We provide a brief introduction to Bayesian inverse problems and Bayesian estimators emphasizing their similarities and differences to the classical regularized least-squares approach to inverse problems. We then analyze Kalman filtering techniques for nonlinear systems, specifically the well-known Ensemble Kalman Filter (EnKF) and the recently proposed Polynomial Chaos Expansion Kalman Filter (PCE-KF), in this Bayesian framework and show how they relate to the solution of Bayesian inverse problems.
CITATION STYLE
Ernst, O. G., Sprungk, B., & Starkloff, H. J. (2014). Bayesian inverse problems and kalman filters. Lecture Notes in Computational Science and Engineering, 102, 133–159. https://doi.org/10.1007/978-3-319-08159-5_7
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