This dissertation deals with attitude estimation of multicopters. Mainly the use of multicopter dynamic model in order to gain accuracy is investigated. It shows that the usage of multicopter dynamic model brings advantage contrary to other known algorithms for attitude estimation such as GPS/INS or complementary filter. Besides others one goal is to study the possibilities to estimate the parameters of dynamic model on-line. Further the influence of wind speed to estimation accuracy is also investigated. The algorithms are based on a nonlinear Kalman filter. The use of dynamic model of multicopters reveals the possibility of estimating attitude with bounded error even without periodic measurement of absolute position. One of the results of the dissertation is a new algorithm which does not require information about the thrust of multicopter propellers.

Electrophysiology has produced a wealth of information concerning characteristic patterns of neural activity underlying movement control in non-human primates. Such patterns differentiate functional classes of neurons and illuminate neural computations underlying different stages of motor planning and execution. The scarcity of high-resolution electrophysiological recordings in humans has hindered such descriptions of brain activity during uniquely human acts such as speech production. The goal of this dissertation was to identify and quantitatively characterize canonical temporal profiles of neural activity measured using surface and depth electrocorticography electrodes while pre-surgical epilepsy patients read aloud monosyllabic utterances. An unsupervised iterative clustering procedure was combined with a novel Kalman filter-based trend analysis to identify characteristic activity time courses that occurred across multiple subjects. A nonlinear distance measure was used to emphasize similarity at key portions of the activity profiles, including signal peaks. Eight canonical activity patterns were identified. These activity profiles fell broadly into two classes: symmetric profiles in which activity rises and falls at approximately the same rate, and ramp profiles in which activity rises relatively quickly and falls off gradually. Distinct characteristic time courses were found during four different task stages: early processing of the orthographic stimulus, phonological-to-motor processing, motor execution, and auditory processing of self-produced speech, with activity offset ramps in earlier stages approximately matching activity onset rates in later stages. The addition of an anatomical constraint to the distance measure to encourage clusters to form within local brain regions did not significantly change results. The anatomically constrained results showed a further subdivision of the eight canonical activity patterns, with the subdivisions primarily stemming from sub-clusters that are anatomically distinct across different brain regions, but maintained the base activity pattern of their parent cluster from the analysis without the anatomically constrained distance measure. The analysis tools developed herein provide a powerful means for identifying and quantitatively characterizing the neural computations underlying human speech production and may apply to other cognitive and behavioral domains.

More often than not, we cannot directly measure many phenomena that are crucial to us. However, we usually have access to certain partial observations on the phenomena of interest as well as a mathematical model of them. The filtering problem seeks estimation of the phenomena given all the accumulated partial information. In this thesis, we study several topics concerning the numerical approximation of the filtering problem. First, we study the continuous-time filtering problem. Given high-frequency ob- servations in discrete-time, we perform double discretization of the non-linear filter to allow for filter estimation with particle filter. By using the multilevel strategy, given any ε > 0, our algorithm achieve an MSE level of O(ε2) with a cost of O(ε−3), while the particle filter requires a cost of O(ε−4). Second, we propose a de-bias scheme for the particle filter under the partially observed diffusion model. The novel scheme is free of innate particle filter bias and discretization bias, through a double randomization method of [14]. Our estimator is perfectly parallel and achieves a similar cost reduction to the multilevel particle filter. Third, we look at a high-dimensional linear Gaussian state-space model in con- tinuous time. We propose a novel multilevel estimator which requires a cost of O(ε−2 log(ε)2) compared to ensemble Kalman-Bucy filters (EnKBFs) which requiresO(ε−3) for an MSE target of O(ε2). Simulation results verify our theory for models of di- mension ∼ 106. Lastly, we consider the model estimation through learning an unknown parameter that characterizes the partially observed diffusions. We propose algorithms to provide unbiased estimates of the Hessian and the inverse Hessian, which allows second-order optimization parameter learning for the model.

