State space modelling of extreme values with particle filters

State space models are a flexible class of Bayesian model that can be used to smoothly capture non-stationarity. Observations are assumed independent given a latent state process so that their distribution can change gradually over time. Sequential Monte Carlo methods known as particle filters provide an approach to inference for such models whereby observations are added to the fit sequentially. Though originally developed for on-line inference, particle filters, along with related particle smoothers, often provide the best approach for off-line inference. This thesis develops new results for particle filtering and in particular develops a new particle smoother that has a computational complexity that is linear in the number of Monte Carlo samples. This compares favourably with the quadratic complexity of most of its competitors resulting in greater accuracy within a given time frame. The statistical analysis of extremes is important in many fields where the largest or smallest values have the biggest effect. Accurate assessments of the likelihood of extreme events are crucial to judging how severe they could be. While the extreme values of a stationary time series are well understood, datasets of extremes often contain varying degrees of non-stationarity. How best to extend standard extreme value models to account for non-stationary series is a topic of ongoing research. The thesis develops inference methods for extreme values of univariate and multivariate non-stationary processes using state space models fitted using particle methods. Though this approach has been considered previously in the univariate case, we identify problems with the existing method and provide solutions and extensions to it. The application of the methodology is illustrated through the analysis of a series of world class athletics running times, extreme temperatures at a site in the Antarctic, and sea-level extremes on the east coast of England

Sequential Dynamic Leadership Inference Using Bayesian Monte Carlo Methods

Hierarchy and leadership interactions commonly occur in animal groups, crowds of people and in vehicle motions. Such interactions are often affected by one or more individuals who possess key domain information (e.g. final destination, environmental constraints and best routes) or pertinent traits (e.g. better navigation, sensing and decision making capabilities) compared with the rest of the group. This paper presents a framework for the automatic identification of group structure and leadership from noisy sensory observations of tracked groups. Accordingly, a new leader-follower model is developed which assumes the dynamics of the group to be a multivariate Ornstein–Uhlenbeck process with the designated leader(s) drifting to the destination and followers reverting to the leaders’ state. Sequential Monte Carlo (SMC) approaches, and specifically the sequential Markov chain Monte Carlo (SMCMC) approach, are adopted to infer, probabilistically, the evolving leadership structure. A Rao-Blackwellisation scheme is employed such that the kinematic state of the objects in the group is inferred in closed form by Kalman filtering. Experiments show that the proposed techniques can successfully determine the leadership structures in challenging scenarios with a corresponding enhancement in tracking accuracy through direct consideration of the leadership interactions of the group

Robotic Crop Interaction in Agriculture for Soft Fruit Harvesting

Autonomous tree crop harvesting has been a seemingly attainable, but elusive, robotics goal for the past several decades. Limiting grower reliance on uncertain seasonal labour is an economic driver of this, but the ability of robotic systems to treat each plant individually also has environmental benefits, such as reduced emissions and fertiliser use. Over the same time period, effective grasping and manipulation (G&M) solutions to warehouse product handling, and more general robotic interaction, have been demonstrated. Despite research progress in general robotic interaction and harvesting of some specific crop types, a commercially successful robotic harvester has yet to be demonstrated. Most crop varieties, including soft-skinned fruit, have not yet been addressed. Soft fruit, such as plums, present problems for many of the techniques employed for their more robust relatives and require special focus when developing autonomous harvesters. Adapting existing robotics tools and techniques to new fruit types, including soft skinned varieties, is not well explored. This thesis aims to bridge that gap by examining the challenges of autonomous crop interaction for the harvesting of soft fruit. Aspects which are known to be challenging include mixed obstacle planning with both hard and soft obstacles present, poor outdoor sensing conditions, and the lack of proven picking motion strategies. Positioning an actuator for harvesting requires solving these problems and others specific to soft skinned fruit. Doing so effectively means addressing these in the sensing, planning and actuation areas of a robotic system. Such areas are also highly interdependent for grasping and manipulation tasks, so solutions need to be developed at the system level. In this thesis, soft robotics actuators, with simplifying assumptions about hard obstacle planes, are used to solve mixed obstacle planning. Persistent target tracking and filtering is used to overcome challenging object detection conditions, while multiple stages of object detection are applied to refine these initial position estimates. Several picking motions are developed and tested for plums, with varying degrees of effectiveness. These various techniques are integrated into a prototype system which is validated in lab testing and extensive field trials on a commercial plum crop. Key contributions of this thesis include I. The examination of grasping & manipulation tools, algorithms, techniques and challenges for harvesting soft skinned fruit II. Design, development and field-trial evaluation of a harvester prototype to validate these concepts in practice, with specific design studies of the gripper type, object detector architecture and picking motion for this III. Investigation of specific G&M module improvements including: o Application of the autocovariance least squares (ALS) method to noise covariance matrix estimation for visual servoing tasks, where both simulated and real experiments demonstrated a 30% improvement in state estimation error using this technique. o Theory and experimentation showing that a single range measurement is sufficient for disambiguating scene scale in monocular depth estimation for some datasets. o Preliminary investigations of stochastic object completion and sampling for grasping, active perception for visual servoing based harvesting, and multi-stage fruit localisation from RGB-Depth data. Several field trials were carried out with the plum harvesting prototype. Testing on an unmodified commercial plum crop, in all weather conditions, showed promising results with a harvest success rate of 42%. While a significant gap between prototype performance and commercial viability remains, the use of soft robotics with carefully chosen sensing and planning approaches allows for robust grasping & manipulation under challenging conditions, with both hard and soft obstacles

