Parameter estimation for large systems is a difficult problem, and the solution approaches are computationally expensive. The polynomial chaos approach has been shown to be more efficient than Monte Carlo for quantifying the effects of uncertainties on the system response. This article compares two new computational approaches for parameter estimation based on the polynomial chaos theory for parameter estimation: a Bayesian approach, and an approach using an extended Kalman filter (EKF) to obtain the polynomial chaos representation of the uncertain states and the uncertain parameters. The two methods are applied to a non-linear four-degree-of-freedom roll plane model of a vehicle, in which an uncertain mass with an uncertain position is added on the roll bar. When using appropriate excitations, the results obtained with both approaches are close to the actual values of the parameters, and both approaches can work with noisy measurements. The EKF approach has an advantage over the Bayesian approach: the estimation comes in the form of a posteriori probability densities of the estimated parameters. However, it can yield poor estimations when dealing with non-identifiable systems, and it is recommended to repeat the estimation with different sampling rates in order to verify the coherence of the results with the EKF approach. The Bayesian approach is more robust, can recognize non-identifiability, and use regularization techniques if necessary.
Available at: http://works.bepress.com/eblanchard/1/