Abrupt Motion Tracking via Nearest Neighbor Field Driven Stochastic Sampling

Stochastic sampling based trackers have shown good performance for abrupt motion tracking so that they have gained popularity in recent years. However, conventional methods tend to use a two-stage sampling paradigm, in which the search space needs to be uniformly explored with an inefficient preliminary sampling phase. In this paper, we propose a novel sampling-based method in the Bayesian filtering framework to address the problem. Within the framework, nearest neighbor field estimation is utilized to compute the importance proposal probabilities, which guide the Markov chain search towards promising regions and thus enhance the sampling efficiency; given the motion priors, a smoothing stochastic sampling Monte Carlo algorithm is proposed to approximate the posterior distribution through a smoothing weight-updating scheme. Moreover, to track the abrupt and the smooth motions simultaneously, we develop an abrupt-motion detection scheme which can discover the presence of abrupt motions during online tracking. Extensive experiments on challenging image sequences demonstrate the effectiveness and the robustness of our algorithm in handling the abrupt motions.Comment: submitted to Elsevier Neurocomputin

Electron spin resonance of nitrogen-vacancy centers in optically trapped nanodiamonds

Using an optical tweezers apparatus, we demonstrate three-dimensional control of nanodiamonds in solution with simultaneous readout of ground-state electron-spin resonance (ESR) transitions in an ensemble of diamond nitrogen-vacancy (NV) color centers. Despite the motion and random orientation of NV centers suspended in the optical trap, we observe distinct peaks in the measured ESR spectra qualitatively similar to the same measurement in bulk. Accounting for the random dynamics, we model the ESR spectra observed in an externally applied magnetic field to enable d.c. magnetometry in solution. We estimate the d.c. magnetic field sensitivity based on variations in ESR line shapes to be ~50 microTesla/Hz^1/2. This technique may provide a pathway for spin-based magnetic, electric, and thermal sensing in fluidic environments and biophysical systems inaccessible to existing scanning probe techniques.Comment: 29 pages, 13 figures for manuscript and supporting informatio

Bayesian Approaches to Tracking, Sensor Fusion and Intent Prediction

This thesis presents work on the development of model-based Bayesian approaches to object tracking and intent prediction. Successful navigation/positioning applications rely fundamentally on the choice of appropriate dynamic model and the design of effective tracking algorithms capable of maximising the use of the structure of the dynamic system and the information from sensors. While the tracking problem with frequent and accurate position data has been well studied, we push back the frontiers of current technology where an object can undergo fast manoeuvres and position fixes are limited. On the other hand, intent prediction techniques which extract higher level information such as the intended destination of a moving object can be designed, given the ability to perform successful tracking. Such techniques can play important roles in various application areas, including traffic monitoring, intelligent human computer interaction systems and autonomous route planning. In the first part of this thesis Bayesian tracking methods are designed based on a standard fix-rate setting in which the dynamic system is formulated into a Markovian state space form. We show that the combination of an intrinsic coordinate dynamic model and sensors in the object's body frame leads to novel state space models according to which efficient proposal kernels can be designed and implemented by the sequential Monte Carlo (SMC) methods. Also, sequential Markov chain Monte Carlo schemes are considered for the first time to tackle the sequential batch inference problems due to the presence of infrequent position data. Performance evaluation on both synthetic and real-world data shows that the proposed algorithms are superior to simpler particle filters, implying that they can be favourable alternatives to tracking problems with inertial sensors. The modelling assumption that leads to Markovian state space models can be restrictive for real-world systems as it stipulates that the state sequence has to be synchronised with the observations. In the second major part of this thesis we relax this assumption and work with a more natural class of models, termed variable rate models. We generalise the existing variable rate intrinsic model to incorporate acceleration, speed, distance and position data and introduce new variable rate particle filtering methods tailored to the derived model to accommodate multi-sensor multi-rate tracking scenarios. The proposed algorithms can achieve substantial improvements in terms of tracking accuracy and robustness over a bootstrap variable rate particle filter. Moreover, full Bayesian inference schemes for the learning of both the hidden state and system parameters are presented, with numerical results illustrating their effectiveness. The last part of the thesis is about designing efficient intent prediction algorithms within a Bayesian framework. A pseudo-observation based approach to the incorporation of destination knowledge is introduced, making the mathematics of the dynamical model and the observation process consistent with the Markov state process. Based on the new interpretation, two algorithms are proposed to sequentially estimate the probability of all possible endpoints. Whilst the synthetic maritime surveillance data demonstrate that the proposed methods can achieve comparable prediction performance with reduced computational cost in comparison to the existing bridging distribution based methods, the results on an extensive freehand pointing database, which contains 95 three-dimensional pointing trajectories, show that the new algorithms can outperform other state-of-the-art techniques. Some sensitivity tests are also performed, confirming the good robustness of the introduced methods against model mismatches

Multi-agent Collision Avoidance Using Interval Analysis and Symbolic Modelling with its Application to the Novel Polycopter

