This work describes a framework for simultaneous estimation and modeling (SEAM) of dynamic systems using non-Gaussian belief fusion by first presenting the relevant fundamental formulations, then building upon these formulations incrementally towards a more general and ubiquitous framework. Multi-Gaussian belief fusion (MBF) is introduced as a natural and effective method of fusing non-Gaussian probability distribution functions (PDFs) in arbitrary dimensions efficiently and with no loss of accuracy. Construction of some multi-Gaussian structures for potential use in MBF is addressed. Furthermore, recursive Bayesian estimation (RBE) is developed for linearized systems with uncertainty in model parameters, and a rudimentary motion model correction stage is introduced. A subsequent improvement to motion model correction for arbitrarily non-Gaussian belief is developed, followed by application to observation models. Finally, SEAM is generalized to fully nonlinear and non-Gaussian systems. Several parametric studies were performed on simulated experiments in order to assess the various dependencies of the SEAM framework and validate its effectiveness in both estimation and modeling. The results of these studies show that SEAM is capable of improving estimation when uncertainty is present in motion and observation models as compared to existing methods. Furthermore, uncertainty in model parameters is consistently reduced as these parameters are updated throughout the estimation process. SEAM and its constituents have potential uses in robotics, target tracking and localization, state estimation, and more. / Doctor of Philosophy / The simultaneous estimation and modeling (SEAM) framework and its constituents described in this dissertation aim to improve estimation of signals where significant uncertainty would normally introduce error. Such signals could be electrical (e.g. voltages, currents, etc.), mechanical (e.g. accelerations, forces, etc.), or the like. Estimation is accomplished by addressing the problem probabilistically through information fusion. The proposed techniques not only improve state estimation, but also effectively "learn" about the system of interest in order to further refine estimation. Potential uses of such methods could be found in search-and-rescue robotics, robust control algorithms, and the like. The proposed framework is well-suited for any context where traditional estimation methods have difficulty handling heightened uncertainty.

The present work introduces a methodology to obtain a discrete time state space representation of an electrical network using the nodal [G] matrix of the Electromagnetic Transients Program (EMTP) solution. This is the first time the connection between the EMTP nodal analysis solution and a corresponding state-space formulation is presented. Compared to conventional state space solutions, the nodal EMTP solution is computationally much more efficient. Compared to the phasor solutions used in transient stability analysis, the proposed approach captures a much wider range of eigenvalues and system operating states. A fundamental advantage of extracting the system eigenvalues directly from the EMTP solution is the ability of the EMTP to follow the characteristics of nonlinearities. The system's trajectory can be accurately traced and the calculated eigenvalues and eigenvectors correctly represent the system's instantaneous dynamics. In addition, the algorithm can be used as a tool to identify network partitioning subsystems suitable for real-time hybrid power system simulator environments, including the implementation of multi-time scale solutions. The proposed technique can be implemented as an extension to any EMTP-based simulator. Within our UBC research group, it is aimed at extending the capabilities of our real-time PC-cluster Object Virtual Network Integrator (OVNI) simulator.

The present work introduces a methodology to obtain a discrete time state space representation of an electrical network using the nodal [G] matrix of the Electromagnetic Transients Program (EMTP) solution. This is the first time the connection between the EMTP nodal analysis solution and a corresponding state-space formulation is presented. Compared to conventional state space solutions, the nodal EMTP solution is computationally much more efficient. Compared to the phasor solutions used in transient stability analysis, the proposed approach captures a much wider range of eigenvalues and system operating states. A fundamental advantage of extracting the system eigenvalues directly from the EMTP solution is the ability of the EMTP to follow the characteristics of nonlinearities. The system's trajectory can be accurately traced and the calculated eigenvalues and eigenvectors correctly represent the system's instantaneous dynamics. In addition, the algorithm can be used as a tool to identify network partitioning subsystems suitable for real-time hybrid power system simulator environments, including the implementation of multi-time scale solutions. The proposed technique can be implemented as an extension to any EMTP-based simulator. Within our UBC research group, it is aimed at extending the capabilities of our real-time PC-cluster Object Virtual Network Integrator (OVNI) simulator.