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This dissertation describes the development of a method for simultaneous localization and mapping (SLAM)algorithm which is suitable for high dimensional vehicle and map states. The goal of SLAM is to be able to navigate autonomously without the use of external aiding sources for vehicles. SLAM's combination of the localization and mapping problems makes it especially difficult to solve accurately and efficiently, due to the shear size of the unknown state vector. The vehicle states are typically constant in number while the map states increase with time. The increasing number of unknowns in the map state makes it impossible to use traditional Kalman filters to solve the problem- the covariance matrix grows too large and the computational complexity becomes too overwhelming. Particle filters have proved beneficial for alleviating the complexity of the SLAM problem for low dimensional vehicle states, but there is little work done for higher dimensional states. This research provides an Gaussian Mixture Model based alternative to the particle filtering SLAM methods, and provides a further partition that alleviates the vehicle state dimensionality problem with the standard particle filter. A SLAM background and basic theory is provided in the early chapters. A description of the new algorithm is provided in detail. Simulations are run demonstrating the performance of the algorithm, and then an aerial SLAM platform is developed for further testing. The aerial SLAM system uses a RGBD camera as well as an inertial measurement unit to collect SLAM data, and the ground truth is captured using an indoor optical motion capture system. Details on image processing and specifics on the inertial integration are provided. The performance of the algorithm is compared to a state of the art particle filtering based SLAM algorithm, and the results are discussed. Further work performed while working in the industry is described, which involves SLAM for adding transponders onto long-baseline acoustic arrays and stereo-inertial SLAM for 3D reconstruction of deep-water sub-sea structures. Finally, a neatly packaged production line version of the stereo-inertial SLAM system presented.

A detailed analysis and design of a navigation algorithm for a spacecraft to achieve precision lunar descent and landing is presented. The Inertial Navigation System (INS) was employed as the primary navigation system. To increase the accuracy and precision of the navigation system, the INS was integrated with aiding sensors - a star camera, an altimeter and a terrain camera. An unscented Kalman filter was developed to integrate the aiding sensor measurements with the INS measurements, and to estimate the current position, velocity and attitude of the spacecraft. The errors associated with the accelerometer and gyro measurements are also estimated as part of the navigation filter. An STK scenario was utilized to simulate the truth data for the navigation system. The navigation filter developed was tested and simulated, and from the results obtained, the position, velocity and attitude of the spacecraft were observed to be well estimated.

Autonomous underwater vehicles (AUVs) have the potential to dramatically improve safety, quality of life and general scientific knowledge. Our coasts, lakes and rivers are filled with various forms of marine infrastructure including dams, bridges, ship hulls, communication lines, and oil rigs. Each of these structures requires regular inspection, and current methods utilize divers, which is dangerous, expensive, and time consuming. AUVs have the potential to alleviate these difficulties and enable more regular inspection of these structures. Furthermore, there are significant scientific discoveries in the fields of geology, marine biology and medicine that AUV exploration of our oceans will enable. Since field trials of AUVs can be both expensive and high-risk, making a simulation method to generate data for algorithm development is a necessity. For this purpose, we present HoloOcean, an open-source, fully-featured, underwater robotics simulator. Built upon Unreal Engine 4 (UE4), HoloOcean comes equipped with multi-agent communications, common underwater sensors, high-fidelity graphics, and a novel sonar simulation method. Our novel sonar simulation framework is built upon an octree structure, allowing for rapid data generation and flexible usage to simulate a variety of sonars. Further, we have augmented this simulation to incorporate various probabilistic models to account for the heavy noise found in sonar imagery. Simulation enables development of many algorithms such as mapping, localization, structure from motion, controls, and many others. Localization is one essential algorithm for AUV navigation. Recent developments in the utilization of Lie Groups for robotic localization have lead to dramatic performance improvements in convergence and uncertainty characterization. One such method, the Invariant Extended Kalman Filter (InEKF), leverages that invariant error dynamics defined on matrix Lie Groups satisfy a log-linear differential equation. We lay out the various practical decisions required for the InEKF, and show that the primary sensors used in underwater robotics with minor modifications can be used in the InEKF. We show the convergence improvements of the InEKF over the quaternion-based extended Kalman filter (QEKF) on HoloOcean data, both in low and high uncertainty scenarios.

