Particle filters + system identification.
A placeholder.
1 State augmentation
The classic; just include the parameter vector in the state vector and give it a “small” magnitude random evolution. (But how small?)
2 Via MCMC
a.k.a. particle MCMC. See Frei and Künsch (2012). Kantas et al. (2015) and Fearnhead and Künsch (2018) introduce more.
3 References
Evensen. 2009. Data Assimilation - The Ensemble Kalman Filter.
Fearnhead, and Künsch. 2018. “Particle Filters and Data Assimilation.” Annual Review of Statistics and Its Application.
Frei, and Künsch. 2012. “Sequential State and Observation Noise Covariance Estimation Using Combined Ensemble Kalman and Particle Filters.” Monthly Weather Review.
Kantas, Doucet, Singh, et al. 2015. “On Particle Methods for Parameter Estimation in State-Space Models.” Statistical Science.
Künsch. 2013. “Particle Filters.” Bernoulli.
Lindsten. 2011. “Rao-Blackwellised Particle Methods for Inference and Identification.”
Liu, Zhuo, Cheng, et al. 2019. “Understanding and Accelerating Particle-Based Variational Inference.” In Proceedings of the 36th International Conference on Machine Learning.
Maurais, and Marzouk. 2024. “Sampling in Unit Time with Kernel Fisher-Rao Flow.”