Recursive Bayesian state and parameter estimation using polynomial chaos theory

This paper joins polynomial chaos theory with Bayesian estimation to recursively estimate the states and unknown parameters of asymptotically stable, linear, time invariant, state-space systems. This paper studies the proposed algorithms from a pole/zero locations perspective. The estimator has fixed pole locations that are independent of the estimation algorithm (and the estimated variables). Only the estimator zero locations are affected by estimation. This paper uses a 3rd order differential equation to study the behavior of the proposed estimator. It uses pole/zero maps and Bode plots to observe how the polynomial chaos based estimators vary the system zero locations to make the expanded polynomial chaos output most like (in some Bayesian sense) the 3rd order system output.