<p> Bayesian filtering refers to the process of sequentially estimating the current state of a complex dynamic system from noisy partial measurements using Bayes' rule. This thesis considers Bayesian filtering as applied to an important class of state estimation problems, which is describable by a discrete-time nonlinear state-space model with additive Gaussian noise. It is known that the conditional probability density of the state given the measurement history or simply the posterior density contains all information about the state. For nonlinear systems, the posterior density cannot be described by a finite number of sufficient statistics, and an approximation must be made instead.</p> <p> The approximation of the posterior density is a challenging problem that has engaged many researchers for over four decades. Their work has resulted in a variety of approximate Bayesian filters. Unfortunately, the existing filters suffer from possible divergence, or the curse of dimensionality, or both, and it is doubtful that a single filter exists that would be considered effective for applications ranging from low to high dimensions. The challenge ahead of us therefore is to derive an approximate nonlinear Bayesian filter, which is theoretically motivated, reasonably accurate, and easily extendable to a wide range of applications at a minimal computational cost.</p> <p> In this thesis, a new approximate Bayesian filter is derived for discrete-time nonlinear filtering problems, which is named the cubature Kalman filter. To develop this filter, it is assumed that the predictive density of the joint state-measurement random variable is Gaussian. In this way, the optimal Bayesian filter reduces to the problem of how to compute various multi-dimensional Gaussian-weighted moment integrals. To numerically compute these integrals, a third-degree spherical-radial cubature rule is proposed. This cubature rule entails a set of cubature points scaling linearly with the state-vector dimension. The cubature Kalman filter therefore provides an efficient solution even for high-dimensional nonlinear filtering problems. More remarkably, the cubature Kalman filter is the closest known approximate filter in the sense of completely preserving second-order information due to the maximum entropy principle. For the purpose of mitigating divergence, and improving numerical accuracy in systems where there are apparent computer roundoff difficulties, the cubature Kalman filter is reformulated to propagate the square roots of the error-covariance matrices. The formulation of the (square-root) cubature Kalman filter is validated through three different numerical experiments, namely, tracking a maneuvering ship, supervised training of recurrent neural networks, and model-based signal detection and enhancement. All three experiments clearly indicate that this powerful new filter is superior to other existing nonlinear filters. </p> / Thesis / Doctor of Philosophy (PhD)

Decisions for asset allocation and protection are predicated upon accurate knowledge of the current operating environment as well as correctly characterizing the evolution of the environment over time. The desired kinematic and kinetic states of objects in question cannot be measured directly in most cases and instead are inferred or estimated from available measurements using a filtering process. Often, nonlinear transformations between the measurement domain and desired state domain distort the state domain probability density function yielding a form which does not necessarily resemble the form assumed in the filtering algorithm. The distortion effect must be understood in greater detail and appropriately accounted for so that even if sensors, state estimation algorithms, and state propagation algorithms operate in different domains, they can all be effectively utilized without any information loss due to domain transformations. This research presents an analytical investigation into understanding how non-linear transformations of stochastic, but characterizable, processes affect state and uncertainty estimation with direct application to space object surveillance and space- craft attitude determination. Analysis is performed with attention to construction of the state domain probability density function since state uncertainty and correlation are derived from the statistical moments of the probability density function. Analytical characterization of the effect nonlinear transformations impart on the structure of state probability density functions has direct application to conventional non- linear filtering and propagation algorithms in three areas: (1) understanding how smoothing algorithms used to estimate indirectly observed states impact state uncertainty, (2) justification or refutation of assumed state uncertainty distribution for more realistic uncertainty quantification, and (3) analytic automation of initial state estimate and covariance in lieu of user tuning. A nonlinear filtering algorithm based upon Bayes’ Theorem is presented to ac- count for the impact nonlinear domain transformations impart on probability density functions during the measurement update and propagation phases. The algorithm is able to accommodate different combinations of sensors for state estimation which can also be used to hypothesize system parameters or unknown states from available measurements because information is able to appropriately accounted for.

