The dissertation research investigates estimating of power system static and dynamic states (e.g. rotor angle, rotor speed, mechanical power, voltage magnitude, voltage phase angle, mechanical reference point) as well as identification of synchronous generator parameters. The research has two focuses: i. Synchronous generator dynamic model states and parameters estimation using real-time PMU data. ii.Integrate PMU data and conventional measurements to carry out static state estimation. The first part of the work focuses on Phasor Measurement Unit (PMU) data-based synchronous generator states and parameters estimation. In completed work, PMU data-based synchronous generator model identification is carried out using Unscented Kalman Filter (UKF). The identification not only gives the states and parameters related to a synchronous generator swing dynamics but also gives the states and parameters related to turbine-governor and primary and secondary frequency control. PMU measurements of active power and voltage magnitude, are treated as the inputs to the system while voltage phasor angle, reactive power, and frequency measurements are treated as the outputs. UKF-based estimation can be carried out at real-time. Validation is achieved through event play back to compare the outputs of the simplified simulation model and the PMU measurements, given the same input data. Case studies are conducted not only for measurements collected from a simulation model, but also for a set of real-world PMU data. The research results have been disseminated in one published article. In the second part of the research, new state estimation algorithm is designed for static state estimation. The algorithm contains a new solving strategy together with simultaneous bad data detection. The primary challenge in state estimation solvers relates to the inherent non-linearity and non-convexity of measurement functions which requires using of Interior Point algorithm with no guarantee for a global optimum solution and higher computational time. Such inherent non-linearity and non-convexity of measurement functions come from the nature of power flow equations in power systems. The second major challenge in static state estimation relates to the bad data detection algorithm. In traditional algorithms, Largest Normalized Residue Test (LNRT) has been used to identify bad data in static state estimation. Traditional bad data detection algorithm only can be applied to state estimation. Therefore, in a case of finding any bad datum, the SE algorithm have to rerun again with eliminating found bad data. Therefore, new simultaneous and robust algorithm is designed for static state estimation and bad data identification. In the second part of the research, Second Order Cone Programming (SOCP) is used to improve solving technique for power system state estimator. However, the non-convex feasible constraints in SOCP based estimator forces the use of local solver such as IPM (interior point method) with no guarantee for quality answers. Therefore, cycle based SOCP relaxation is applied to the state estimator and a least square estimation (LSE) based method is implemented to generate positive semi-definite programming (SDP) cuts. With this approach, we are able to strengthen the state estimator (SE) with SOCP relaxation. Since SDP relaxation leads the power flow problem to the solution of higher quality, adding SDP cuts to the SOCP relaxation makes Problem’s feasible region close to the SDP feasible region while saving us from computational difficulty associated with SDP solvers. The improved solver is effective to reduce the feasible region and get rid of unwanted solutions violate cycle constraints. Different Case studies are carried out to demonstrate the effectiveness and robustness of the method. After introducing the new solving technique, a novel co-optimization algorithm for simultaneous nonlinear state estimation and bad data detection is introduced in this dissertation. ${\ell}_1$-Norm optimization of the sparse residuals is used as a constraint for the state estimation problem to make the co-optimization algorithm possible. Numerical case studies demonstrate more accurate results in SOCP relaxed state estimation, successful implementation of the algorithm for the simultaneous state estimation and bad data detection, and better state estimation recovery against single and multiple Gaussian bad data compare to the traditional LNRT algorithm.

As wireless devices become more common, the ability to position a wireless device has become a topic of importance. Accurate positioning through technologies such as the Global Positioning System is possible for outdoor environments. Indoor environments pose a different challenge, and research continues to position users indoors. Due to the prevalence of wireless local area networks (WLANs) in many indoor spaces, it is prudent to determine their capabilities for the purposes of positioning. Signal strength and time based positioning systems have been studied for WLANs. Direction or angle of arrival (AOA) based positioning will be possible with multiple antenna arrays, such as those included with upcoming devices based on the IEEE 802.11n standard. The potential performance of such a system is evaluated. The positioning performance of such a system depends on the accuracy of the AOA estimation as well as the positioning algorithm. Two different maximum-likelihood (ML) derived algorithms are used to determine the AOA of the mobile user: a specialized simple ML algorithm, and the space- alternating generalized expectation-maximization (SAGE) channel parameter estimation algorithm. The algorithms are used to determine the error in estimating AOAs through the use of real wireless signals captured in an indoor office environment. The statistics of the AOA error are used in a positioning simulation to predict the positioning performance. A least squares (LS) technique as well as the popular extended Kalman filter (EKF) are used to combine the AOAs to determine position. The position simulation shows that AOA- based positioning using WLANs indoors has the potential to position a wireless user with an accuracy of about 2 m. This is comparable to other positioning systems previously developed for WLANs. / Applied Science, Faculty of / Engineering, School of (Okanagan) / Graduate

