Dynamics-Informed Gaussian Process Models in Stone Soup

Kalman filtering is widely used for object tracking applications but often relies on predefined motion models, which limits its adaptability to nonlinear or uncertain trajectories. Formulating a Gaussian Process (GP) as a linear Gaussian state-space model provides a data-driven alternative for efficient sequential inference within a Kalman filtering framework. This paper extends the Integrated GP (iGP) model to introduce three novel variants: the Twice-Integrated GP (iiGP), the Dynamics-Informed Integrated GP (iDGP), and the Dynamics-Informed Twice-Integrated GP (iiDGP). The dynamics-informed models incorporate system dynamics alongside data-driven modelling, enabling more accurate tracking of motion under uncertain environments. The twice-integrated models enforce smoother motion patterns while maintaining the flexibility of GPs as driving noise. These models are implemented in the Stone Soup tracking framework. We discuss the software design, implementation challenges, and present evaluation results on synthetic and insect motion trajectory data. Results highlight the benefits of incorpo-rating dynamical information in GP-based tracking models, as well as the trade-offs between adaptability and robustness.