Today’s heavy duty vehicles are equipped with safety and comfort systems, e.g. ABS and ESP, which totally or partly take over the vehicle in certain risk situations. When these systems become more and more autonomous more robust positioning is needed. In the right conditions the GPS system provides precise and robust positioning. However, in harsh environments, e.g. dense urban areas and in dense forests, the GPS signals may be affected by multipaths, which means that the signals are reflected on their way from the satellites to the receiver. This can cause large errors in the positioning and thus can give rise to devastating effects for autonomous systems. This thesis evaluate different methods to enhance a low cost GPS in harsh environments, with focus on mitigating multipaths. Mainly there are four different methods: Regular Unscented Kalman filter, probabilistic multipath mitigation, Unscented Kalman filter with vehicle sensor input and probabilistic multipath mitigation with vehicle sensor input. The algorithms will be tested and validated on real data from both dense forest areas and dense urban areas. The results show that the positioning is enhanced, in particular when integrating the vehicle sensors, compared to a low cost GPS.

This thesis gives a unified framework to formulate and solve resource management problems in radar systems. / As a crucial factor in improving radar performance for multiple target tracking (MTT), resource management problems are analyzed in this thesis with regard to sensor platform path planning, beam scheduling, and burst parameter design. This thesis addresses problems to deploy or adapt radar configurations for multisensor-multitarget tracking, including 1) the path planning of movable receivers and power allocation of transmitted signals, 2) the optimal beam steering of high-precision pencil beams, and 3) the pulsed repetition frequency (PRF) set selection and waveform design. Firstly, the coordinated sensor management on the ends of both receivers and transmitters for a multistatic radar is studied. A multistatic radar system consists of fixed transmitters and movable receivers. To form better transmitter-target-receiver geometry and to establish an effective power allocation scheme to illuminate targets with different priorities, a joint path planning and power allocation problems, which determines the moving trajectories of receivers mounted on unmanned airborne vehicles (UAVs) and the power allocation scheme of transmitted signals over a limited time horizon, is formulated as a weighted-sum optimization. The problem is solved with a genetic algorithm (GA) with a novel pre-selection operator. The pre-selection operator, which takes advantage of the receding horizon control (RHC) framework to improve population structures prior to the next generation, can accelerate the convergence of GA. Secondly, the beam steering strategies for a cooperative phased array radar system with high-precision beams are developed. Pencil beams with narrow beamwidth, which are designated to track targets for a phased array radar, offer efficient performance in an energy-saving design, but can cause partial observations. The novel concept of expected Cramér-Rao lower bound (EPCRLB) is proposed to model partial observations. A formulation based on PCRLB is given and solved with a hierarchical genetic algorithm (HGA). An optimal strategy based on EPCRLB, which is effective in performance and efficient in time, is proposed. Finally, a joint pulsed repetition frequency (PRF) set selection and waveform design is studied. The problem tries to improve blind zone maps while preventing targets from falling into blind zones. Waveform parameters are then optimized for the system to provide better tracking accuracy. The problem is first formulated as a bi-objective optimization problem and solved with a multiple-objective genetic algorithm. Then, a two-step strategy that prioritizes the visibility of targets is developed. Numerical results demonstrate the effectiveness of proposed strategies over simple approaches. / Thesis / Doctor of Philosophy (PhD) / This thesis formulates resource management problems in various radar systems. The problems use PCRLB, a theoretically achievable lower bound for estimators, as a metric to optimize, and help the configuration of radar resources in an efficient manner. Effective strategies and improved algorithms are proposed to solve the problems.

Temporal phenomena in a range of disciplines are more naturally modelled in continuous-time than coerced into a discrete-time formulation. Differential systems form the mainstay of such modelling, in fields from physics to economics, geoscience to neuroscience. While powerful, these are fundamentally limited by their determinism. For the purposes of probabilistic inference, their extension to stochastic differential equations permits a continuous injection of noise and uncertainty into the system, the model, and its observation. This thesis considers Bayesian filtering for state and parameter estimation in general non-linear, non-Gaussian systems using these stochastic differential models. It identifies a number of challenges in this setting over and above those of discrete time, most notably the absence of a closed form transition density. These are addressed via a synergy of diverse work in numerical integration, particle filtering and high performance distributed computing, engineering novel solutions for this class of model. In an area where the default solution is linear discretisation, the first major contribution is the introduction of higher-order numerical schemes, particularly stochastic Runge-Kutta, for more efficient simulation of the system dynamics. Improved runtime performance is demonstrated on a number of problems, and compatibility of these integrators with conventional particle filtering and smoothing schemes discussed. Finding compatibility for the smoothing problem most lacking, the major theoretical contribution of the work is the introduction of two novel particle methods, the kernel forward-backward and kernel two-filter smoothers. By harnessing kernel density approximations in an importance sampling framework, these attain cancellation of the intractable transition density, ensuring applicability in continuous time. The use of kernel estimators is particularly amenable to parallelisation, and provides broader support for smooth densities than a sample-based representation alone, helping alleviate the well known issue of degeneracy in particle smoothers. Implementation of the methods for large-scale problems on high performance computing architectures is provided. Achieving improved temporal and spatial complexity, highly favourable runtime comparisons against conventional techniques are presented. Finally, attention turns to real world problems in the domain of Functional Magnetic Resonance Imaging (fMRI), first constructing a biologically motivated stochastic differential model of the neural and hemodynamic activity underlying the observed signal in fMRI. This model and the methodological advances of the work culminate in application to the deconvolution and effective connectivity problems in this domain.

