-infinity filter are integrated into a unified framework to yield various centralized and decentralized robust dynamic state estimators. These new estimators include the GM-iterated extended Kalman filter (GM-IEKF), the GM-UKF, the H-infinity UKF and the robust H-infinity UKF. The GM-IEKF is able to handle observation and innovation outliers but its statistical efficiency is low in the presence of non-Gaussian system process and measurement noise. The GM-UKF addresses this issue and achieves a high statistical efficiency under a broad range of non-Gaussian process and observation noise while maintaining the robustness to observation and innovation outliers. A reformulation of the GM-UKF with multiple hypothesis testing further enables it to handle structural outliers. However, the GM-UKF may yield biased state estimates in presence of large system uncertainties. To this end, the H-infinity UKF that relies on robust control theory is proposed. It is shown that H-infinity is able to bound the system uncertainties but lacks of robustness to outliers and non-Gaussian noise. Finally, the robust H-infinity filter framework is proposed that leverages the H-infinity criterion to bound system uncertainties while relying on the robustness of GM-estimator to filter out non-Gaussian noise and suppress outliers. Furthermore, these new robust estimators are applied for system bus frequency monitoring and control and synchronous generator model parameter calibration. Case studies of several different IEEE standard systems show the efficiency and robustness of the proposed estimators. / Ph. D.

It is a well-known fact that a power system contains many sources of uncertainties. These uncertainties coming from the loads, the renewables, the model and the measurement, etc, are influencing the steady state and dynamic response of the power system. Facing this problem, traditional methods, such as the Monte Carlo method and the Perturbation method, are either too time consuming or suffering from the strong nonlinearity in the system. To solve these, this Dissertation will mainly focus on developing the polynomial chaos based method to replace the traditional ones. Using it, the uncertainties from the model and the measurement are propagated through the polynomial chaos bases at a set of collocation points. The approximated polynomial chaos coefficients contain the statistical information. The method can greatly accelerate the calculation efficiency while not losing the accuracy, even when the system is highly stressed. In this dissertation, both the forward problem and the inverse problem of uncertainty quantification will be discussed. The forward problems will include the probabilistic power flow problem and statistical power system dynamic simulations. The generalized polynomial chaos method, the adaptive polynomial chaos-ANOVA method and the multi-element polynomial chaos method will be introduced and compared. The case studies show that the proposed methods have great performances in the statistical analysis of the large-scale power systems. The inverse problems will include the state and parameter estimation problem. A novel polynomial-chaos-based Kalman filter will be proposed. The comparison studies with other traditional Kalman filter demonstrate the good performances of the proposed Kalman filter. We further explored the area dynamic parameter estimation problem under the Bayesian inference framework. The polynomial-chaos-expansions are treated as the response surface of the full dynamic solver. Combing with hybrid Markov chain Monte Carlo method, the proposed method yields very high estimation accuracy while greatly reducing the computing time. For both the forward problem and the inverse problems, the polynomial chaos based methods haven shown great advantages over the traditional methods. These computational techniques can improve the efficiency and accuracy in power system planning, guarantee the rationality and reliability in power system operations, and, finally, speed up the power system dynamic security assessment. / PHD / It is a well-known fact that a power system state is inherently stochastic. Sources of stochasticity include load random variations, renewable energy intermittencies, and random outages of generating units, lines, and transformers, to cite a few. These stochasticities translate into uncertainties in the models that are assumed to describe the steady-sate and dynamic behavior of a power system. Now, these models are themselves approximate since they are based on some assumptions that are typically violated in practice. Therefore, it does not come as a surprise if recent research activities in power systems are focusing on how to cope with uncertainties when dealing with power system planning, monitoring and control. This Dissertation is developing polynomial-chaos-based method in quantifying, and managing these uncertainties. Three major topics, including uncertainty quantification, state estimation and parameter estimation are discussed. The developed method can improve the efficiency and accuracy in power system planning, guarantee the rationality and reliability in power system operations in dealing with the uncertainties, and, finally, enhancing the resilience of the power systems.

