This thesis presents a means for representing and computing beliefs in the form of arbitrary probability density functions with a guarantee for the ongoing validity of such beliefs over indefinte time frames. The foremost aspect of this proposal is the introduction of a general, theoretical, solution to the guaranteed state estimation problem from within the recursive Bayesian estimation framework. The solution presented here determines the minimum space required, at each stage of the estimation process, to represent the belief with limited, or no, loss of information. Beyond this purely theoretical aspect, a number of numerical techniques, capable of determining the required space and performing the appropriate spatial reconfiguration, whilst also computing and representing the belief functions, are developed. This includes a new, hybrid particle-element approach to recursive Bayesian estimation. The advantage of spatial reconfiguration as presented here is that it ensures that the belief functions consider all plausible states of the target system, without altering the recursive Bayesian estimation equations used to form those beliefs. Furthermore, spatial reconfiguration as proposed in this dissertation enhances the estimation process since it allows computational resources to be concentrated on only those states considered plausible. Autonomous maritime search and rescue is used as a focus application throughout this dissertation since the searching-and-tracking requirements of the problem involve uncertainty, the use of arbitrary belief functions and dynamic target systems. Nevertheless, the theoretical development in this dissertation has been kept general and independent of an application, and as such the theory and techniques presented here may be applied to any problem involving dynamic Bayesian beliefs. A number of numerical experiments and simulations show the efficacy of the proposed spatially reconfigurable representations, not only in ensuring the validity of the belief functions over indefinite time frames, but also in reducing computation time and improving the accuracy of function approximation. Improvements of an order of magnitude were achieved when compared with traditional, spatially static representations.

This thesis presents a means for representing and computing beliefs in the form of arbitrary probability density functions with a guarantee for the ongoing validity of such beliefs over indefinte time frames. The foremost aspect of this proposal is the introduction of a general, theoretical, solution to the guaranteed state estimation problem from within the recursive Bayesian estimation framework. The solution presented here determines the minimum space required, at each stage of the estimation process, to represent the belief with limited, or no, loss of information. Beyond this purely theoretical aspect, a number of numerical techniques, capable of determining the required space and performing the appropriate spatial reconfiguration, whilst also computing and representing the belief functions, are developed. This includes a new, hybrid particle-element approach to recursive Bayesian estimation. The advantage of spatial reconfiguration as presented here is that it ensures that the belief functions consider all plausible states of the target system, without altering the recursive Bayesian estimation equations used to form those beliefs. Furthermore, spatial reconfiguration as proposed in this dissertation enhances the estimation process since it allows computational resources to be concentrated on only those states considered plausible. Autonomous maritime search and rescue is used as a focus application throughout this dissertation since the searching-and-tracking requirements of the problem involve uncertainty, the use of arbitrary belief functions and dynamic target systems. Nevertheless, the theoretical development in this dissertation has been kept general and independent of an application, and as such the theory and techniques presented here may be applied to any problem involving dynamic Bayesian beliefs. A number of numerical experiments and simulations show the efficacy of the proposed spatially reconfigurable representations, not only in ensuring the validity of the belief functions over indefinite time frames, but also in reducing computation time and improving the accuracy of function approximation. Improvements of an order of magnitude were achieved when compared with traditional, spatially static representations.

This dissertation proposes a novel computer modeling (DTFLOP modeling) technique to predict the real-time behavior of dynamic systems. The proposed DTFLOP modeling classifies the computation into the sequential computation, which is conducted on the CPU, and the parallel computation, which is performed on the GPU and formulates the data transmission between the CPU and the GPU using the parameters of the memory access speed and the floating point operations to be carried out on the CPU and the GPU by relating the calculation rate respectively. With the help of the proposed DTFLOP modeling it is possible to estimate the time cost for computing the model that represents a dynamic system given a certain computer. The proposed DTFLOP modeling can be utilized as a general method to analyze the computation of a model related to a dynamic system and two real life systems are selected to demonstrate its performance, the cooperative autonomous vehicle system and the full-field measurement system. For the cooperative autonomous vehicle system a novel parallel grid-based RBE technique is firstly proposed. The formulations are derived by identifying the parallel computation in the prediction and correction processes of the RBE. A belief fusion technique, which fuses not only the observation information but also the target motion information, has hen been proposed. The proposed DTFLOP modeling is validated using the proposed parallel grid-based RBE technique with the GPU implementation by comparing the estimated time cost with the actual time cost of the parallel grid-based RBE. The superiority of the proposed parallel grid-based RBE technique is investigated by a number of numerical examples in comparison with the conventional grid-based RBE technique. The belief fusion technique is examined by a simulated target search and rescue test and it is observed to maintain more information of the target compared with the conventional observation fusion technique and eventually leads to the better performance of the target search and rescue. For the full-field measurement system a novel parallel DCT full-field measurement technique for measuring the displacement and strain field on the deformed surface of a structure is proposed. The proposed parallel DCT full-field measurement technique measures the displacement and strain field by tracking the centroids of the marked dots on the deformed surface. It identifies and develops the parallel computation in the image analysis and the field estimation processes and then is implemented into the GPU to accelerate the conventional full-field measurement techniques. The detail strategy of the GPU implementation is also developed and presented. The corresponding software package, which also includes a graphic user interface, and the hardware system consist of two digital cameras, LED lights and adjustable support legs to accommodate indoor or outdoor experimental environments are proposed. The proposed DTFLOP modeling is applied to the proposed parallel DCT full-field measurement technique to estimate its performance and the well match with the actual performance demonstrates the DTFLOP modeling. A number of both simulated and real experiments, including the tensile, compressive and bending experiments in the laboratory and outdoor environments, are performed to validate and demonstrate the proposed parallel DCT full-field measurement technique. / Ph. D.