During strong earthquakes structural systems exhibit nonlinear behavior due to low-cycle fatigue, cracking, yielding and/or fracture of constituent elements. After a seismic event it is essential to assess the state of damage of structures and determine if they can safely resist aftershocks or future strong motions. The current practice in post-earthquake damage assessment relies mainly on visual inspections and local testing. These approaches are limited to the ability of inspectors to reach all potentially damaged locations, and are typically intended to detect damage near the outer surfaces of the structure leaving the possibility of hidden undetected damage. Some structures in seismic prone-regions are instrumented with an array of sensors that measure their acceleration at different locations. We operate under the premise that acceleration response measurements contain information about the state of damage of structures, and it is of interest to extract this information and use it in post-earthquake damage assessment and decision making strategies. The objective of this dissertation is to show that Bayesian filters can be successfully employed to estimate the nonlinear dynamic response of instrumented structural systems. The estimated response is subsequently used for structural damage diagnosis. Bayesian filters combine dynamic response measurements at limited spatial locations with a nonlinear dynamic model to estimate the response of stochastic dynamical systems at the model degrees-of-freedom. The application of five filters is investigated: the extended, unscented and ensemble Kalman filters, the particle filter and the model-based observer. The main contributions of this dissertation are summarized as follows: i) Development of a filtering-based mechanistic damage assessment framework; ii) Experimental validation of Bayesian filters in small and large-scale structures; iii) Uncertainty quantification and propagation of response and damage estimates computed using Bayesian filters.

Résumé indisponible. / Résumé indisponible.

This report is a summary of the development of sensor integration for low-cost crash avoidance for over-land commercial trucks. The goal of the project was to build and test a system composed of low-cost commercially available sensors arranged on a truck trailer to monitor the environment around the truck. The system combines the data from each sensor to increase the reliability of the sensor using a probabilistic data fusion approach. A combination of ultrasonic and magnetoresistive sensors was used in this study. In addition, Radar and digital imaging were investigated as reference signals and possible candidates for additional sensor integration. However, the primary focus of this work is the integration of the ultrasonic and magnetoresistive sensors. During the investigation the individual sensors were evaluated for their use in the system. This included communication with vendors and lab and field testing. In addition, the sensors were modeled using an analytical mathematical model to help understand and predict the sensor behavior. Next, an algorithm was developed to fuse the data from the individual sensors. A probabilistic approach was used based on Bayesian filtering with a prediction-correction algorithm. Sensor fusion was implemented using joint a probability algorithm. The output of the system is a prediction of the likelihood of the presence of a vehicle in a given region near the host truck trailer. The algorithm was demonstrated on the fusion of an ultrasonic sensor and a magnetic sensor. Testing was conducted using both a light pickup truck and also with a class 8 truck. Various scenarios were evaluated to determine the system performance. These included vehicles passing the host truck from behind and the host truck passing vehicles. Also scenarios were included to test the system at distinguishing other vehicles from objects that are not vehicles such as sign posts, walls or railroads that could produce electronic signals similar to those of vehicles and confuse the system. The test results indicate that the system was successful at predicting the presence and absence of vehicles and also successful at eliminating false positives from objects that are not vehicles with overall accuracy ranging from 90 to 100% depending on the scenario. Some additional improvements in the performance are expected with future improvements in the algorithm discussed in the report. The report includes a discussion of the mapping of the algorithm output with the implementation of current and future safety and crash avoidance technologies based on the level of confidence of the algorithm output and the seriousness of the impending crash scenario. For example, irreversible countermeasures such as firing an airbag or engaging the brakes should only be initiated if the confidence of the signal is very high, while reversible countermeasures such as warnings to the driver or nearby vehicles can be initiated with a relatively lower confidence. The results indicate that the system shows good potential as a low cost alternative to competing systems which require multiple, high cost sensors. Truck fleet operators will likely adopt technology only if the costs are justified by reduced damage and insurance costs, therefore developing an effective crash avoidance system at a low cost is required for the technology to be adopted on a large scale.

