Enhanced Polynomial Chaos-Based Extended Kalman Filter Technique for Parameter Estimation

Abstract

The generalized polynomial chaos (gPC) mathematical technique, when integrated with the extended Kalman filter (EKF) method, provides a parameter estimation and state tracking method. The truncation of the series expansions degrades the link between parameter convergence and parameter uncertainty which the filter uses to perform the estimations. An empirically derived correction for this problem is implemented, which maintains the original parameter distributions. A comparison is performed to illustrate the improvements of the proposed approach. The method is demonstrated for parameter estimation on a regression system, where it is compared to the recursive least squares (RLS) method.