Nonlinear estimation with polynomial chaos and higher order moment updates

In this paper we present a nonlinear estimation algorithm that combines generalized polynomial chaos theory and higher moment updates. Polynomial chaos theory is used to predict the evolution of uncertainty of the nonlinear random process, and higher order moment updates are used to estimate the posterior non Gaussian probability density function of the random process. The moments are updated using a linear gain. The nonlinear estimation algorithm is then applied to the duffing oscillator system with initial condition uncertainty and its performance is compared with linear estimators based on extended Kalman filtering framework. We observe that this estimator outperforms the linear estimator when measurements are not available very frequently, thus highlighting the need for nonlinear estimator in such scenarios.