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.