一种分层贝叶斯包络卡尔曼滤波器
A Hierarchical Bayes Ensemble Kalman Filter
摘要：
一个新的合奏过滤器，允许在先验分布的不确定性，提出和测试。该滤波器依赖于给定模型误差和可预测性误差协方差矩阵的状态的条件高斯分布。后者被视为随机矩阵和更新的分层贝叶斯方案随着国家。协方差矩阵的（超）先验分布被假设为逆Wishart。新的分层贝叶斯包络滤波器（HBEF）同化集合成员作为广义观测，并允许普通观测影响协方差。允许系综成员的实际概率分布与真实概率分布不同。提出了一种近似，导致一个切实可行的分析算法。新的过滤器进行了研究，在数值实验与双随机一变量模型的“真理”。该模型允许在每个时刻评估真值方差和真值滤波误差方差。根据其初级和次级滤波器的性能，HBEF在广泛的滤波机制中表现出优于Myrseth和Omre（2010）的EnKF和HEnKF。
英文摘要：
A new ensemble filter that allows for the uncertainty in the prior distribution is proposed and tested. The filter relies on the conditional Gaussian distribution of the state given the model-error and predictability-error covariance matrices. The latter are treated as random matrices and updated in a hierarchical Bayes scheme along with the state. The (hyper)prior distribution of the covariance matrices is assumed to be inverse Wishart. The new Hierarchical Bayes Ensemble Filter (HBEF) assimilates ensemble members as generalized observations and allows ordinary observations to influence the covariances. The actual probability distribution of the ensemble members is allowed to be different from the true one. An approximation that leads to a practicable analysis algorithm is proposed. The new filter is studied in numerical experiments with a doubly stochastic one-variable model of "truth". The model permits the assessment of the variance of the truth and the true filtering error variance at each time instance. The HBEF is shown to outperform the EnKF and the HEnKF by Myrseth and Omre (2010) in a wide range of filtering regimes in terms of performance of its primary and secondary filter.
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