Given a sequence of possibly sparse and noisy GPS traces and a map of the road network, map matching algorithms can infer the most accurate trajectory on the road network. However, if the road network is wrong (for example due to missing or incorrectly mapped roads, missing parking lots, misdirected turn restrictions or misdirected one-way streets) standard map matching algorithms fail to reconstruct the correct trajectory. In this paper, an algorithm to tracking vehicles able to move both on and off the known road network is formulated. It efficiently unifies existing hidden Markov model (HMM) approaches for map matching and standard free-space tracking methods (e.g. Kalman smoothing) in a principled way. The algorithm is a form of interacting multiple model (IMM) filter subject to an additional assumption on the type of model interaction permitted, termed here as semi-interacting multiple model (sIMM) filter. A forward filter (suitable for real-time tracking) and backward MAP sampling step (suitable for MAP trajectory inference and map matching) are described. The framework set out here is agnostic to the specific tracking models used, and makes clear how to replace these components with others of a similar type. In addition to avoiding generating misleading map matching trajectories, this algorithm can be applied to learn map features by detecting unmapped or incorrectly mapped roads and parking lots, incorrectly mapped turn restrictions and road directions.

Stop signs and traffic signals are ubiquitous in the modern urban landscape to control traffic flows and improve road safety. Including them in digital maps of the road network is essential for geospatial services, e.g., assisted navigation, logistics, ride-sharing and autonomous driving. This paper proposes to infer them by exclusively relying on large-scale anonymized vehicle telemetry data, which is available for companies offering such services. Vehicle patterns from telemetry data at each intersection are extracted, and we employ a convolutional neural network for the task of labeling these driver patterns. We train our neural network in San Francisco, and choose to test the model in Palo Alto, whose urban layout is significantly different from the urban layout of San Francisco, in order to prove the generality of the algorithm. At a confidence threshold of 90%, our classifier achieves 96.6% accuracy and 66.0% coverage in detecting three classes of traffic control elements: stop signs, traffic signals, and neither. Our work paves a way for inferring traffic control elements for automated map updates.

Accurate route prediction and distance calculation is an integral part of processing GPS data, particularly in the ride-sharing industry. One common approach has been to map match GPS data to estimate driving traces under noise and sparsity conditions. However, map-matched traces have proven to be at most as good as the underlying map data. Incorrect or missing map data can lead to large, improbable deviations, even when the geometry of the underlying raw GPS data is within tolerance of the actual route. Ideally, we want to take advantage of both the map-matched route and the GPS data to minimize the distance error. Therefore, we propose a method to classify the noise level (or trustworthiness) of small sub-sections of the input data on any given route to conditionally select between using the raw GPS data and the map-matched route as the best estimate of the driving path. For the classifier, each section is treated as an image matrix and is fed through a convolutional neural network trained only on a large amount of synthetic data. The result is a classifier that achieves human-level performance and can be used in a real-time system to reduce distance errors between the predicted and ground-truth traces of actual ride data.

The study of functional networks in the brain is essential in order to gain a better insight into its diverse set of operations and to characterise the associated normal and abnormal behaviors. Present methods of analysing fMRI data to obtain functional connectivity are largely limited to approaches such as correlation, regression, and independent component analysis, which give simple point estimates. By contrast, we propose a stochastic linear model in a Bayesian setting and employ Markov chain Monte Carlo methods to approximate posterior distributions of full connectivity and covariance matrices. Through the use of a Bayesian probabilistic framework, distributional estimates of the linkage strengths are obtained as opposed to point estimates, and the uncertainty of the existence of such links is accounted for. We decompose the connectivity matrix as the Hadamard product of binary indicators and real-valued variables, and formulate an efficient joint-sampling scheme to infer them. The well-characterised somato-motor network is examined in a self-paced, right-handed finger opposition task-based experiment, while nodes from the visual network are used for contrast during the same experiment. Unlike for the visual network, significant changes in connectivity are found in the motor network during the task. Our work provides a distributional metric for functional connectivity along with causality information, and contributes to the collection of network level descriptors of brain functions.

This paper presents a method for inferring interaction strength and structure amongst targets in multiple target tracking (MTT) applications. By making simple assumptions, it is shown how an efficient and well-mixing MCMC inference method can be developed to learn about the relationships between tracked targets, including leader-follower relationships, group relationships and the influence of targets on others. This network structure of influence between targets is inferred in a sparse way, setting many interaction terms to zero and allowing for more efficient inference and clearer structural conclusions to be drawn. The effectiveness of the method is demonstrated on both synthetic and real animal flocking data.