Robust Multi-target Tracking with Bootstrapped-GLMB Filter

This dissertation presents novel multi-target tracking algorithms that obviate the need for prior knowledge of system parameters such as clutter rate, detection probabilities, and birth models. Information on these parameters is unknown but important to tracking performance. The proposed algorithms exploit the advantages of existing RFS trackers and filters by bootstrapping them. This configuration inherits the efficiency of tracking target trajectories from the RFS trackers and low complexity in parameter estimation from the RFS filters

Sequential Modelling and Inference of High-frequency Limit Order Book with State-space Models and Monte Carlo Algorithms

The high-frequency limit order book (LOB) market has recently attracted increasing research attention from both the industry and the academia as a result of expanding algorithmic trading. However, the massive data throughput and the inherent complexity of high-frequency market dynamics also present challenges to some classic statistical modelling approaches. By adopting powerful state-space models from the field of signal processing as well as a number of Bayesian inference algorithms such as particle filtering, Markov chain Monte Carlo and variational inference algorithms, this thesis presents my extensive research into the high-frequency limit order book covering a wide scope of topics. Chapter 2 presents a novel construction of the non-homogeneous Poisson process to allow online intensity inference of limit order transactions arriving at a central exchange as point data. Chapter 3 extends a baseline jump diffusion model for market fair-price process to include three additional model features taken from real-world market intuitions. In Chapter 4, another price model is developed to account for both long-term and short-term diffusion behaviours of the price process. This is achieved by incorporating multiple jump-diffusion processes each exhibiting a unique characteristic. Chapter 5 observes the multi-regime nature of price diffusion processes as well as the non-Markovian switching behaviour between regimes. As such, a novel model is proposed which combines the continuous-time state-space model, the hidden semi-Markov switching model and the non-parametric Dirichlet process model. Additionally, building upon the general structure of the particle Markov chain Monte Carlo algorithm, I further propose an algorithm which achieves sequential state inference, regime identification and regime parameters learning requiring minimal prior assumptions. Chapter 6 focuses on the development of efficient parameter-learning algorithms for state-space models and presents three algorithms each demonstrating promising results in comparison to some well-established methods. The models and algorithms proposed in this thesis not only are practical tools for analysing high-frequency LOB markets, but can also be applied in various areas and disciplines beyond finance

