A stochastic parameter estimation method based on the unscented transformation

Data assimilation-based parameter estimation methods have great potential in atmospheric and oceanic sciences to allow for timely and robust state determination and prediction. Physical models used in atmospheric and oceanic sciences exhibit strong nonlinearities, non-Gaussian state distribution, and high dimensional state vectors; therefore they do not lend themselves to the traditional Kalman filtering. The Ensemble Kalman filter is an appealing method to replace the traditional Kalman filter for atmospheric and oceanic data assimilation purposes due to its ability to capture the main modes of high dimensional state distribution for nonlinear systems. In the presents of heavy nonlinearities there still many exist modeling errors which are accounted for by stochastic forcing terms. The stochastic parameters are extracted from the data though the data assimilation process by augmenting the state vector to include these stochastic parameters. Ensembles are also generated in the new augmented state vector allowing for non-Gaussian distributions in theses parameters. Although the state distribution may exhibit non-Gaussian effects, the stochastic parameters may not. This fact can be used to take advantage of efficient Gaussian based estimation techniques. This work focuses on stochastic parameter estimation using a hybrid Ensemble Kalman filter and Unscented Kalman filter approach. An Ensemble filter is designed to estimate the deterministic state vector and approximate its non-Gaussian distribution in an efficient manner, while a Unscented Kalman filter approach is used to estimate the stochastic parameters while assuming Gaussian distributions in these parameters. The traditional unscented transformation is very computational expressive for high dimensional systems and therefore for atmospheric and oceanic sciences application it is not feasible. A Square-Root Unscented Kalman filter is implemented allowing for a high dimensional stochastic state vector. Finally simulation results are presented to highlight the benefit of the proposed approach.