Adding changepoints to a linear Gaussian state space model, such that it can switch between multiple regimes of action, provides a powerful extension which allows more complex system behaviour to be described. However, it also means that more sophisticated algorithms are needed for parameter estimation. This paper addresses the task of Bayesian learning of changepoint model parameters using MCMC. Standard Gibbs-based algorithms can suffer from poor mixing, because of the correlation between the changepoints and parameters. To avoid this, algorithms must propose changes to both simultaneously, but naive implementations of this variety generally do not perform well. The idea of using an annealed sequence of distributions to bridge between two changepoint sequences allows us to improve the mixing. We show how to implement such a scheme for a general class of linear changepoint transition models and demonstrate with a simple simulation.

Examining the dynamic aspects of functional networks in the brain is imperative in order to obtain a thorough description and to gain a better insight into its several features. Present methods of analysing brain data in task-conditions mainly include concatenation followed by temporal correlation. We employ Markov Chain Monte Carlo methods, namely Metropolis within Gibbs sampling, on a stochastic model to infer dynamic functional connectivity in such conditions. By using a Bayesian probabilistic framework, distributional estimates of the linkage strengths are obtained as opposed to point estimates, and the uncertainty of the existence of such links is accounted for. The methodology is applied to fMRI data from a finger opposition paradigm with task and fixation conditions, investigating the dynamics of the well characterised somato-motor network while using the visual network as a control case.

Linear Gaussian state-space models are ubiquitous in signal processing, and an important procedure is that of estimating system parameters from observed data. Rather than making a single point estimate, it is often desirable to conduct Bayesian learning, in which the entire posterior distribution of the unknown parameters is sought. This can be achieved using Markov chain Monte Carlo. On some occasions it is possible to deduce the form of the unknown system matrices in terms of a small number of scalar parameters, by considering the underlying physical processes involved. Here we study the case where this is not possible, and the entire matrices must be treated as unknowns. An efficient Gibbs sampling algorithm exists for the basic formulation of linear model. We extend this to the more challenging situation where the transition model is possibly degenerate, i.e., the transition covariance matrix is singular. Appropriate Markov kernels are devised and demonstrated with simulations.

This paper presents an online (sequential) method for sparse system estimation in dynamic systems with linear Gaussian state evolution and nonlinear and/or non-Gaussian observations. Estimation is based on an Automatic Relevance Determination (ARD) prior for the elements of the system matrix A, with an online Expectation-Maximization algorithm used within a particle filter for sequential estimation. The method is demonstrated to work effectively on an example system.

This paper examines the use of blocking strategies for Particle Gibbs sampling schemes for high dimensional latent state space models with interacting components. Such strategies are particularly advantageous for high-dimensional systems because they allow multiple lower-dimensional blocks to be sampled, avoiding the curse of dimensionality within the particle filter. This paper presents algorithms for blocked Particle Gibbs sampling, as well as examining several special cases. Analogies to the bootstrap particle filter are given, along with an optimal proposal in the case of Gaussian systems with linear Gaussian observations. The paper demonstrates blocking schemes on realistic example applications: tracking multiple interacting targets and data assimilation for a nonlinear diffusion system. The effect of block size and number of particles used on computational efficiency is also examined through experiments, which demonstrate that the optimal blocking strategy is both problem and algorithm dependent and results from a compromise between the improved efficiency of blocking in Gibbs schemes and the "curse of dimensionality" in the particle filter.

In this paper we present a Bayesian method for parameter estimation in linear Jump-Langevin systems, i.e. systems driven by a linear, mean-reverting jump-diffusion trend process. Such models have been applied successfully to trend following in finance, in order to develop momentum-based trading strategies. Parameter estimation is based around a reversible-jump MCMC method for jump-time inference. Parameter estimation is demonstrated on both synthetic and financial time series, and estimated parameters are compared with ad hoc parameter estimates used in earlier work.

Recent empirical research has discovered that linkages among fMRI signals of the brain in resting-state have meaningful temporal variations. Most current studies of brain networks assume that these linkages are constant. We propose a model and an accompanying algorithm to infer and track changes in these interaction strengths, thus providing a more comprehensive way to study brain dynamics. The stochastic model employed is akin to one used for neuronal states (DCM) and a Rao-Blackwellized filtering algorithm is set up for tracking purposes. Our results show that time-varying interactions among brain regions can be successfully found which have the potential of providing great clinical value.

