Extend symplectic filtering to parameter estimation and nonlinear observations

Develop extensions of the adaptive symplectic filtering framework that incorporate a parameter-estimation procedure for evolving the probability distribution over the parameter space and accommodate nonlinear measurement operators.

Background

The paper develops an adaptive filtering method for reconstructing parametric Hamiltonian dynamics from finitely many linear measurements, using evolving symplectic approximation spaces and dynamically placed sensors. Its analysis and numerical experiments assume that the observations are linear and that the parameter distribution is fixed rather than estimated online.

The authors explicitly identify two unresolved extensions: augmenting the framework with parameter estimation so that the probability distribution over the parameter space can evolve, and extending the methodology from linear observations to nonlinear measurement operators. These directions would broaden the method toward joint state–parameter inference and more general sensing models.

References

Several directions remain open for future investigation. A natural extension of the current work is to augment the framework with a parameter estimation procedure, which would allow one to evolve the probability distribution over the parameter space. Another possible direction is the extension of our methodology beyond linear observations to account for nonlinear measurement operators.

— Symplectic filtering of Hamiltonian dynamics with moving sensors  (2609.35647 - Mula et al., 28 Sep 2026) in Section Conclusions