In recent years, the design, fabrication, and control of robotic systems inspired by biology has gained renewed attention due to the potential improvements in efficiency, maneuverability, and adaptability with which animals interact with their environments. Motion studies of biological systems such as humans, fish, insects, birds and bats are often used as a basis for robotic system design. Often, these studies are conducted by recording natural motions of the system of interest using a few high-resolution, high-speed cameras. Such equipment enables the use of standard methods for corresponding features and producing three-dimensional reconstructions of motion. These studies are then interpreted by a designer for kinematic, dynamic, and control systems design of a robotic system. This methodology generates impressive robotic systems which imitate their biological counter parts. However, the equipment used to study motion is expensive and designer interpretation of kinematics data requires substantial time and talent, can be difficult to identify correctly, and often yields kinematic inconsistencies between the robot and biology. To remedy these issues, this dissertation leverages the use of low-cost, low-speed, low-resolution cameras for tracking bat flight and presents a methodology for automatically learning physical geometry which restricts robotic joints to a motion submanifold identified from motion capture data. To this end, we present a spatially recursive state estimator which incorporates inboard state correction for producing accurate state estimates of bat flight. Using these state estimates, we construct a Gaussian process dynamic model (GPDM) of bat flight which is the first nonlinear dimensionality reduction of flapping flight in bats. Additionally, we formulate a novel method for learning robotic joint geometry directly from the experimental observations. To do this, we leverage recent developments in learning theory which derive analytical-empirical potential energy fields for identifying an underlying motion submanifold. We use these energy fields to optimize a compliant structure around a single degree-of-freedom elbow joint and to design rigid structures around spherical joints for an entire bat wing. Validation experiments show that the learned joint geometry restricts the motion of the joints to those observed during experiment. / Ph. D. / In recent years, robots modeled after biological systems have become increasingly prevalent. Such robots are often designed based on motion capture experiments of the animal they aim to imitate. The motion studies are typically conducted using commercial motion capture systems such as ViconTM or OptiTrackTM or a few high-speed, high-resolution cameras such as those marketed by PhotronTM or PhantomTM. These systems allow for automated processing of video sequences into three-dimensional reconstructions of the biological motion using standard image processing and state estimation techniques. The motion data is then used to drive robotic system designs such as the SonyTM AiboTM dog and the Boston Dynamics Atlas humanoid robot. While the motion capture data forms a basis for these impressive robots, the progression from data to robotic system is neither algorithmic nor rigorous and requires substantial interpretation by a human. In contrast, this dissertation presents a novel experimental and computational framework which uses low-speed, low-resolution cameras for capturing the complex motion of bats in flight and introduces a methodology which uses the motion capture data to directly design geometry which restricts the motion of joints to the motions observed in experiment. The advantage of our method is that the designer only needs to specify a general joint geometry such as a ball or pin joint, and geometry which restricts the motion is automatically identified. To do this, we learn an energy field over the set of kinematic configurations observed during experiment. This energy field “pushes” system trajectories towards those experimentally observed trajectories. We then learn compliant or rigid geometry which approximates this energy field to physically restrict the range of motion of the joint. We validate our method by fabricating joint geometry designed using both these approaches and present experiments which confirm that the reachable set of the joint is approximately the same as the set of configurations observed during experiments.

This thesis presents several new techniques for developing safe and flexible human-robot interaction tasks where human operators cooperate with robotic manipulators. The contributions of this thesis are divided in two fields: the development of safety strategies which modify the normal behavior of the robotic manipulator when the human operator is near the robot and the development of dexterous manipulation tasks for in-hand manipulation of objects with a multi-fingered robotic hand installed at the end-effector of a robotic manipulator. / Valencian Government by the research project "Infraestructura 05/053". Spanish Ministry of Education and Science by the pre-doctoral grant AP2005-1458 and the research projects DPI2005-06222 and DPI2008-02647, which constitute the research framework of this thesis.