The study of randomly excited nonlinear dynamical systems forms the focus of this thesis. We discuss two classes of problems: first, the characterization of nonlinear random response of the system before it comes into existence and, the second, assimilation of measured responses into the mathematical model of the system after the system comes into existence. The first class of problems constitutes forward problems while the latter belongs to the class of inverse problems. An outstanding feature of these problems is that they are almost always not amenable for exact solutions. We tackle in the present study these two classes of problems using Monte Carlo simulation tools in conjunction with Markov process theory, Bayesian model updating strategies, and particle filtering based dynamic state estimation methods. It is well recognized in literature that any successful application of Monte Carlo simulation methods to practical problems requires the simulation methods to be reinforced with effective means of controlling sampling variance. This can be achieved by incorporating any problem specific qualitative and (or) quantitative information that one might have about system behavior in formulating estimators for response quantities of interest. In the present thesis we outline two such approaches for variance reduction. The first of these approaches employs a substructuring scheme, which partitions the system states into two sets such that the probability distribution of the states in one of the sets conditioned on the other set become amenable for exact analytical solution. In the second approach, results from data based asymptotic extreme value analysis are employed to tackle problems of time variant reliability analysis and updating of this reliability. We exemplify in this thesis the proposed approaches for response estimation and model updating by considering wide ranging problems of interest in structural engineering, namely, nonlinear response and reliability analyses under stationary and (or) nonstationary random excitations, response sensitivity model updating, force identification, residual displacement analysis in instrumented inelastic structures under transient excitations, problems of dynamic state estimation in systems with local nonlinearities, and time variant reliability analysis and reliability model updating. We have organized the thesis into eight chapters and three appendices. A resume of contents of these chapters and appendices follows. In the first chapter we aim to provide an overview of mathematical tools which form the basis for investigations reported in the thesis. The starting point of the study is taken to be a set of coupled stochastic differential equations, which are obtained after discretizing spatial variables, typically, based on application of finite element methods. Accordingly, we provide a summary of the following topics: (a) Markov vector approach for characterizing time evolution of transition probability density functions, which includes the forward and backward Kolmogorov equations, (b) the equations governing the time evolution of response moments and first passage times, (c) numerical discretization of governing stochastic differential equation using Ito-Taylor’s expansion, (d) the partial differential equation governing the time evolution of transition probability density functions conditioned on measurements for the study of existing instrumented structures, (e) the time evolution of response moments conditioned on measurements based on governing equations in (d), and (f) functional recursions for evolution of multidimensional posterior probability density function and posterior filtering density function, when the time variable is also discretized. The objective of the description here is to provide an outline of the theoretical formulations within which the problems of response estimation and model updating are formulated in the subsequent chapters of the present thesis. We briefly state the class of problems, which are amenable for exact solutions. We also list in this chapter major text books, research monographs, and review papers relevant to the topics of nonlinear random vibration analysis and dynamic state estimation. In Chapter 2 we provide a review of literature on solutions of problems of response analysis and model updating in nonlinear dynamical systems. The main focus of the review is on Monte Carlo simulation based methods for tackling these problems. The review accordingly covers numerical methods for approximate solutions of Kolmogorov equations and associated moment equations, variance reduction in simulation based analysis of Markovian systems, dynamic state estimation methods based on Kalman filter and its variants, particle filtering, and variance reduction based on Rao-Blackwellization. In this review we chiefly cover papers that have contributed to the growth of the methodology. We also cover briefly, the efforts made in applying the ideas to structural engineering problems. Based on this review, we identify the problems of variance reduction using substructuring schemes and data based extreme value analysis and, their incorporation into response estimation and model updating strategies, as problems requiring further research attention. We also identify a range of problems where these tools could be applied. We consider the development of a sequential Monte