中文摘要：

数据同化是在动力学模型的运行过程中不断融合新的观测信息的方法论,Bayes理论是数据同化的基石。从原理、方法和符号系统为Bayes滤波在数据同化中的应用勾勒一个统一的框架。首先对连续数据同化和顺序数据同化的各种方法做了分类,然后给出了非线性系统顺序数据同化的Bayes递推滤波形式,并在此基础上介绍了典型的顺序数据同化方法——粒子滤波和集合Kal-man滤波。粒子滤波实质上是一种基于递推Bayes估计和Monte Carlo模拟的滤波方法,而集合Kalman滤波相当于一种权值相等的粒子滤波。Bayes滤波理论为顺序数据同化提供了更广义的理论框架,从基础的数学理论上揭示了数据同化的基本原理。

英文摘要：

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.