This thesis has explored if it is feasible to produce a good estimation of the rotational position of a stepper motor by using sensor fusion schemes to merge a sensorless position estimation (based on the back electromotive force) with the measurement from a magnetic rotational position sensor. The purpose was to find a cheaper alternative for position feedback in closed loop control from conventionally used rotational encoders and resolvers. Beyond the sensor fusion a suitable position control logic was also developed to verify the concept of a low cost closed loop hybrid stepper motor solution for high precision position applications. The sensor fusion and position control were simulated offline to first test the feasibility of the implementation, after which laboratory tests were performed to assess online performance. The extended Kalman filter implemented improved the performance of the magnetic rotational position sensor which was used exclusively at lower speeds (between 0-75 rpm) by decreasing its root-mean-square error by almost half from 0.0733 unfiltered to 0.0370 filtered (in mechanical degrees). When fusing both position signals at higher rotational speeds (75-400rpm) did the extended Kalman filter clearly improve position estimation accuracy compared to the single sources. It is not meaningful however to discuss the numeric improvement of the filter at these working points as this result is not conclusive but based on some fortunate conditions. This is because the two signals used for the fusion is diverging towards positive and negative error respectively for increasing rotational speeds making the fused estimate result in between. This basically means that the result from the fusion is outperforming two very bad signals, and is then not meaningful to use as a measure of how well the fusion is actually performing. Further work on the raw signals used for fusion need to be performed before a proper assessment on the fusion performance could be made.

Reliability is an important issue across industry. This is due to a number of drivers such as the requirement of high safety levels within industries such as aviation, the need for mission success with military equipment, or to avoid monetary losses (due to unplanned outage) within the process and many other industries. The application of fault detection and identification helps to identify the presence of faults to improve mission success or increase up-time of plant equipment. Implementation of such systems can take the form of pattern recognition, statistical and geometric classifiers, soft computing methods or complex model based methods. This study deals with the latter, and focuses on a specific type of model, the Kalman filter. The Kalman filter is an observer which estimates the states of a system, i.e. the physical variables, based upon its current state and knowledge of its inputs. This relies upon the creation of a mathematical model of the system in order to predict the outputs of the system at any given time. Feedback from the plant corrects minor deviation between the system and the Kalman filter model. Comparison between this prediction of outputs and the real output provides the indication of the presence of a fault. On systems with several inputs and outputs banks of these filters can used in order to detect and isolate the various faults that occur in the process and its sensors and actuators. The thesis examines the application of the diagnostic techniques to a laboratory scale aircraft fuel system test-rig. The first stage of the research project required the development of a mathematical model of the fuel rig. Test data acquired by experiment is used to validate the system model against the fuel rig. This nonlinear model is then simplified to create several linear state space models of the fuel rig. These linear models are then used to develop the Kalman filter Fault Detection and Identification (FDI) system by application of appropriate tuning of the Kalman filter gains and careful choice of residual thresholds to determine fault condition boundaries and logic to identify the location of the fault. Additional performance enhancements are also achieved by implementation of statistical evaluation of the residual signal produced and by automatic threshold calculation. The results demonstrate the positive capture of a fault condition and identification of its location in an aircraft fuel system test-rig. The types of fault captured are hard faults such sensor malfunction and actuator failure which provide great deviation of the residual signals and softer faults such as performance degradation and fluid leaks in the tanks and pipes. Faults of a smaller magnitude are captured very well albeit within a larger time range. The performance of the Fault Diagnosis and Identification was further improved by the implementation of statistically evaluating the residual signal and by the development of automatic threshold determination. Identification of the location of the fault is managed by the use of mapping the possible fault permutations and the Kalman filter behaviour, this providing full discrimination between any faults present. Overall the Kalman filter based FDI developed provided positive results in capturing and identifying a system fault on the test-rig.