Carlo scheme, which incorporates a substructuring strategy, for the analysis of nonlinear dynamical systems under random excitations in Chapter 3. The proposed substructuring ensures that a part of the system states conditioned on the remaining states becomes Gaussian distributed and is amenable for an exact analytical solution. The use of Monte Carlo simulations is subsequently limited for the analysis of the remaining system states. This clearly results in reduction in sampling variance since a part of the problem is tackled analytically in an exact manner. The successful performance of the proposed approach is illustrated by considering response analysis of a single degree of freedom nonlinear oscillator under random excitations. Arguments based on variance decomposition result and Rao-Blackwell theorems are presented to demonstrate that the proposed variance reduction indeed is effective. In Chapter 4, we modify the sequential Monte Carlo simulation strategy outlined in the preceding chapter to incorporate questions of dynamic state estimation when data on measured responses become available. Here too, the system states are partitioned into two groups such that the states in one group become Gaussian distributed when conditioned on the states in the other group. The conditioned Gaussian states are subsequently analyzed exactly using the Kalman filter and, this is interfaced with the analysis of the remaining states using sequential importance sampling based filtering strategy. The development of this combined Kalman and sequential importance sampling filtering method constitutes one of the novel elements of this study. The proposed strategy is validated by considering the problem of dynamic state estimation in linear single and multi-degree of freedom systems for which exact analytical solutions exist. In Chapter 5, we consider the application of the tools developed in Chapter 4 for a class of wide ranging problems in nonlinear random vibrations of existing systems. The nonlinear systems considered include single and multi-degree of freedom systems, systems with memoryless and hereditary nonlinearities, and stationary and nonstationary random excitations. The specific applications considered include nonlinear dynamic state estimation in systems with local nonlinearities, estimation of residual displacement in instrumented inelastic dynamical system under transient random excitations, response sensitivity model updating, and identification of transient seismic base motions based on measured responses in inelastic systems. Comparisons of solutions from the proposed substructuring scheme with corresponding results from direct application of particle filtering are made and a satisfactory mutual agreement is demonstrated. We consider next questions on time variant reliability analysis and corresponding model updating in Chapters 6 and 7, respectively. The research effort in these studies is focused on exploring the application of data based asymptotic extreme value analysis for problems on hand. Accordingly, we investigate reliability of nonlinear vibrating systems under stochastic excitations in Chapter 6 using a two-stage Monte Carlo simulation strategy. For systems with white noise excitation, the governing equations of motion are interpreted as a set of Ito stochastic differential equations. It is assumed that the probability distribution of the maximum over a specified time duration in the steady state response belongs to the basin of attraction of one of the classical asymptotic extreme value distributions. The first stage of the solution strategy consists of selection of the form of the extreme value distribution based on hypothesis testing, and, the next stage involves the estimation of parameters of the relevant extreme value distribution. Both these stages are implemented using data from limited Monte Carlo simulations of the system response. The proposed procedure is illustrated with examples of linear/nonlinear systems with single/multiple degrees of freedom driven by random excitations. The predictions from the proposed method are compared with the results from large scale Monte Carlo simulations, and also with the classical analytical results, when available, from the theory of out-crossing statistics. Applications of the proposed method for vibration data obtained from laboratory conditions are also discussed. In Chapter 7 we consider the problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations. Here we assume that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes’ theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplified by considering the reliability analysis of a few low dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on limited amount of pertinent Monte Carlo simulations. A summary of the contributions made and a few suggestions for future work are presented in Chapter 8. The thesis also contains three appendices. Appendix A provides details of the order 1.5 strong Taylor scheme that is extensively employed at several places in the thesis. The formulary pertaining to the bootstrap and sequential importance sampling particle filters is provided in Appendix B. Some of the results on characterizing conditional probability density functions that have been used in the development of the combined Kalman and sequential importance sampling filter in Chapter 4 are elaborated in Appendix C.

