Efficient Sequetial Data Assimilation for the Joint Distributios of System States

Complex systems are often described by models with unavoidable errors. By combining model forecasts and data, sequential data assimilation keeps correcting forecast dynamics from drastic instability. Over the years, methods like ensemble Kalman filter and particle filter have been developed for nonlinear systems, while requiring high computational costs due to huge sampling size. We propose a novel framework for assimilating nonlinear systems with desirable accuracies and much smaller sampling size, as well as obtaining joint distributions of any sub-dimensions. Through a numerical example of 10-dimensional nonlinear system, we demonstrate that the new assimilation framework provides an effective behavior.