We propose a novel probabilistic inference approach that permits predicting, well in advance, the intended destination of a pointing gesture aimed at selecting an icon on an in-vehicle interactive display. It models the partial 3D pointing track as a Markov bridge terminating at a nominal destination. The solution introduced leads to a low-complexity Kalman-filter-type implementation and is applicable in other areas in which early detection of the destination of a tracked object is beneficial. Data collected in an instrumented vehicle illustrate that the proposed technique can infer the intent notably early in the pointing gesture. This can drastically reduce the pointing task time and visual-cognitive-manual attention required.

This paper presents an O(n 4 ) time method for filtering and sampling of a time-varying n × n system matrix A t in a restricted class of time-varying linear systems of the form X t = A t X t-1 + C t + ε t , via a matrix-variate normal formulation. This allows larger systems within this class to be inferred via Gibbs sampling in reasonable time than is possible with methods that rely on vectorization of the system matrix, followed by standard Kalman filtering, which run in O(n 6 ) time. It is shown how to apply the method to vector autoregression problems with time-varying system matrices (TVP-VAR problems). Noisy observations of the underlying system state are also accommodated in a straightforward way.

Pointing tasks, for example to select a target on a graphical user interface, form a significant part of human-computer interactions. This has triggered a notable interest in intent prediction methods to reduce the pointing duration whilst using a mouse in a 2D set-up. In this paper, we introduce a Bayesian intentionality prediction approach for pointing in 3D environments. It infers the intended item on a touchscreen interface from the available partial user's pointing finger trajectory by utilising signal models that incorporate the destination. The pointing finger is continuously tracked using a Leap Motion controller. The objective is to improve the interactive display system usability in vehicle environments by enhancing the selection accuracy, expediting the system response and possibly providing feedback to the user as a form of assistive selection routine. The substantial gains furnished by applying the proposed predictors are demonstrated using data collected in a vehicle.

In many tracking applications map information is available, giving useful prior information about the movement of targets. In this paper we show how map information can be used to assist in tracking of an unknown and time varying number of targets, without constraining targets to always travel along roads. A continuous time on-/off-road switching motion model is developed, and a fully Bayesian sequential MCMC inference scheme, based on the MCMC-Particles algorithm, is given. This is demonstrated by tracking a variable number of realistic ground targets, fusing simulated data from multiple airborne camera sensors on two sensor platforms. MCMC-Particles is found to out-perform a Resample-Move particle flter for this problem.

This chapter shows how sparse solutions can be obtained for a range of problems in a Bayesian setting by using prior models on sparsity structure. As an example, a model to remove impulse and background noise from audio signals via their representation in time-frequency space using Gabor wavelets is presented. A number of prior models for the sparse structure of the signal in this space are introduced, including simple Bernoulli priors on each coefficient, Markov chains linking neighbouring coefficients in time or frequency, and Markov random fields, imposing two dimensional coherence on the coefficients. The effect of each of these priors on the reconstruction of a corrupted audio signal is shown. Impulse removal is also covered, with similar sparsity priors being applied to the location of impulse noise in the audio signal. Inference is performed by sampling from the posterior distribution of the model variables using a Gibbs sampler.

Making a selection on an in-vehicle touchscreen entails undertaking a pointing gesture that can be subjected to a high level of perturbation due to road and/or driving conditions. This can lead to erroneous user input and requires further attention that would otherwise be available for driving. In this paper, we propose a low-complexity sequential Monte Carlo filtering method that removes the perturbations present in a highly non-linear pointing hand/finger trajectory. This latter is tracked using a 3D vision sensory device. The preprocessing introduced allows the intended destination on the interactive display to be determined, which can substantially reduce the duration of the pointing task and associated attention. The benefits of the proposed approach are illustrated using data from in-vehicle tests.

This article aims to explain the Nested Benders algorithm for the solution of large-scale stochastic programming problems in a way that is intelligible to someone coming to it for the first time. In doing so it gives an explanation of Benders decomposition and of its application to two-stage stochastic programming problems (also known in this context as the L-shaped method), then extends this to multi-stage problems as the Nested Benders algorithm. The article is aimed at readers with some knowledge of linear and possibly stochastic programming but aims to develop most concepts from simple principles in an understandable way. The focus is on intuitive understanding rather than rigorous proofs.

This paper introduces a new method of simultaneous object tracking (localization) and environment mapping for objects moving in a potential feld environment. Only weak non-parametric assumptions are made about the shape of the potential function using a Gaussian process prior. A second-and-a-half order numerical scheme for object motion in a potential feld is formulated and it is shown how to use this for potential inference. The method improves tracking performance in structured environments, as is illustrated by its application to urban car tracking. Hidden environmental structure such as the location of obstructions can also be revealed. Prior knowledge (e.g. from maps) can easily be incorporated and can then be updated using feedback from tracking. Information from multiple targets can also be handled in a straightforward manner.