- The following material was prepared as a part of a workshop on recent advances in uncertainty analysis & estimation. This workshop was conducted at 2014 and 2015 American Control Conference (ACC) in collaboration with Dr. Raktim Bhattacharya at Texas A&M. A part of this material was also presented at a workshop (in collaboration with Dr. Manoranjan Majji) at Air Force Research Laboratories (AFRL), Kirkland during the summer of 2017.
| PreliminaryStuff | This talk reviews basic concepts related to random variables, random process, conditional probability density function, maximum likelihood estimation, maximum a-posteriori estimation and minimum variance filter. |
| “Optimal” Quadrature Methods | This talk reviews Gaussian quadrature methods as well as recently developed Conjugate Unscented Transformation (CUT) approach to accurately evaluate expectation integrals in high dimension space while minimizing the number of simulations. |
| Spectral Methods | This talk discuss the spectral methods (such as Polynomial Chaos) and their connection to the higher order state transition tensors for the dynamical systems. |
| Solution to the Kolmogorov Equation [p1] & [p2] | This talk reviews the analytical solutions for the Fokker-Planck-Kolmogorov (FPK) equation as well as numerical methods to solve the Kolmogorov equation. This talk discuss that how one can make use of recent advances in approximation theory to not only break the “curse of dimensionality” but can also pose the the pdf evolution problem as a convex optimization problem with guaranteed convergence. |
| Application to Estimation & Filtering | This talk reviews the concept of model-data fusion, which has its birth with the development of Kalman filter for linear system. It is discussed that how various uncertainty propagation methods introduced in prior sections can be used along with Bayes’ rule to find system state and parameter estimates. |
- P. Singla, A. Patra, J. L. Palma and B. Pitman, Workshop for Probabilistic Analysis of Volcanic Hazards, University at Buffalo, 16-19 May, 2011. (A good introduction to Polynomial Chaos Quadrature Method for Uncertainty Characterization)