[pt] A importância da estrutura a termo da taxa de juros dificilmente é exagerada. A estrutura a termo agrega de forma sucinta uma quantidade enorme de informação sobre o estado presente e sobre as expectativas futuras da economia de um país. Nesse trabalho, utilizando técnicas de estimação por filtro de Kalman, estimamos, com dados brasileiros, quatro modelos teóricos da ETTJ, todos casos particulares do modelo afim estudado por Duffie e Kan (1996). Analisamos o resultado de nossas estimações tendo em vista o comportamento histórico da ETTJ brasileira durante o período. Comparamos os modelos entre si, apontando para aqueles que melhor se ajustam aos dados observados. Avaliamos que nossos resultados suportam resultados anteriores de que a hipótese das expectativas não é verificada na ETTJ brasileira. / [en] The importance of the term structure of interest rates is hardly exaggerated. The term structure succinctly summarizes an enormous quantity of information about the actual state and about the future expectations of/ for the economy of a country. Within this work, using Kalman filter estimation techniques, we estimate, with Brazilian data, four different models of the term structure, all particular cases of the affine model studied by Duffie and Kan (1996). We analyze the parameter estimates relating it to the historical behavior of Brazilian data during the sample period. We compare the models among them, choosing the one most successful in fitting the data. Our results support a previous result regarding the non-validity of the expectation hypotheses in the Brazilian term structure.

Le modèle RiskMetrics développé par la Banque JP Morgan suite à l'amendement des accords de Bâle de 1988 a été érigé comme mesure de risque financier pour faire face aux importantes perturbations ayant affecté les marchés bancaires internationaux. Communément appelé Value at Risk, il a été admis par l'ensemble des organes et institutions financiers comme une mesure de risque cohérente. Malgré sa popularité, elle est le sujet de beaucoup de controverses. En effet, les paramètres d'estimation du système RiskMetrics sont supposés fixes au cours du temps ce qui est contraire aux caractéristiques des marchés financiers. Deux raisons valables permettent de justifier cette instabilité temporelle : * la présence d'agents hétérogènes fait qu'on n'analyse plus la VaR en se focalisant sur une seule dimension temporelle mais plutôt sur des fréquences de trading (nous recourons pour cela à la méthode Wavelet). * la structure des séries financières qui d'habitude est affectée par les phénomènes de crash, bulle etc. Ceux-ci peuvent être considérés comme des variables cachées qu'on doit prendre en compte dans l'évaluation du risque. Pour cela, nous recourons à la modélisation espace d'états et au filtre de Kalman. Nous savons d'emblée que les performances de la VaR s'évaluent en recourant au test de backtesting. Celui-ci repose sur la technique de régression roulante qui montre une faille évidente : Nous ne pouvons pas connaitre le processus gouvernant la variation des paramètres, il n'y a pas endogénéisation de la dynamique de ceux-ci. Pour apporter une solution à ce problème, nous proposons une application du filtre de Kalman sur les modèles VaR et WVaR. Ce filtre, par ses fonctions corrige de manière récursive les paramètres dans le temps. En ces termes nous définissons une mesure de risque dit SVaR qui en réalité est la VaR obtenue par une actualisation des paramètres d'estimation. Elle permet une estimation précise de la volatilité qui règne sur le marché financier. Elle donne ainsi la voie à toute institution financière de disposer de suffisamment de fonds propres pour affronter le risque de marché. / The RiskMetrics model developed by the bank JP Morgan following the amendment of Basel accords 1988 was erected as a measure of financial risk to deal with important disturbances affecting international banking markets. Commonly known as Value at Risk, it was accepted by all bodies and financial institutions to be a coherent risk measure. Despite its popularity, it is the subject of many controversies. Indeed, the estimation parameters of RiskMetrics are assumed to be fixed over time, which is contrary to the characteristics of financial markets. Two valid reasons are used to justify temporal instability : *Due to the presence of heterogenous agents the VaR is not analysed by focusing on a single temporal dimension but rather on trading frequencies (we use Wavelet method for it). *The structure of financial time series wich is usually affected by the crash bubble phenomenons and so on. These can be considered as hidden variables that we must take into account in the risk assessment. For this, we use state space modeling and kalman filter. We immediately know that performances of the VaR are evaluated using backtesting test. This is based on the technique of rolling regression wich shows an obvious break : We can not know the processes governing the variation of parameters; there is no endogeneisation dynamics thereof. To provide a solution to this problem, we propose an application of the kalman filter on VaR and WVaR models. This filter recursively corrects by its functions the parameters of time. In these terms we define a risk measure called SVaR wich in realitity is the VaR obtained by updating estimation parameters. It provides an accurate estimate of the volatility existing in the financial market. It thus gives way to any financial institution to have enough capital to face market risk.

