Monomial cubature rules since “Stroud”: a compilation
Journal of Computational and Applied Mathematics
Asymmetric Cubature Formulae with Few Points in High Dimension for Symmetric Measures
SIAM Journal on Numerical Analysis
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics
Journal of Computational Physics
Numerical integration formulas of degree two
Applied Numerical Mathematics
A generalized polynomial chaos based ensemble Kalman filter with high accuracy
Journal of Computational Physics
A survey of convergence results on particle filtering methods forpractitioners
IEEE Transactions on Signal Processing
High-degree cubature Kalman filter
Automatica (Journal of IFAC)
Hi-index | 31.45 |
Filtering is an approach for incorporating observed data into time-evolving systems. Instead of a family of Dirac delta masses that is widely used in Monte Carlo methods, we here use the Wiener chaos expansion for the parametrization of the conditioned probability distribution to solve the nonlinear filtering problem. The Wiener chaos expansion is not the best method for uncertainty propagation without observations. Nevertheless, the projection of the system variables in a fixed polynomial basis spanning the probability space might be a competitive representation in the presence of relatively frequent observations because the Wiener chaos approach not only leads to an accurate and efficient prediction for short time uncertainty quantification, but it also allows to apply several data assimilation methods that can be used to yield a better approximate filtering solution. The aim of the present paper is to investigate this hypothesis. We answer in the affirmative for the (stochastic) Lorenz-63 system based on numerical simulations in which the uncertainty quantification method and the data assimilation method are adaptively selected by whether the dynamics is driven by Brownian motion and the near-Gaussianity of the measure to be updated, respectively.