Non-Gaussian parameter estimation using generalized polynomial chaos expansion with extended Kalman filtering

Kalman Filter (KF) based parameter estimation assumes Gaussianity of the system parameters and thus propagates only the first two moments of the states. Application of Particle filter or Ensemble Kalman filter to estimate non-Gaussian parameters, although more accurate, is computationally expensive. Generalized polynomial chaos (gPC) is well-known as an effective tool to describe any dynamic system with stationary uncertainty through a set of orthogonal basis functions and associated coefficients. This article couples gPC with Extended KF (EKF) algorithm in which the uncertainty propagation from parameter to measurement is described through gPC expansion of parameters and outputs. Subsequently, the gPC coefficients of the parameter expansion are estimated from available measurements employing EKF. Thus, instead of selecting the system parameters as states, we consider the associated parameter gPC coefficients as state variables which reduces the problem of estimating the complete distribution of parameters down to identification of a few gPC coefficients. The proposed method is tested on systems with either Gaussian or non-Gaussian parameters. The error in estimating non-Gaussian parameters using KF based techniques is demonstrated.