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WIP: Dynamics-Informed Gaussian process transition models #1140
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…lity with downstream models. Updated variable names for clarity.
…eded for transition matrix calculation
…ls to construct time vector for prediction
…ond markov approximation implementation
…lemented as a special case of the dynamic GP. Documentation to be updated.
…g numerical methods
…lidation and rename kernel methods for clarity
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Summary:
This PR introduces new Gaussian Process (GP)-based linear Gaussian transition models into the Stone Soup library. These models combine the benefits of data-driven and mechanics-informed tracking, offering greater flexibility for tracking applications where standard kinematic models may be insufficient.
This is submitted as a draft PR to facilitate submitting the paper "Dynamics-Informed Gaussian Process models in Stone Soup" for Fusion 2025, since unit tests and documentation are not ready. Any feedback on design choices, usability and integration is welcomed.
Key additions include:
Currently, these models are implemented for the case where the driving GP has the squared exponential (SE) covariance function, as the analytical expressions for their covariance functions have been derived in [1] and the new Fusion paper. Alternative kernels can be implemented by overriding class methods. These models integrate directly into the existing Kalman filtering framework.
Changes Introduced:
models.transition.linear
classes:SlidingWindowGP
,IntegratedGP
,DynamicsInformedIntegratedGP
,TwiceIntegratedGP
, andDynamicsInformedTwiceIntegratedGP
.GPPredictorWrapper
to support GP-based state propagation. The GP models have attributerequires_track
set toTrue
. The wrapper passes track history to the GP model to extract timestamps for computing the covariance matrices. See discussion in PR #564 on GPs. Alternative approaches may be preferred?See this GitHub repo for example usage.
References
[1] F. Lydeard, B. I. Ahmad, and S. Godsill, “Integrated Gaussian Processes for Tracking,” IEEE Open Journal of Signal Processing, pp. 1–9, 2025.