Particles, points and positions: recent advances in modelling and  processing of agile objects


In this talk, the speaker will describe state-space models based on point process theory and Lévy processes, allowing very flexible modelling of continuous time non-Gaussian behaviours. In contrast with most of the classical models which use Brownian motion assumptions, the proposed approach is based on pure jump-driven Lévy processes driving stochastic diferential equations, leading to powerful models based on, for example, α-stable or Generalised hyperbolic processes (including Student-t, variance-gamma and normal-inverse Gaussian). We are able to construct a full state-space model (The 'Lévy state-space model') driven by such continuous time processes, observed at distrete time, as well as deriving central limit style theorems that prove Gaussianity of certain series residual terms, and inference for these models can be carried out using highly efficient Rao-Blackwellised versions of particle filters and sequential Markov chain Monte Carlo. The models  can find application in non-Gaussian channel modelling, tracking of agile objects such as birds or drones, in financial prediction and in analysis of vibrational data under non-Gaussian perturbation. We will also describe recent advances in extending standard Gaussian process regression into non-Gaussian regimes through use of an underlying Lévy process of jump type, allowing more flexible and realistic modelling of non-Gaussian process regressions.

Some recent papers on the topic:


Simon Godsill is Professor of Statistical Signal Processing in the Engineering Department at Cambridge University. He is also a Professorial Fellow and tutor at Corpus Christi College Cambridge. He coordinates an active research group in Signal Inference and its Applications and is Head of the Information Engineering Division at Cambridge. His group specialises in Bayesian computational methodology, multiple object tracking, audio and music processing, and financial time series modeling. A particular methodological theme over recent years has been the development of novel techniques for optimal Bayesian filtering and smoothing, using Sequential Monte Carlo (Particle Filtering) and Markov chain Monte Carlo methods. Prof. Godsill has published extensively in journals, books and international conference proceedings, and has given a number of invited and plenary addresses at conferences such as the Valencia conference on Bayesian Statistics (twice), the IEEE Statistical Signal Processing Workshop, the Conference on Bayesian Inference for Stochastic Processes (BISP), the IEEE Workshop on Machine Learning in Signal Processing (2013), FUSION (2016) and SSPD (2022). He co-authored the Springer text Digital Audio Restoration with Prof. Peter Rayner in 1998. He was technical chair of the IEEE NSSPW workshop in 2006 on sequential and nonlinear filtering methods, and has been on the conference panel for numerous other conferences/workshops. Prof. Godsill has served as Associate Editor for IEEE Tr. Signal Processing and the journal Bayesian Analysis. He was Theme Leader in Tracking and Reasoning over Time for the UK’s Data and Information Fusion Defence Technology Centre (DIF-DTC) and Principal Investigator on many grants funded by the EU, EPSRC, QinetiQ, General Dynamics, dstl/MOD, ARL, Microsoft UK, Citibank, Mastercard, Google, DSO Singapore, Huawei and Jaguar Landrover. In 2009-10 he was co-organiser of an 18 month research program in Sequential Monte Carlo Methods at the SAMSI Institute in North Carolina and in 2014 he co-organised a research programme at the Isaac Newton Institute on Sequential Monte Carlo methods. In 2018 he was General Chair of the FUSION Conference in Cambridge. Two of his journal papers have received Best Paper awards from the IEEE and IET. He continues to be a Director of CEDAR Audio Ltd. (which has received numerous accolades over the years, including a technical Oscar), and for which he was a founding staff member in 1988.