Due to some technical and environmental constraints, expanding the current electric power generation and transmission system is being challenged by even increasing the deployment of distributed renewable generation and storage systems. Energy storage can be used to store energy from utility during low-demand (off-peak) hours and deliver this energy back to the utility during high-demand (on-peak) hours. Furthermore, energy storage can be used with renewable sources to overcome some of their limitations such as their strong dependence on the weather conditions, which cannot be perfectly predicted, and their unmatched or out-of-synchronization generation peaks with the demand peaks. Generally, energy storage enhances the performance of distributed renewable sources and increases the efficiency of the entire power system. Moreover, energy storage allows for leveling the load, shaving peak demands, and furthermore, transacting power with the utility grid. This research proposes an energy management system (EMS) to manage the operation of distributed grid-tied battery micro-storage systems for stationary applications when operated with and without renewable sources. The term "micro" refers to the capacity of the energy storage compared to the grid capacity. The proposed management system employs four dynamic models; economic model, battery model, and load and weather forecasting models. These models, which are the main contribution of this research, are used in order to optimally control the operation of the micro-storage system (MSS) to maximize the economic return for the end-user when operated in an electricity spot market system. Chapter 1 presents an introduction to the drawbacks of the current power system, the role of energy storage in deregulated electricity markets, limitations of renewable sources, ways for participating in spot electricity markets, and an outline of the main contributions in this dissertation. In Chapter 2, some hardware design considerations for distributed micro-storage systems as well as some economic analyses are presented. Chapters 3 and 4 propose a battery management system (BMS) that handles three main functions: battery charging, state-of-charge (SOC) estimation and state-of-health (SOH) estimation. Chapter 5 proposes load and weather forecasting models using artificial neural networks (ANNs) to develop an energy management strategy to control the operation of the MSS in a spot market system when incorporated with other renewable energy sources. Finally, conclusions and future work are presented in Chapter 6.

The focus of this research is on the development of vibration response-based damage detection in civil engineering structures. Modal parameter-based and model identification-based approaches have been considered. In the modal parameter-based approach, the flexibility and curvature flexibility matrices of the structure are used to identify the damage. It is shown that changes in these matrices can be related to changes in stiffness values of individual structural members. Using this relationship, a method is proposed to solve for the change in stiffness values. The application of this approach is demonstrated on the benchmark problem developed by the joint International Association of Structural Control and American Society of Civil Engineers Structural Health Monitoring task group. The proposed approach is found to be effective in identifying various damage scenarios of this benchmark problem. The effect of missing modes on the damage identification scheme is also studied. The second method for damage identification aims at identifying sudden changes in stiffness for real time applications. It is shown that the high-frequency content of the response acceleration can be used to identify the instant at which a structure suffers a sudden reduction in its stiffness value. Using the Gibb's phenomenon, it is shown why a high-pass filter can be used for identifying such damages. The application of high-pass filters is then shown in identifying sudden stiffness changes in a linear multi-degree-of-freedom system and a bilinear single degree of freedom system. The impact of measurement noise on the identification approach is also studied. The noise characteristics under which damage identification can or cannot be made are clearly identified. The issue of quantification of the stiffness reduction by this approach is also examined. It is noted that even if the time at which the reduction in stiffness happens can be identified, the quantification of damage requires the knowledge of system displacement values. In principle, such displacements can be calculated by numerical integration of the acceleration response, but the numerical integrations are known to suffer from the low frequency drift error problems. To avoid the errors introduced due to numerical integration of the acceleration response, an approach utilizing the unscented Kalman filter is developed to track the sudden changes in stiffness values. This approach is referred to as the adaptive unscented Kalman filter (AUKF) approach. The successful application of the proposed AUKF approach is shown on two multi-degree of freedom systems that experience sudden loss of stiffness values while subjected to earthquake induced base excitation. / Ph. D.

This thesis proposes a new maximum power point tracking (MPPT) method for photovoltaic (PV) systems using Kalman filter. The Perturbation & Observation (P&O) method is widely used due to its easy implementation and simplicity. The P&O usually requires a dithering scheme to reduce noise effects, but the dithering scheme slows the tracking response time. Tracking speed is the most important factor for improving efficiency under frequent environmental change. The proposed method is based on the Kalman filter. An adaptive MPPT algorithm which uses an instantaneous power slope has introduced, but process and sensor noises disturb its estimations. Thus, applying the Kalman filter to the adaptive algorithm is able to reduce tracking failures by the noises. It also keeps fast tracking performance of the adaptive algorithm, so that enables using the Kalman filter to generate more powers under rapid weather changes than using the P&O. For simulations, a PV system is introduced with a 30kW array and MPPT controller designs using the Kalman filter and P&O. Simulation results are provided the comparison of the proposed method and the P&O on transient response for sudden system restart and irradiation changes in different noise levels. The simulations are also performed using real irradiance data for two entire days, one day is smooth irradiance changes and the other day is severe irradiance changes. The proposed method has showed the better performance when the irradiance is severely fluctuating than the P&O while the two methods have showed the similar performances on the smooth irradiance changes. / Master of Science