This thesis introduces a multi-Bayesian framework for detection and classification of features in environments abundant with error-inducing noise. The approach takes advantage of Bayesian correction and classification in three distinct stages. The corrective scheme described here extracts useful but highly stochastic features from a data source, whether vision-based or otherwise, to aid in higher-level classification. Unlike many conventional methods, these features’ uncertainties are characterized so that test data can be correctively cast into the feature space with probability distribution functions that can be integrated over class decision boundaries created by a quadratic Bayesian classifier. The proposed approach is specifically formulated for road crack detection and characterization, which is one of the potential applications. For test images assessed with this technique, ground truth was estimated accurately and consistently with effective Bayesian correction, showing a 33% improvement in recall rate over standard classification. Application to road cracks demonstrated successful detection and classification in a practical domain. The proposed approach is extremely effective in characterizing highly probabilistic features in noisy environments when several correlated observations are available either from multiple sensors or from data sequentially obtained by a single sensor. / Master of Science / Humans have an outstanding ability to understand things about the world around them. We learn from our youngest years how to make sense of things and perceive our environment even when it is not easy. To do this, we inherently think in terms of probabilities, updating our belief as we gain new information. The methods introduced here allow an autonomous system to think similarly, by applying a fairly common probabilistic technique to the task of perception and classification. In particular, road cracks are observed and classified using these methods, in order to develop an autonomous road condition monitoring system. The results of this research are promising; cracks are identified and correctly categorized with 92% accuracy, and the additional “intelligence” of the system leads to a 33% improvement in road crack assessment. These methods could be applied in a variety of contexts as the leading edge of robotics research seeks to develop more robust and human-like ways of perceiving the world.

This dissertation proposes a new framework to Non-Field-of-view (NFOV) sound source localization and tracking in indoor environments. The approach takes advantage of sound signal information to localize target position through auditory sensors combination with other sensors within grid-based recursive estimation structure for tracking using nonlinear and non-Gaussian observations. Three approaches to NFOV target localization are investigated. These techniques estimate target positions within the Recursive Bayesian estimation (RBE) framework. The first proposed technique uses a numerical fingerprinting solution based on acoustic cues of a fixed microphone array in a complex indoor environment. The Interaural level differences (ILDs) of microphone pair from a given environment are constructed as an a priori database, and used for calculating the observation likelihood during estimation. The approach was validated in a parametrically controlled testing environment, and followed by real environment validations. The second approach takes advantage of acoustic sensors in combination with an optical sensor to assist target estimation in NFOV conditions. This hybrid of the two sensors constructs observation likelihood through sensor fusion. The third proposed model-based technique localizes the target by taking advantage of wave propagation physics: the properties of sound diffraction and reflection. This approach allows target localization without an a priori knowledge database which is required for the first two proposed techniques. To demonstrate the localization performance of the proposed approach, a series of parameterized numerical and experimental studies were conducted. The validity of the formulation and applicability to the actual environment were confirmed. / Ph. D.

