Bayesian State Estimation in PDE Systems
Palestrante: Dr. Markus Neumayer
Institute of Electrical Measurement and Measurement Signal Processing
Graz University of Technology, Austria
The Bayesian inferential framework provides a powerful mathematical formalism to estimate states and/or parameters of physical systems or signals given data and a model. The formulation can be applied to both, static as well as dynamic problems. For the later so called sequential Bayesian estimators have to be applied. While classical approaches like the Kalman filter or the extended Kalman filter conquer the problem by some Gaussian assumption, the Particle Filter requires no assumptions about noise/and or parameter distributions. This advantage comes to the costs of inherently increased computational efforts due to the use of an underlying sampling scheme. The computational costs heavily increase for problems where the underlying physical process is governed by PDE systems. This talk addresses the topic of Bayesian State estimation and presents techniques for improved implementations of Bayesian state estimation techniques with a special focus on the Particle filter.
Markus Neumayer studied electrical engineering at Graz University of Technology from 2003 to 2008 where he focused on measurement and process automation. Since 2008 he is with the Institute of Electrical Measurement and Measurement Signal Processing where he specialized on inverse problems with a special focus on statistical methods. In 2010/11 he was with the Department of Physics at the University of Otago, Dunedin/NZ, where he did research on Bayesian Methods under the supervision of Prof. Colin Fox, as well as Prof. Jari Kaipio (University of Auckland/NZ). He finished his PhD in 2011 with honors. His research and teaching interests include physical modeling of measurement problems/systems and sensors, numerical methods, inverse problems, Bayesian methods and signal processing. His PhD was awarded by the Austrian government in 2012 (Award of Excellence). In 2012 he also received an award from the Styrian government for his contributions in the field of numerical simulations.