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WIP: Dynamics-Informed Gaussian process transition models #1140

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@nfcc2 nfcc2 commented Mar 5, 2025

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:

  • Sliding Window GP: A basic zero-mean GP models position using a windowed subset of past states.
  • Integrated GP (iGP): As proposed in [1], where an iGP models target position, and the target velocity is a stochastic process purely driven by a GP disturbance.
  • Dynamics-Informed Integrated GP (iDGP): A novel GP formulation where the target velocity evolves under a first-order differential equation with a GP disturbance.
  • Twice-Integrated GP (iiGP) and Dynamics-Informed Twice-Integrated GP (iiDGP): Integrated versions of the iGP and iDGP respectively. A GP models target position while the driving GP acts as a disturbance on acceleration.

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:

  • Added models.transition.linear classes: SlidingWindowGP, IntegratedGP, DynamicsInformedIntegratedGP, TwiceIntegratedGP, and DynamicsInformedTwiceIntegratedGP.
  • Added wrapper class GPPredictorWrapper to support GP-based state propagation. The GP models have attribute requires_track set to True. 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.

nfcc2 added 30 commits October 30, 2024 18:06
…lity with downstream models. Updated variable names for clarity.
…lemented as a special case of the dynamic GP. Documentation to be updated.
…lidation and rename kernel methods for clarity
nfcc2 and others added 30 commits January 29, 2025 17:22
…steps needed for transition matrix calculation"

This reverts commit 483b12e.
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