This thesis describes the work done to implement and develop position and trajectory control of a quadcopter. The quadcopter was originally equipped with sensors and software to estimate and control the quadcopter's orientation, but did not estimate the current position. A GPS module, GPS antenna and a LIDAR have been added to measure the position in three dimensions. Filters have been implemented and developed to estimate the position, velocity and acceleration. Four controllers have been designed that use these estimates: one PID controller and one LQ controller for vertical movement, and a position controller and a trajectory controller for horizontal movement. The position controller maintains a constant position, while the trajectory controller maintains a constant velocity while travelling along a straight line. These position and trajectory controllers calculate the reference angles required to direct the thrust necessary to control the quadcopter's movement. Additionally, an algorithm has been developed to decrease overshoot by predicting future trajectories. These controllers have proven to be successful at controlling the quadcopter's position in all three dimensions, both in practice during outdoor flight and in simulations.

A recording of the defense presentation for this dissertation is available at: http://hdl.handle.net/10754/625197 / Steady-state elliptic partial differential equations (PDEs) are frequently used to model a diverse range of physical phenomena. The source and boundary data estimation problems for such PDE systems are of prime interest in various engineering disciplines including biomedical engineering, mechanics of materials and earth sciences. Almost all existing solution strategies for such problems can be broadly classified as optimization-based techniques, which are computationally heavy especially when the problems are formulated on higher dimensional space domains. However, in this dissertation, feedback based state estimation algorithms, known as state observers, are developed to solve such steady-state problems using one of the space variables as time-like. In this regard, first, an iterative observer algorithm is developed that sweeps over regular-shaped domains and solves boundary estimation problems for steady-state Laplace equation. It is well-known that source and boundary estimation problems for the elliptic PDEs are highly sensitive to noise in the data. For this, an optimal iterative observer algorithm, which is a robust counterpart of the iterative observer, is presented to tackle the ill-posedness due to noise. The iterative observer algorithm and the optimal iterative algorithm are then used to solve source localization and estimation problems for Poisson equation for noise-free and noisy data cases respectively. Next, a divide and conquer approach is developed for three-dimensional domains with two congruent parallel surfaces to solve the boundary and the source data estimation problems for the steady-state Laplace and Poisson kind of systems respectively. Theoretical results are shown using a functional analysis framework, and consistent numerical simulation results are presented for several test cases using finite difference discretization schemes.

The mining industry is constantly under pressure to improve productivity, effciency and safety. Although an increased use of automation technology has the potential of con- tributing to improvements in all three factors mines have been relatively slow to make use of automation technology. Automation in the underground mining environment is a challenging prospect for a number of reasons not least of which being the diffculties and associated costs of installing infrastructure in this hazardous environment. The work described in this dissertation focuses on the modelling of a Load-Haul-Dump or LHD vehicle for the purpose of autonomous navigation and control. Considerable progress has been made in automating underground mining vehicles in recent years, and successful test installations have been made. There are still however a number of shortcomings in the existing autonomous underground mine vehicle navigation systems. This dissertation attempts to address some of these problems through the development of a more accurate vehicle model for an LHD vehicle incorporating some vehicle and tyre dynamics thereby potentially reducing the number of sensors and the amount of installed infrastructure necessary to implement the vehicle navigation system. Simulation results are provided for different vehicle modelling techniques and the results are compared and discussed in terms of their suitability for physical implementation in an underground mine. / Dissertation (MEng (Electronic Engineering))--University of Pretoria, 2007. / Electrical, Electronic and Computer Engineering / MEng / unrestricted