Coordination is fundamental component of autonomy when a system is defined by multiple mobile agents. For unmanned aerial systems (UAS), challenges originate from their low-level systems, such as their flight dynamics, which are often complex. The thesis begins by examining these low-level dynamics in an analysis of several well known UAS using a novel symbolic component-based framework. It is shown how this approach is used effectively to define key model and performance properties necessary of UAS trajectory control. This is demonstrated initially under the context of linear quadratic regulation (LQR) and model predictive control (MPC) of a quadcopter. The symbolic framework is later extended in the proposal of a novel UAS platform, referred to as the ``Polycopter" for its morphing nature. This dual-tilt axis system has unique authority over is thrust vector, in addition to an ability to actively augment its stability and aerodynamic characteristics. This presents several opportunities in exploitative control design. With an approach to low-level UAS modelling and control proposed, the focus of the thesis shifts to investigate the challenges associated with local trajectory generation for the purpose of multi-agent collision avoidance. This begins with a novel survey of the state-of-the-art geometric approaches with respect to performance, scalability and tolerance to uncertainty. From this survey, the interval avoidance (IA) method is proposed, to incorporate trajectory uncertainty in the geometric derivation of escape trajectories. The method is shown to be more effective in ensuring safe separation in several of the presented conditions, however performance is shown to deteriorate in denser conflicts. Finally, it is shown how by re-framing the IA problem, three dimensional (3D) collision avoidance is achieved. The novel 3D IA method is shown to out perform the original method in three conflict cases by maintaining separation under the effects of uncertainty and in scenarios with multiple obstacles. The performance, scalability and uncertainty tolerance of each presented method is then examined in a set of scenarios resembling typical coordinated UAS operations in an exhaustive Monte-Carlo analysis

Molecular Dynamics Simulation

Condensed matter systems, ranging from simple fluids and solids to complex multicomponent materials and even biological matter, are governed by well understood laws of physics, within the formal theoretical framework of quantum theory and statistical mechanics. On the relevant scales of length and time, the appropriate ‘first-principles’ description needs only the Schroedinger equation together with Gibbs averaging over the relevant statistical ensemble. However, this program cannot be carried out straightforwardly—dealing with electron correlations is still a challenge for the methods of quantum chemistry. Similarly, standard statistical mechanics makes precise explicit statements only on the properties of systems for which the many-body problem can be effectively reduced to one of independent particles or quasi-particles. [...

Computational Methods for Bayesian Inference in Complex Systems

Bayesian methods are critical for the complete understanding of complex systems. In this approach, we capture all of our uncertainty about a system’s properties using a probability distribution and update this understanding as new information becomes available. By taking the Bayesian perspective, we are able to effectively incorporate our prior knowledge about a model and to rigorously assess the plausibility of candidate models based upon observed data from the system. We can then make probabilistic predictions that incorporate uncertainties, which allows for better decision making and design. However, while these Bayesian methods are critical, they are often computationally intensive, thus necessitating the development of new approaches and algorithms. In this work, we discuss two approaches to Markov Chain Monte Carlo (MCMC). For many statistical inference and system identification problems, the development of MCMC made the Bayesian approach possible. However, as the size and complexity of inference problems has dramatically increased, improved MCMC methods are required. First, we present Second-Order Langevin MCMC (SOL-MC), a stochastic dynamical system-based MCMC algorithm that uses the damped second-order Langevin stochastic differential equation (SDE) to sample a desired posterior distribution. Since this method is based on an underlying dynamical system, we can utilize existing work in the theory for dynamical systems to develop, implement, and optimize the sampler's performance. Second, we present advances and theoretical results for Sequential Tempered MCMC (ST-MCMC) algorithms. Sequential Tempered MCMC is a family of parallelizable algorithms, based upon Transitional MCMC and Sequential Monte Carlo, that gradually transform a population of samples from the prior to the posterior through a series of intermediate distributions. Since the method is population-based, it can easily be parallelized. In this work, we derive theoretical results to help tune parameters within the algorithm. We also introduce a new sampling algorithm for ST-MCMC called the Rank-One Modified Metropolis Algorithm (ROMMA). This algorithm improves sampling efficiency for inference problems where the prior distribution constrains the posterior. In particular, this is shown to be relevant for problems in geophysics. We also discuss the application of Bayesian methods to state estimation, disturbance detection, and system identification problems in complex systems. We introduce a Bayesian perspective on learning models and properties of physical systems based upon a layered architecture that can learn quickly and flexibly. We then apply this architecture to detecting and characterizing changes in physical systems with applications to power systems and biology. In power systems, we develop a new formulation of the Extended Kalman Filter for estimating dynamic states described by differential algebraic equations. This filter is then used as the basis for sub-second fault detection and classification. In synthetic biology, we use a Bayesian approach to detect and identify unknown chemical inputs in a biosensor system implemented in a cell population. This approach uses the tools of Bayesian model selection.</p

Simulation methods for reliability-based design optimization and model updating of civil engineering structures and systems