Development of dynamic state estimation techniques and their applications in problems of identification in structural engineering have been taken up. The thrust of the study has been the identification of structural systems that exhibit nonlinear behavior, mainly in the form of constitutive and geometric nonlinearities. Methods encompassing both linearization based strategies and those involving nonlinear filtering have been explored. The applications of derivative-free locally transversal linearization (LTL) and multi-step transversal linearization (MTrL) schemes for developing newer forms of the extended Kalman filter (EKF) algorithm have been explored. Apart from the inherent advantages of these methods in avoiding gradient calculations, the study also demonstrates their superior numerical accuracy and considerably less sensitivity to the choice of step sizes. The range of numerical illustrations covers SDOF as well as MDOF oscillators with time-invariant parameters and those with discontinuous temporal variations. A new form of the sequential importance sampling (SIS) filter is developed which explores the scope of the existing SIS filters to cover nonlinear measurement equations and more general forms of noise involving multiplicative and (or) Gaussian/ non-Gaussian noises. The formulation of this method involves Ito-Taylor’s expansions of the nonlinear functions in the measurement equation and the development of the ideal ispdf while accounting for the non-Gaussian terms appearing in the governing equation. Numerical illustrations on parameter identification of a few nonlinear oscillators and a geometrically nonlinear Euler–Bernoulli beam reveal a remarkably improved performance of the proposed methods over one of the best known algorithms, i.e. the unscented particle filter. The study demonstrates the applicability of diverse range of mathematical tools including Magnus’ functional expansions, theory of SDE-s, Ito-Taylor’s expansions and simulation and characterization of the non-Gaussian random variables to the problem of nonlinear structural system identification.

Ziel der vorliegenden Arbeit ist die Entwicklung eines Verfahrens zur automatisierten Integration funkbasierter drahtloser Sensornetze (engl. Wireless Sensor Network, kurz WSN) in die jeweilige Anwendungsumgebung. Die Sensornetze realisieren dort neben Kommunikationsaufgaben vor allem die Bestimmung von Ortsinformationen. Das Betriebshofmanagement im ÖPNV stellt dabei eine typische Anwendung dar. So wird auf der Grundlage permanent verfügbarer Positionskoordinaten von Bussen und Bahnen als mobile Objekte im Verkehrsumfeld eine effizientere Betriebsführung ermöglicht. Die Datenbasis in dieser Arbeit bilden zum einen geometrische Beziehungen im Sensornetz, die aus Gründen der Verfügbarkeit lediglich durch paarweise Distanzen zwischen den mobilen Objekten und den im Umfeld fest installierten Ankern beschrieben sind. Zum anderen kann auf vorhandenes digitales Kartenmaterial in Form von Vektor- und Rasterkarten bspw. von GIS-Diensten zurückgegriffen werden. Die Argumente für eine Automatisierung sind naheliegend. Einerseits soll der Aufwand der Positionskalibrierung nicht mit der Anzahl verbauter Anker skalieren, was sich ausschließlich automatisiert realisieren lässt. Dadurch werden gleichzeitig symptomatische Fehlerquellen, die aus einer manuellen Systemintegration resultieren, eliminiert. Andererseits soll die Automatisierung ein echtzeitfähiges Betreiben (z.B. Rekalibrierung und Fernwartung) gewährleisten, sodass kostenintensive Wartungs- und Servicedienstleistungen entfallen. Das entwickelte Verfahren generiert zunächst aus den Sensordaten mittels distanzbasierter simultaner Lokalisierung und Kartenerstellung (engl. Range-Only Simultaneous Localization and Mapping, kurz RO-SLAM) relative Positionsinformationen für Anker und mobile Objekte. Anschließend führt das Verfahren diese Informationen im Rahmen einer kooperativen Kartenerstellung zusammen. Aus den relativen, kooperativen Ergebnissen und dem zugrundeliegenden Kartenmaterial wird schließlich ein anwendungsspezifischer absoluter Raumbezug hergestellt. Die Ergebnisse der durchgeführten Verfahrensevaluation belegen anhand generierter semi-realer Sensordaten sowie definierter Testszenarien die Funktions- und Leistungsfähigkeit des entwickelten Verfahrens. Sie beinhalten qualifizierende Aussagen und zeigen darüber hinaus statistisch belastbare Genauigkeitsgrenzen auf.:Abbildungsverzeichnis...............................................X Tabellenverzeichnis...............................................XII Abkürzungsverzeichnis............................................XIII