Numerical models often fail to accurately simulate and forecast a hydrological state in operation due to its inherent uncertainties. Data Assimilation (DA) is a promising technology that uses real-time observations to modify a model's parameters and internal variables to make it more representative of the actual state of the system it describes. In this thesis, hydrological DA is first reviewed from the perspective of its objective, scope, applications and the challenges it faces. Special attention is then given to nonlinear Kalman filters such as the Extended Kalman Filter (EKF). Based on a review of the existing studies, it is found that the potential of EKF has not been fully exploited. The Soil and Water Assessment Tool (SWAT) is a semi-distributed rainfall-runoff model that is widely used in agricultural water management and flood forecasting. However, studies of hydrological DA that are based on distributed models are relatively rare because hydrological DA is still in its infancy, with many issues to be resolved, and linear statistical models and lumped rainfall-runoff models are often used for the sake of simplicity. This study aims to fill this gap by assimilating streamflow and surface soil moisture observations into the SWAT model to improve its state simulation and forecasting capability. Unless specifically defined, all ‘forecasts’ in Italic font are based on the assumption of a perfect knowledge of the meteorological forecast. EKF is chosen as the DA method for its solid theoretical basis and parsimonious implementation procedures. Given the large number of parameters and storage variables in SWAT, only the watershed scale variables are included in the state vector, and the Hydrological Response Unit (HRU) scale variables are updated with the a posteriori/a priori ratio of their watershed scale counterparts. The Jacobian matrix is calculated numerically by perturbing the state variables. Two case studies are carried out with real observation data in order to verify the effectiveness of EKF assimilation. The upstream section of the Senegal River (above Bakel station) in western Africa is chosen for the streamflow assimilation, and the USDA ARS Little Washita experimental watershed is chosen to examine surface soil moisture assimilation. In the case of streamflow assimilation, a spinoff study is conducted to compare EKF state-parameter assimilation with a linear autoregressive (AR) output assimilation to improve SWAT’s flood forecasting capability. The influence of precipitation forecast uncertainty on the effectiveness of EKF assimilation is discussed in the context of surface soil moisture assimilation. In streamflow assimilation, EKF was found to be effective mostly in the wet season due to the weak connection between runoff, soil moisture and the curve number (CN2) in dry seasons. Both soil moisture and CN2 were significantly updated in the wet season despite having opposite update patterns. The flood forecast is moderately improved for up to seven days, especially in the flood period by applying the EKF subsequent open loop (EKFsOL) scheme. The forecast is further improved with a newly designed quasi-error update scheme. Comparison between EKF and AR output assimilation in flood forecasting reveals that while both methods can improve forecast accuracy, their performance is influenced by the hydrological regime of the particular year. EKF outperformed the AR model in dry years, while AR outperformed the EKF in wet years. Compared to AR, EKF is more robust and less sensitive to the length of the forecast lead time. A combined EKF-AR method provides satisfying results in both dry and wet years. The assimilation of surface soil moisture is proved effective in improving the full profile soil moisture and streamflow estimate. The setting of state and observation vector has a great impact on the assimilation results. The state vector with streamflow and all-layer soil moisture outperforms other, more complicated state vectors, including those augmented with intermediate variables and model parameters. The joint assimilation of surface soil moisture and streamflow observation provides a much better estimate of soil moisture compared to assimilating the streamflow only. The updated SWAT model is sufficiently robust to issue improved forecasts of soil moisture and streamflow after the assimilation is ‘unplugged’. The error quantification is found to be critical to the performance of EKF assimilation. Nevertheless, the application of an adaptive EKF shows no advantages over using the trial and error method in determining time-invariant model errors. The robustness of EKF assimilation is further verified by explicitly perturbing the precipitation ‘forecast’ in the EKF subsequent forecasts. The open loop model without previous EKF update is more vulnerable to erroneous precipitation estimates. Compared to streamflow forecasting, soil moisture forecasting is found to be more resilient to erroneous precipitation input.