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

Visual Navigation in Unknown Environments

Navigation in mobile robotics involves two tasks, keeping track of the robot's position and moving according to a control strategy. In addition, when no prior knowledge of the environment is available, the problem is even more difficult, as the robot has to build a map of its surroundings as it moves. These three problems ought to be solved in conjunction since they depend on each other. This thesis is about simultaneously controlling an autonomous vehicle, estimating its location and building the map of the environment. The main objective is to analyse the problem from a control theoretical perspective based on the EKF-SLAM implementation. The contribution of this thesis is the analysis of system's properties such as observability, controllability and stability, which allow us to propose an appropriate navigation scheme that produces well-behaved estimators, controllers, and consequently, the system as a whole. We present a steady state analysis of the SLAM problem, identifying the conditions that lead to partial observability. It is shown that the effects of partial observability appear even in the ideal linear Gaussian case. This indicates that linearisation alone is not the only cause of SLAM inconsistency, and that observability must be achieved as a prerequisite to tackling the effects of linearisation. Additionally, full observability is also shown to be necessary during diagonalisation of the covariance matrix, an approach often used to reduce the computational complexity of the SLAM algorithm, and which leads to full controllability as we show in this work.Focusing specifically on the case of a system with a single monocular camera, we present an observability analysis using the nullspace basis of the stripped observability matrix. The aim is to get a better understanding of the well known intuitive behaviour of this type of systems, such as the need for triangulation to features from different positions in order to get accurate relative pose estimates between vehicle and camera. Through characterisation the unobservable directions in monocular SLAM, we are able to identify the vehicle motions required to maximise the number of observable states in the system. When closing the control loop of the SLAM system, both the feedback controller and the estimator are shown to be asymptotically stable. Furthermore, we show that the tracking error does not influence the estimation performance of a fully observable system and viceversa, that control is not affected by the estimation. Because of this, a higher level motion strategy is required in order to enhance estimation, specially needed while performing SLAM with a single camera. Considering a real-time application, we propose a control strategy to optimise both the localisation of the vehicle and the feature map by computing the most appropriate control actions or movements. The actions are chosen in order to maximise an information theoretic metric. Simulations and real-time experiments are performed to demonstrate the feasibility of the proposed control strategy

Degradation Vector Fields with Uncertainty Considerations

The focus of this work is on capturing uncertainty in remaining useful life (RUL) estimates for machinery and constructing some latent dynamics that aid in interpreting those results. This is primarily achieved through sequential deep generative models known as Dynamical Variational Autoencoders (DVAEs). These allow for the construction of latent dynamics related to the RUL estimates while being a probabilistic model that can quantify the uncertainties of the estimates

Robust vision based slope estimation and rocks detection for autonomous space landers

As future robotic surface exploration missions to other planets, moons and asteroids become more ambitious in their science goals, there is a rapidly growing need to significantly enhance the capabilities of entry, descent and landing technology such that landings can be carried out with pin-point accuracy at previously inaccessible sites of high scientific value. As a consequence of the extreme uncertainty in touch-down locations of current missions and the absence of any effective hazard detection and avoidance capabilities, mission designers must exercise extreme caution when selecting candidate landing sites. The entire landing uncertainty footprint must be placed completely within a region of relatively flat and hazard free terrain in order to minimise the risk of mission ending damage to the spacecraft at touchdown. Consequently, vast numbers of scientifically rich landing sites must be rejected in favour of safer alternatives that may not offer the same level of scientific opportunity. The majority of truly scientifically interesting locations on planetary surfaces are rarely found in such hazard free and easily accessible locations, and so goals have been set for a number of advanced capabilities of future entry, descent and landing technology. Key amongst these is the ability to reliably detect and safely avoid all mission critical surface hazards in the area surrounding a pre-selected landing location. This thesis investigates techniques for the use of a single camera system as the primary sensor in the preliminary development of a hazard detection system that is capable of supporting pin-point landing operations for next generation robotic planetary landing craft. The requirements for such a system have been stated as the ability to detect slopes greater than 5 degrees and surface objects greater than 30cm in diameter. The primary contribution in this thesis, aimed at achieving these goals, is the development of a feature-based,self-initialising, fully adaptive structure from motion (SFM) algorithm based on a robust square-root unscented Kalman filtering framework and the fusion of the resulting SFM scene structure estimates with a sophisticated shape from shading (SFS) algorithm that has the potential to produce very dense and highly accurate digital elevation models (DEMs) that possess sufficient resolution to achieve the sensing accuracy required by next generation landers. Such a system is capable of adapting to potential changes in the external noise environment that may result from intermittent and varying rocket motor thrust and/or sudden turbulence during descent, which may translate to variations in the vibrations experienced by the platform and introduce varying levels of motion blur that will affect the accuracy of image feature tracking algorithms. Accurate scene structure estimates have been obtained using this system from both real and synthetic descent imagery, allowing for the production of accurate DEMs. While some further work would be required in order to produce DEMs that possess the resolution and accuracy needed to determine slopes and the presence of small objects such as rocks at the levels of accuracy required, this thesis presents a very strong foundation upon which to build and goes a long way towards developing a highly robust and accurate solution