Symbolverzeichnis................................................XVII 1 Einleitung........................................................1 1.1 Stand der Technik...............................................3 1.2 Entwickeltes Verfahren im Überblick.............................4 1.3 Wissenschaftlicher Beitrag......................................7 1.4 Gliederung der Arbeit...........................................8 2 Grundlagen zur Verfahrensumsetzung...............................10 2.1 Überblick zu funkbasierten Sensornetzen........................10 2.1.1 Aufbau und Netzwerk..........................................11 2.1.2 System- und Technologiemerkmale..............................12 2.1.3 Selbstorganisation...........................................13 2.1.4 Räumliche Beziehungen........................................14 2.2 Umgebungsrepräsentation........................................18 2.2.1 Koordinatenbeschreibung......................................19 2.2.2 Kartentypen..................................................20 2.3 Lokalisierung..................................................22 2.3.1 Positionierung...............................................23 2.3.2 Tracking.....................................................28 2.3.3 Koordinatentransformation....................................29 3 Zustandsschätzung dynamischer Systeme............................37 3.1 Probabilistischer Ansatz.......................................38 3.1.1 Satz von Bayes...............................................39 3.1.2 Markov-Kette.................................................40 3.1.3 Hidden Markov Model..........................................42 3.1.4 Dynamische Bayes‘sche Netze..................................43 3.2 Bayes-Filter...................................................45 3.2.1 Extended Kalman-Filter.......................................48 3.2.2 Histogramm-Filter............................................51 3.2.3 Partikel-Filter..............................................52 3.3 Markov Lokalisierung...........................................58 4 Simultane Lokalisierung und Kartenerstellung.....................61 4.1 Überblick......................................................62 4.1.1 Objektbeschreibung...........................................63 4.1.2 Umgebungskarte...............................................65 4.1.3 Schließen von Schleifen......................................70 4.2 Numerische Darstellung.........................................72 4.2.1 Formulierung als Bayes-Filter................................72 4.2.2 Diskretisierung des Zustandsraums............................74 4.2.3 Verwendung von Hypothesen....................................74 4.3 Initialisierung des Range-Only SLAM............................75 4.3.1 Verzögerte und unverzögerte Initialisierung..................75 4.3.2 Initialisierungsansätze......................................76 4.4 SLAM-Verfahren.................................................80 4.4.1 Extended Kalman-Filter-SLAM..................................81 4.4.2 Incremental Maximum Likelihood-SLAM..........................90 4.4.3 FastSLAM.....................................................99 5 Kooperative Kartenerstellung....................................107 5.1 Aufbereitung der Ankerkartierungsergebnisse...................108 5.2 Ankerkarten-Merging-Verfahren.................................110 5.2.1 Auflösen von Mehrdeutigkeiten...............................110 5.2.2 Erstellung einer gemeinsamen Ankerkarte.....................115 6 Herstellung eines absoluten Raumbezugs..........................117 6.1 Aufbereitung der Lokalisierungsergebnisse.....................117 6.1.1 Generierung von Geraden.....................................119 6.1.2 Generierung eines Graphen...................................122 6.2 Daten-Matching-Verfahren......................................123 6.2.1 Vektorbasierte Karteninformationen..........................125 6.2.2 Rasterbasierte Karteninformationen..........................129 7 Verfahrensevaluation............................................133 7.1 Methodischer Ansatz...........................................133 7.2 Datenbasis....................................................135 7.2.1 Sensordaten.................................................137 7.2.2 Digitales Kartenmaterial....................................143 7.3 Definition von Testszenarien..................................145 7.4 Bewertung.....................................................147 7.4.1 SLAM-Verfahren..............................................148 7.4.2 Ankerkarten-Merging-Verfahren...............................151 7.4.3 