Mathematics

Dynamical inverse problems appear naturally in several application areas in which the goal is to retrieve information from indirect observation of a target that does not remain stationary during the observation process. Particle filtering methods provide a way to address non-linear evolution models and non-linear observation models, and uncertainty quantification of the estimate is naturally built in the methodology. Particle filtering methods are closely related to classical Bayesian filtering methods such as Kalman filtering and its various extensions, and they carry a similarity to Bayesian sampling methods such as Markov chain Monte Carlo (MCMC) techniques. In these lectures, particle filtering methods are derived from basic principles, and demonstrated through concrete applications. The lectures are partly based on the material in the monograph  D. Calvetti and E. Somersalo (2023) Bayesian Scientific Computing, Springer.