Non-Gaussian Process Regression

Standard GPs offer a flexible modelling tool for well-behaved processes. However, deviations from Gaussianity are expected to appear in real world datasets, with structural outliers and shocks routinely observed. In these cases GPs can fail to model uncertainty adequately and may over-smooth inferences. Here we extend the GP framework into a new class of time-changed GPs that allow for straightforward modelling of heavy-tailed non-Gaussian behaviours, while retaining a tractable conditional GP structure through an infinite mixture of non-homogeneous GPs representation. The conditional GP structure is obtained by conditioning the observations on a latent transformed input space and the random evolution of the latent transformation is modelled using a L\'{e}vy process which allows Bayesian inference in both the posterior predictive density and the latent transformation function. We present Markov chain Monte Carlo inference procedures for this model and demonstrate the potential benefits compared to a standard GP

Generalised Hyperbolic State-space Models for Inference in Dynamic Systems

In this work we study linear vector stochastic differential equation (SDE) models driven by the generalised hyperbolic (GH) L\'evy process for inference in continuous-time non-Gaussian filtering problems. The GH family of stochastic processes offers a flexible framework for modelling of non-Gaussian, heavy-tailed characteristics and includes the normal inverse-Gaussian, variance-gamma and Student-t processes as special cases. We present continuous-time simulation methods for the solution of vector SDE models driven by GH processes and novel inference methodologies using a variant of sequential Markov chain Monte Carlo (MCMC). As an example a particular formulation of Langevin dynamics is studied within this framework. The model is applied to both a synthetically generated data set and a real-world financial series to demonstrate its capabilities

Consensus-based Distributed Variational Multi-object Tracker in Multi-Sensor Network

The growing need for accurate and reliable tracking systems has driven significant progress in sensor fusion and object tracking techniques. In this paper, we design two variational Bayesian trackers that effectively track multiple targets in cluttered environments within a sensor network. We first present a centralised sensor fusion scheme, which involves transmitting sensor data to a fusion center. Then, we develop a distributed version leveraging the average consensus algorithm, which is theoretically equivalent to the centralised sensor fusion tracker and requires only local message passing with neighbouring sensors. In addition, we empirically verify that our proposed distributed variational tracker performs on par with the centralised version with equal tracking accuracy. Simulation results show that our distributed multi-target tracker outperforms the suboptimal distributed sensor fusion strategy that fuses each sensor's posterior based on arithmetic sensor fusion and an average consensus strategy

Variational Tracking and Redetection for Closely-spaced Objects in Heavy Clutter

The non-homogeneous Poisson process (NHPP) is a widely used measurement model that allows for an object to generate multiple measurements over time. However, it can be difficult to efficiently and reliably track multiple objects under this NHPP model in scenarios with a high density of closely-spaced objects and heavy clutter. Therefore, based on the general coordinate ascent variational filtering framework, this paper presents a variational Bayes association-based NHPP tracker (VB-AbNHPP) that can efficiently perform tracking, data association, and learning of target and clutter rates with a parallelisable implementation. In addition, a variational localisation strategy is proposed, which enables rapid rediscovery of missed targets from a large surveillance area under extremely heavy clutter. This strategy is integrated into the VB-AbNHPP tracker, resulting in a robust methodology that can automatically detect and recover from track loss. This tracker demonstrates improved tracking performance compared with existing trackers in challenging scenarios, in terms of both accuracy and efficiency

Jump Particle Filtering Framework for Joint Target Tracking and Intent Recognition

This paper presents a Bayesian framework for inferring the posterior of the extended state of a target, incorporating its underlying goal or intent, such as any intermediate waypoints and/or final destination. The methodology is thus for joint tracking and intent recognition. Several novel latent intent models are proposed here within a virtual leader formulation. They capture the influence of the target's hidden goal on its instantaneous behaviour. In this context, various motion models, including for highly maneuvering objects, are also considered. The a priori unknown target intent (e.g. destination) can dynamically change over time and take any value within the state space (e.g. a location or spatial region). A sequential Monte Carlo (particle filtering) approach is introduced for the simultaneous estimation of the target's (kinematic) state and its intent. Rao-Blackwellisation is employed to enhance the statistical performance of the inference routine. Simulated data and real radar measurements are used to demonstrate the efficacy of the proposed techniques.Comment: Submitted to IEEE Transactions on Aerospace and Electronic Systems (T-AES

Joint Acoustic Source Location and Orientation Estimation Using Sequential Monte Carlo

Standard acoustic source localization algorithms attempt to estimate the instantaneous location of a source based only on current data from a microphone sensor array. This is done regardless of previous location estimates. However more recent Sequential Monte Carlo based approaches have instead posed the problem using an evolving state-space framework. In this paper we take this approach further by exploiting the directionality of human speech sources. This allows us to estimate the orientation of the source within the room. Finally combining previous source localization methods with this work we outline how both parameters- location and orientation- may be estimated jointly. Examples are given of performance in a typically reverberant real office environment for both a stationary and a moving source. 1