A non-Gaussian Bayesian filter for sequential data assimilation with non-intrusive polynomial chaos expansion.

Non-Gaussian data assimilation is vital for several applications with nonlinear dynamical systems, including geosciences, socio-economics, infectious disease modeling, and autonomous navigation. Widespread adoption of non-Gaussian data assimilation requires easy-to-implement schemes. We develop, implement, and apply an efficient nonlinear non-Gaussian data assimilation scheme using non-intrusive stochastic collocation-based polynomial chaos expansion (PCE) and Gaussian mixture model (GMM) priors fit to the state's uncertainty. First, we represent the uncertainty in a dynamical system using PCE and propagate it using the stochastic collocation method until an assimilation time. Then, we convert the polynomial basis prior to its equivalent Karhunen-Loeve (KL) form, fit a GMM in the subspace and perform a Bayesian filtering step. Thereafter, the posterior polynomial basis is recovered from the posterior GMM in the KL form, and uncertainty propagation is continued using the stochastic collocation method. The derivation and new equations required for the above conversions are presented. We apply the new scheme to an illustrative population growth dynamics application and a complex fluid flow problem for demonstrating its capabilities. In both cases, our filter accurately captures the non-Gaussian statistics compared to the polynomial chaos-ensemble Kalman filter and the polynomial chaos-error subspace statistical estimation filter. [ABSTRACT FROM AUTHOR]