Polynomial chaos based method for state and parameter estimation

This paper presents a method for state and parameter estimation based on generalized polynomial chaos theory and Bayes´ theorem. Generalized polynomial chaos theory (gPC) is used to propagate the joint probability density functions (pdfs) for parameter and state through forward dynamic model while the Bayes´ rule is used to fuse the prior pdfs obtained through the gPC process with sensor observations to characterize non-Gaussian posterior density functions for state and parameters. Furthermore, a minimum variance based estimator is also derived which makes use of the gPC process to compute the mean and variance of actual non-Gaussian pdf. Numerical experiments involving two benchmark problems are considered to illustrate the effectiveness of the proposed ideas.