This thesis presents a collection of original contributions pertaining to the subjects of reliability-based design optimization (RBDO) and model updating of civil engineering structures and systems. In this regard, probability theory concepts and tools are instrumental in the formulation of the herein reported developments. Firstly, two approaches are devised for the RBDO of structural dynamical systems under stochastic excitation. Namely, a stochastic search technique is proposed for constrained and unconstrained RBDO problems involving continuous, discrete and mixed discrete-continuous design spaces, whereas an efficient sensitivity assessment framework for linear stochastic structures is implemented to identify optimal designs and evaluate their sensitivities. Moreover, two classes of model updating problems are considered. In this context, the Bayesian interpretation of probability theory plays a key role in the proposed solution schemes. Specifically, contaminant source detection in water distribution networks is addressed by resorting to a sampling-based Bayesian model class selection framework. Furthermore, an effective strategy for Bayesian model updating with structural reliability methods is presented to treat identification problems involving structural dynamical systems, measured response data, and high-dimensional parameter spaces. The approaches proposed in this thesis integrate stochastic simulation techniques as an essential part of their formulation, which allows obtaining non-trivial information about the systems of interest as a byproduct of the solution processes. Overall, the findings presented in this thesis suggest that the reported methods can be potentially adopted as supportive tools for a number of practical decision-making processes in civil engineering.Diese Arbeit stellt eine Sammlung von Beiträgen vor, die sich mit der Reliability-based-Design-Optimization (RBDO) und dem Model updating von Strukturen und Systemen im Bauwesen befassen. In diesem Zusammenhang sind wahrscheinlichkeitstheoretische Konzepte für die Formulierung der hier vorgestellten Entwicklungen von entscheidender Bedeutung. Zunächst werden zwei Ansätze für eine RBDO von strukturdynamischen Systemen unter stochastischer Anregung entwickelt. Es wird eine stochastische Suchtechnik für beschränkte und unbeschränkte RBDO-Probleme vorgeschlagen. Diese beziehen kontinuierliche, diskrete und gemischt diskret-kontinuierliche Designräume ein. Gleichzeitig wird ein effizientes Framework zur Bewertung der Sensitivität lineare stochastische Strukturen implementiert, um optimale Designs zu identifizieren und ihre Sensitivitäten zu bewerten. Darüber hinaus werden zwei Klassen von Problem aus dem Model updating betrachtet. Der Fokus wird hierbei auf die Erkennung von Kontaminationsquellen in Wasserverteilungsnetzen mithilfe eines auf Stichproben basierenden Bayesian-Model-Class-selection-Framework gelegt. Ferner wird eine effektive Strategie zur Bearbeitung von Problemen des Bayesian-Model-updating, die strukturdynamischen Systeme, gemessene Systemantwortdaten und hochdimensionale Parameterräume umfassen, vorgestellt. Die beschriebenen Ansätze verwenden stochastische Simulationstechniken als wesentlicher Bestandteil ihrer Formulierung, wodurch nicht-triviale Informationen über betrachtete Systeme als Nebenprodukt der Lösungsprozesse gewonnen werden können. Insgesamt deuten die vorgestellten Ergebnisse dieser Arbeit darauf hin, dass die beschriebenen Methoden potenziell als unterstützende Elemente in praktischen Entscheidungsproblemen im Zusammenhang mit Strukturen und Systemen im Bauwesen eingesetzt werden können

ESTIMATION-BASED SOLUTIONS TO INCOMPLETE INFORMATION PURSUIT-EVASION GAMES

Differential games are a useful tool both for modeling conflict between autonomous systems and for synthesizing robust control solutions. The traditional study of games has assumed decision agents possess complete information about one another’s strategies and numerical weights. This dissertation relaxes this assumption. Instead, uncertainty in the opponent’s strategy is treated as a symptom of the inevitable gap between modeling assumptions and applications. By combining nonlinear estimation approaches with problem domain knowledge, procedures are developed for acting under uncertainty using established methods that are suitable for applications on embedded systems. The dissertation begins by using nonlinear estimation to account for parametric uncertainty in an opponent’s strategy. A solution is proposed for engagements in which both players use this approach simultaneously. This method is demonstrated on a numerical example of an orbital pursuit-evasion game, and the findings motivate additional developments. First, the solutions of the governing Riccati differential equations are approximated, using automatic differentiation to obtain high-degree Taylor series approximations. Second, constrained estimation is introduced to prevent estimator failures in near-singular engagements. Numerical conditions for nonsingularity are approximated using Chebyshev polynomial basis functions, and applied as constraints to a state estimate. Third and finally, multiple model estimation is suggested as a practical solution for time-critical engagements in which the form of the opponent’s strategy is uncertain. Deceptive opponent strategies are identified as a candidate approach to use against an adaptive player, and a procedure for designing such strategies is proposed. The new developments are demonstrated in a missile interception pursuit-evasion game in which the evader selects from a set of candidate strategies with unknown weights