arXiv subjects

Simon J. Godsill

Publications and source records attributed to Simon J. Godsill.

8 recordsLinked to original sources

arXiv2026

PiVoT: A Variational Solution for Real-time Large-scale Multi-object Detection and Tracking under Heavy Clutter

Multi-object detection and tracking from noisy point clouds remain challenging in many data-scarce radar applications. Current Bayesian trackers based on Poisson measurement models offer a training-free solution but struggle to achieve accuracy and efficiency under severe clutter, large object populations, and full-resolution Doppler point clouds. We address this with PiVoT, a fast, clutter-resilient multi-object tracker for both positional and Doppler measurements. PiVoT performs end-to-end detection and tracking of a large and time-varying number of objects without external clustering or detectors, through joint inference of object states, shapes, existence probabilities, data association, and measurement rates. Its efficiency is driven by several variational inference innovations, such as theoretically justified birth pruning, quadratic-to-linear complexity reductions for exact updates, and a computationally efficient Doppler Poisson model. Experiments show that PiVoT substantially outperforms existing Bayesian trackers in challenging scenes, while also demonstrating exceptional scalability to a thousand objects, robustness to clutter visually inseparable from objects, and real-time operation on full-scale modern automotive radar datasets, where it attains performance comparable to a deep-learning detection benchmark as a training-free joint detector and tracker.

cs.LG↗

arXiv2026

PHAST-Net: Attention-Guided, Physics-Informed Network for Unified Estimation of Ideal Time-Frequency Representations

We introduce PHAST-Net, an attention-guided, physics-informed network for unified estimation of Ideal Time-Frequency Representations (ITFRs), spanning spectral, tempo-based, metrical, and harmonic representations such as Spectrograms, Tempograms, and Metrograms. PHAST-Net learns an application-general mapping from a constellation of wavelet transforms, the proposed Continuous Log-frequency Adaptive Wavelet Transform (CLAWT), to high-resolution, cross-term-suppressed time-frequency (T-F) representations. The proposed constellation of CLAWTs is selected through Cohen's class kernel analysis to maximise curvature coverage in a logarithmic-frequency T-F plane tailored to harmonic signal structure. PHAST-Net further incorporates a proposed physics-informed auxiliary reprojection loss designed to reconstruct the idealised observed CLAWT constellation from the predicted ITFR and the corresponding Cohen's class kernels during training. This auxiliary objective promotes transform consistency and energy conservation, mitigates pathological target sparsity, and enhances optimisation stability. Attention layers further promote effective cross-term suppression across the input constellation. The log-frequency formulation also enables Harmonic PHAST-Net, which estimates a Harmonic ITFR that isolates fundamental structure, supporting robust fundamental-only representations for speech and music, such as derived fundamental Tempograms and Metrograms. We further introduce Spline-PHAST-Net, which parameterises detected and associated T-F ridges as continuous spline trajectories, enabling arbitrary-grid re-rendering and signal reconstruction. Trained on an effectively unbounded procedurally generated dataset, PHAST-Net demonstrates improved accuracy over established approaches, providing a unified framework for high-resolution, cross-term-robust analysis of speech, music, and broader nonstationary signals.

eess.AS↗

arXiv2026

RIFT: Entropy-Optimised Fractional Wavelet Constellations for Ideal Time-Frequency Estimation

We introduce a new method for estimating the Ideal Time-Frequency Representation (ITFR) of complex nonstationary signals. The Reconstructive Ideal Fractional Transform (RIFT) computes a constellation of Continuous Fractional Wavelet Transforms (CFWTs) aligned to different local time-frequency curvatures. This constellation is combined into a single optimised time-frequency energy representation via a localised entropy-based sparsity measure, designed to resolve auto-terms and attenuate cross-terms. Finally, a positivity-constrained Lucy-Richardson deconvolution with total-variation regularisation is applied to estimate the ITFR, achieving auto-term resolution comparable to that of the Wigner-Ville Distribution (WVD), yielding the high-resolution RIFT representation. The required Cohen's class convolutional kernels are fully derived in the paper for the chosen CFWT constellations. Additionally, the optimisation yields an Instantaneous Phase Direction (IPD) field, which allows the localised curvature in speech or music extracts to be visualised and utilised within a Kalman tracking scheme, enabling the extraction of signal component trajectories and the construction of the Spline-RIFT variant. Evaluation on synthetic and real-world signals demonstrates the algorithm's ability to effectively suppress cross-terms and achieve superior time-frequency precision relative to competing methods. This advance holds significant potential for a wide range of applications requiring high-resolution cross-term-free time-frequency analysis.