This thesis is concerned with the Pursuit-and-Evasion (PE) problem where the pursuer aims to minimize the time to capture the evader while the evader tries to prevent capture. In the problem, the evader has two advantages: a higher manoeuvrability and that the pursuer is uncertain about the evader??s state. Cooperation among multiple pursuer vehicles can thus be used to overcome the evader??s advantages. The focus here is on the formulation and development of frameworks and algorithms for cooperation amongst pursuers, aiming at feasible implementation on real and autonomous vehicles. The thesis is split into Parts I and II. Part I considers the problem of capturing an evader of higher manoeuvrability in a deterministic PE game. The approach is the employment of Forward Reachable Set (FRS) analysis in the pursuers?? control. The analysis considers the coverage of the evader??s FRS, which is the set of reachable states at a future time, with the pursuer??s FRS and assumes that the chance of capturing the evader is dependent on the degree of the coverage. Using the union of multiple pursuers?? FRSs intuitively leads to more evader FRS coverage and this forms the mechanism of cooperation. A framework for cooperative control based on the FRS coverage, or FRS-based control, is proposed. Two control algorithms were developed within this framework. Part II additionally introduces the problem of evader state uncertainty due to noise and limited field-of-view of the pursuers?? sensors. A search-and-capture (SAC) problem is the result and a hybrid architecture, which includes multi-sensor estimation using the Particle Filter as well as FRS-based control, is proposed to accomplish the SAC task. The two control algorithms in Part I were tested in simulations against an optimal guidance algorithm. The results show that both algorithms yield a better performance in terms of time and miss distance. The results in Part II demonstrate the effectiveness of the hybrid architecture for the SAC task. The proposed frameworks and algorithms provide insights for the development of effective and more efficient control of pursuer vehicles and can be useful in the practical applications such as defence systems and civil law enforcement.

This thesis is concerned with the Pursuit-and-Evasion (PE) problem where the pursuer aims to minimize the time to capture the evader while the evader tries to prevent capture. In the problem, the evader has two advantages: a higher manoeuvrability and that the pursuer is uncertain about the evader??s state. Cooperation among multiple pursuer vehicles can thus be used to overcome the evader??s advantages. The focus here is on the formulation and development of frameworks and algorithms for cooperation amongst pursuers, aiming at feasible implementation on real and autonomous vehicles. The thesis is split into Parts I and II. Part I considers the problem of capturing an evader of higher manoeuvrability in a deterministic PE game. The approach is the employment of Forward Reachable Set (FRS) analysis in the pursuers?? control. The analysis considers the coverage of the evader??s FRS, which is the set of reachable states at a future time, with the pursuer??s FRS and assumes that the chance of capturing the evader is dependent on the degree of the coverage. Using the union of multiple pursuers?? FRSs intuitively leads to more evader FRS coverage and this forms the mechanism of cooperation. A framework for cooperative control based on the FRS coverage, or FRS-based control, is proposed. Two control algorithms were developed within this framework. Part II additionally introduces the problem of evader state uncertainty due to noise and limited field-of-view of the pursuers?? sensors. A search-and-capture (SAC) problem is the result and a hybrid architecture, which includes multi-sensor estimation using the Particle Filter as well as FRS-based control, is proposed to accomplish the SAC task. The two control algorithms in Part I were tested in simulations against an optimal guidance algorithm. The results show that both algorithms yield a better performance in terms of time and miss distance. The results in Part II demonstrate the effectiveness of the hybrid architecture for the SAC task. The proposed frameworks and algorithms provide insights for the development of effective and more efficient control of pursuer vehicles and can be useful in the practical applications such as defence systems and civil law enforcement.

Pursuant to the federal Clean Water Act (CWA), when a water body has been listed as impaired, Total Maximum Daily Loads (TMDLs) for the water quality constituents causing the impairment must be developed. A TMDL is the maximum daily mass flux of a pollutant that a waterbody can receive and still safely meet water quality standards. The development of a TMDL and demonstrating compliance with a TMDL requires pollutant load estimation. By definition, a pollutant load is the time integral product of flows and concentrations. Consequently, the accuracy of pollutant load estimation is highly dependent on the accuracy of runoff volume estimation. Runoff volume estimation requires the development of reasonable transfer functions to convert precipitation into runoff. In cold climates where a large proportion of precipitation falls as snow, the accumulation and ablation of snowpack must also be estimated. Sequential data assimilation techniques that stochastically combine field measurements and model results can significantly improve the prediction skill of snowmelt and runoff models while also providing estimates of prediction uncertainty. Using the National Weather Service's SNOW-17 and the Sacramento Soil Moisture Accounting (SAC-SMA) models, this study evaluates particle filter based data assimilation algorithms to predict seasonal snow water equivalent (SWE) and runoff within a small watershed in the Lake Tahoe Basin located in California. A non-linear regression model is then used that predicts suspended sediment concentrations (SSC) based on runoff rate and time of year. Runoff volumes and SSC are finally combined to provide an estimate of the average annual sediment load from the watershed with estimates of prediction uncertainty. For the period of simulation (10/1/1991 to 10/1/1996), the mean annual suspended sediment load is estimated to be 753 tonnes/yr with a 95% confidence interval about the mean of 626 to 956 tonnes/yr. The 95% prediction interval for any given year is estimated to range from approximately 86 to 2,940 tonnes/yr.