Daten-Matching-Verfahren....................................152 8 Zusammenfassung und Ausblick....................................163 8.1 Ergebnisse der Arbeit.........................................164 8.2 Ausblick......................................................165 Literaturverzeichnis..............................................166 A Ergänzungen zum entwickelten Verfahren..........................A-1 A.1 Generierung von Bewegungsinformationen........................A-1 A.2 Erweiterung des FastSLAM-Verfahrens...........................A-2 A.3 Ablauf des konzipierten Greedy-Algorithmus....................A-4 A.4 Lagewinkel der Kanten in einer Rastergrafik...................A-5 B Ergänzungen zur Verfahrensevaluation............................A-9 B.1 Geschwindigkeitsprofile der simulierten Objekttrajektorien....A-9 B.2 Gesamtes SLAM-Ergebnis eines Testszenarios....................A-9 B.3 Statistische Repräsentativität...............................A-10 B.4 Gesamtes Ankerkarten-Merging-Ergebnis eines Testszenarios....A-11 B.5 Gesamtes Daten-Matching-Ergebnis eines Testszenarios.........A-18 B.6 Qualitative Ergebnisbewertung................................A-18 B.7 Divergenz des Gesamtverfahrens...............................A-18 / The aim of this work is the development of a method for the automated integration of Wireless Sensor Networks (WSN) into the respective application environment. The sensor networks realize there beside communication tasks above all the determination of location information. Therefore, the depot management in public transport is a typical application. Based on permanently available position coordinates of buses and trams as mobile objects in the traffic environment, a more efficient operational management is made possible. The database in this work is formed on the one hand by geometric relationships in the sensor network, which for reasons of availability are only described by pairwise distances between the mobile objects and the anchors permanently installed in the environment. On the other hand, existing digital map material in the form of vector and raster maps, e.g. obtained by GIS services, is used. The arguments for automation are obvious. First, the effort of position calibration should not scale with the number of anchors installed, which can only be automated. This at once eliminates symptomatic sources of error resulting from manual system integration. Secondly, automation should ensure real-time operation (e.g. recalibration and remote maintenance), eliminating costly maintenance and service. Initially, the developed method estimates relative position information for anchors and mobile objects from the sensor data by means of Range-Only Simultaneous Localization and Mapping (RO-SLAM). The method then merges this information within a cooperative map creation. From the relative, cooperative results and the available map material finally an application-specific absolute spatial outcome is generated. Based on semi-real sensor data and defined test scenarios, the results of the realized method evaluation demonstrate the functionality and performance of the developed method. They contain qualifying statements and also show statistically reliable limits of accuracy.:Abbildungsverzeichnis...............................................X Tabellenverzeichnis...............................................XII Abkürzungsverzeichnis............................................XIII Symbolverzeichnis................................................XVII 1 Einleitung........................................................1 1.1 Stand der Technik...............................................3 1.2 Entwickeltes Verfahren im Überblick.............................4 1.3 Wissenschaftlicher Beitrag......................................7 1.4 Gliederung der Arbeit...........................................8 2 Grundlagen zur Verfahrensumsetzung...............................10 2.1 Überblick zu funkbasierten Sensornetzen........................10 2.1.1 Aufbau und Netzwerk..........................................11 2.1.2 System- und Technologiemerkmale..............................12 2.1.3 Selbstorganisation...........................................13 2.1.4 Räumliche Beziehungen........................................14 2.2 Umgebungsrepräsentation........................................18 2.2.1 Koordinatenbeschreibung......................................19 2.2.2 Kartentypen..................................................20 2.3 Lokalisierung..................................................22 2.3.1 Positionierung...............................................23 2.3.2 Tracking.....................................................28 