The present work introduces a methodology to obtain a discrete time state space representation of an electrical network using the nodal [G] matrix of the Electromagnetic Transients Program (EMTP) solution. This is the first time the connection between the EMTP nodal analysis solution and a corresponding state-space formulation is presented. Compared to conventional state space solutions, the nodal EMTP solution is computationally much more efficient. Compared to the phasor solutions used in transient stability analysis, the proposed approach captures a much wider range of eigenvalues and system operating states. A fundamental advantage of extracting the system eigenvalues directly from the EMTP solution is the ability of the EMTP to follow the characteristics of nonlinearities. The system's trajectory can be accurately traced and the calculated eigenvalues and eigenvectors correctly represent the system's instantaneous dynamics. In addition, the algorithm can be used as a tool to identify network partitioning subsystems suitable for real-time hybrid power system simulator environments, including the implementation of multi-time scale solutions. The proposed technique can be implemented as an extension to any EMTP-based simulator. Within our UBC research group, it is aimed at extending the capabilities of our real-time PC-cluster Object Virtual Network Integrator (OVNI) simulator. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

L'estimation en robotique est un sujet important affecté par les compromis entre certains critères majeurs parmi lesquels nous pouvons citer le temps de calcul et la précision. L'importance de ces deux critères dépend de l'application. Si le temps de calcul n'est pas important pour les méthodes hors ligne, il devient critique lorsque l'application doit s'exécuter en temps réel. De même, les exigences de précision dépendent des applications. Les estimateurs EKF sont largement utilisés pour satisfaire les contraintes en temps réel tout en obtenant une estimation avec des précisions acceptables. Les centrales inertielles (Inertial Measurement Unit - IMU) demeurent des capteurs répandus dnas les problèmes d'estimation de trajectoire. Ces capteurs ont par ailleurs la particularité de fournir des données à une fréquence élevée. La principale contribution de cette thèses est une présentation claire de la méthode de préintégration donnant lieu à une meilleure utilisation des centrales inertielles. Nous appliquons cette méthode aux problèmes d'estimation dans les cas de la navigation piétonne et celle des robots humanoïdes. Nous souhaitons par ailleurs montrer que l'estimation en temps réel à l'aide d'une centrale inertielle à faible coût est possible avec des méthodes d'optimisation tout en formulant les problèmes à l'aide d'un modèle graphique bien que ces méthodes soient réputées pour leurs coûts élevés en terme de calculs. Nous étudions également la calibration des centrales inertielles, une étape qui demeure critique pour leurs utilisations. Les travaux réalisés au cours de cette thèse ont été pensés en gardant comme perspective à moyen terme le SLAM visuel-inertiel. De plus, ce travail aborde une autre question concernant les robots à jambes. Contrairement à leur architecture habituelle, pourrions-nous utiliser plusieurs centrales inertielles à faible coût sur le robot pour obtenir des informations précieuses sur le mouvement en cours d'exécution ? / Estimation in robotics is an important subject affected by trade-offs between some major critera from which we can cite the computation time and the accuracy. The importance of these two criteria are application-dependent. If the computation time is not important for off-line methods, it becomes critical when the application has to run on real-time. Similarly, accuracy requirements are dependant on the applications. EKF estimators are widely used to satisfy real-time constraints while achieving acceptable accuracies. One sensor widely used in trajectory estimation problems remains the inertial measurement units (IMUs) providing data at a high rate. The main contribution of this thesis is a clear presentation of the preintegration theory yielding in a better use IMUs. We apply this method for estimation problems in both pedestrian and humanoid robots navigation to show that real-time estimation using a low- cost IMU is possible with smoothing methods while formulating the problems with a factor graph. We also investigate the calibration of the IMUs as it is a critical part of those sensors. All the development made during this thesis was thought with a visual-inertial SLAM background as a mid-term perspective. Firthermore, this work tries to rise another question when it comes to legged robots. In opposition to their usual architecture, could we use multiple low- cost IMUs on the robot to get valuable information about the motion being executed?