A Bayesian Filter Framework for Sequential Data Assimilation

Data assimilation is a method in which the observations can be merged with model states by taking advantage of consistent constraints from model physics.The Bayes theory can be considered as the very foundation for data assimilation.The purpose of this paper is to provide a unified theory and notation for the application of Bayesian filter in data assimilation.First,various methods of continuous and sequential data assimilation are classified.Secondly,the sequential data assimilation for nonlinear systems is generalized as a recursive Bayesian filter.Then,two typical sequential data assimilation methods,i.e.,the particle filter and the ensemble Kalman filter are represented in the framework of Bayesian filter.The particle filters,in essence,is a Monte Carlo realization of recursive Bayesian filter,and the ensemble Kalman filter is equivalent to the particle filter with equal weights.The theory of Bayesian filter provides a generalized basis for the sequential data assimilation from a more fundamental mathematical viewpoint.