2.3.3 Koordinatentransformation....................................29 3 Zustandsschätzung dynamischer Systeme............................37 3.1 Probabilistischer Ansatz.......................................38 3.1.1 Satz von Bayes...............................................39 3.1.2 Markov-Kette.................................................40 3.1.3 Hidden Markov Model..........................................42 3.1.4 Dynamische Bayes‘sche Netze..................................43 3.2 Bayes-Filter...................................................45 3.2.1 Extended Kalman-Filter.......................................48 3.2.2 Histogramm-Filter............................................51 3.2.3 Partikel-Filter..............................................52 3.3 Markov Lokalisierung...........................................58 4 Simultane Lokalisierung und Kartenerstellung.....................61 4.1 Überblick......................................................62 4.1.1 Objektbeschreibung...........................................63 4.1.2 Umgebungskarte...............................................65 4.1.3 Schließen von Schleifen......................................70 4.2 Numerische Darstellung.........................................72 4.2.1 Formulierung als Bayes-Filter................................72 4.2.2 Diskretisierung des Zustandsraums............................74 4.2.3 Verwendung von Hypothesen....................................74 4.3 Initialisierung des Range-Only SLAM............................75 4.3.1 Verzögerte und unverzögerte Initialisierung..................75 4.3.2 Initialisierungsansätze......................................76 4.4 SLAM-Verfahren.................................................80 4.4.1 Extended Kalman-Filter-SLAM..................................81 4.4.2 Incremental Maximum Likelihood-SLAM..........................90 4.4.3 FastSLAM.....................................................99 5 Kooperative Kartenerstellung....................................107 5.1 Aufbereitung der Ankerkartierungsergebnisse...................108 5.2 Ankerkarten-Merging-Verfahren.................................110 5.2.1 Auflösen von Mehrdeutigkeiten...............................110 5.2.2 Erstellung einer gemeinsamen Ankerkarte.....................115 6 Herstellung eines absoluten Raumbezugs..........................117 6.1 Aufbereitung der Lokalisierungsergebnisse.....................117 6.1.1 Generierung von Geraden.....................................119 6.1.2 Generierung eines Graphen...................................122 6.2 Daten-Matching-Verfahren......................................123 6.2.1 Vektorbasierte Karteninformationen..........................125 6.2.2 Rasterbasierte Karteninformationen..........................129 7 Verfahrensevaluation............................................133 7.1 Methodischer Ansatz...........................................133 7.2 Datenbasis....................................................135 7.2.1 Sensordaten.................................................137 7.2.2 Digitales Kartenmaterial....................................143 7.3 Definition von Testszenarien..................................145 7.4 Bewertung.....................................................147 7.4.1 SLAM-Verfahren..............................................148 7.4.2 Ankerkarten-Merging-Verfahren...............................151 7.4.3 Daten-Matching-Verfahren....................................152 8 Zusammenfassung und Ausblick....................................163 8.1 Ergebnisse der Arbeit.........................................164 8.2 Ausblick......................................................165 Literaturverzeichnis..............................................166 A Ergänzungen zum entwickelten Verfahren..........................A-1 A.1 Generierung von Bewegungsinformationen........................A-1 A.2 Erweiterung des FastSLAM-Verfahrens...........................A-2 A.3 Ablauf des konzipierten Greedy-Algorithmus....................A-4 A.4 Lagewinkel der Kanten in einer Rastergrafik...................A-5 B Ergänzungen zur Verfahrensevaluation............................A-9 B.1 Geschwindigkeitsprofile der simulierten Objekttrajektorien....A-9 B.2 Gesamtes SLAM-Ergebnis eines Testszenarios....................A-9 B.3 Statistische Repräsentativität...............................A-10 B.4 Gesamtes Ankerkarten-Merging-Ergebnis eines Testszenarios....A-11 B.5 Gesamtes Daten-Matching-Ergebnis eines Testszenarios.........A-18 B.6 Qualitative Ergebnisbewertung................................A-18 B.7 Divergenz des Gesamtverfahrens...............................A-18