eess.AS↗

arXiv2025

Distributed Expectation Propagation for Multi-Object Tracking over Sensor Networks

In this paper, we present a novel distributed expectation propagation algorithm for multiple sensors, multiple objects tracking in cluttered environments. The proposed framework enables each sensor to operate locally while collaboratively exchanging moment estimates with other sensors, thus eliminating the need to transmit all data to a central processing node. Specifically, we introduce a fast and parallelisable Rao-Blackwellised Gibbs sampling scheme to approximate the tilted distributions, which enhances the accuracy and efficiency of expectation propagation updates. Results demonstrate that the proposed algorithm improves both communication and inference efficiency for multi-object tracking tasks with dynamic sensor connectivity and varying clutter levels.

eess.SP↗

arXiv2025

State Space Model Programming in Turing.jl

State space models (SSMs) are a powerful and widely-used class of probabilistic models for analysing time-series data across various fields, from econometrics to robotics. Despite their prevalence, existing software frameworks for SSMs often lack compositionality and scalability, hindering experimentation and making it difficult to leverage advanced inference techniques. This paper introduces SSMProblems.jl and GeneralisedFilters.jl, two Julia packages within the Turing.jl ecosystem, that address this challenge by providing a consistent, composable, and general framework for defining SSMs and performing inference on them. This unified interface allows researchers to easily define a wide range of SSMs and apply various inference algorithms, including Kalman filtering, particle filtering, and combinations thereof. By promoting code reuse and modularity, our packages reduce development time and improve the reliability of SSM implementations. We prioritise scalability through efficient memory management and GPU-acceleration, ensuring that our framework can handle large-scale inference tasks.

stat.CO↗

arXiv2017

If and When a Driver or Passenger is Returning to Vehicle: Framework to Infer Intent and Arrival Time

This paper proposes a probabilistic framework for the sequential estimation of the likelihood of a driver or passenger(s) returning to the vehicle and time of arrival, from the available partial track of the user location. The latter can be provided by a smartphone navigational service and/or other dedicated (e.g. RF based) user-to-vehicle positioning solution. The introduced novel approach treats the tackled problem as an intent prediction task within a Bayesian formulation, leading to an efficient implementation of the inference routine with notably low training requirements. It effectively captures the long term dependencies in the trajectory followed by the driver/passenger to the vehicle, as dictated by intent, via a bridging distribution. Two examples are shown to demonstrate the efficacy of this flexible low-complexity technique.

stat.AP↗

arXiv2016

Bayesian Intent Prediction in Object Tracking Using Bridging Distributions

In several application areas, such as human computer interaction, surveillance and defence, determining the intent of a tracked object enables systems to aid the user/operator and facilitate effective, possibly automated, decision making. In this paper, we propose a probabilistic inference approach that permits the prediction, well in advance, of the intended destination of a tracked object and its future trajectory. Within the framework introduced here, the observed partial track of the object is modeled as being part of a Markov bridge terminating at its destination, since the target path, albeit random, must end at the intended endpoint. This captures the underlying long term dependencies in the trajectory, as dictated by the object intent. By determining the likelihood of the partial track being drawn from a particular constructed bridge, the probability of each of a number of possible destinations is evaluated. These bridges can also be employed to produce refined estimates of the latent system state (e.g. object position, velocity, etc.), predict its future values (up until reaching the designated endpoint) and estimate the time of arrival. This is shown to lead to a low complexity Kalman-filter-based implementation of the inference routine, where any linear Gaussian motion model, including the destination reverting ones, can be applied. Free hand pointing gestures data collected in an instrumented vehicle and synthetic trajectories of a vessel heading towards multiple possible harbours are utilised to demonstrate the effectiveness of the proposed approach.

stat.AP↗

arXiv2015

Rao-Blackwellized particle smoothers for conditionally linear Gaussian models

Sequential Monte Carlo (SMC) methods, such as the particle filter, are by now one of the standard computational techniques for addressing the filtering problem in general state-space models. However, many applications require post-processing of data offline. In such scenarios the smoothing problem--in which all the available data is used to compute state estimates--is of central interest. We consider the smoothing problem for a class of conditionally linear Gaussian models. We present a forward-backward-type Rao-Blackwellized particle smoother (RBPS) that is able to exploit the tractable substructure present in these models. Akin to the well known Rao-Blackwellized particle filter, the proposed RBPS marginalizes out a conditionally tractable subset of state variables, effectively making use of SMC only for the "intractable part" of the model. Compared to existing RBPS, two key features of the proposed method are: (i) it does not require structural approximations of the model, and (ii) the aforementioned marginalization is done both in the forward direction and in the backward direction.

stat.CO↗