| SHEN Zheqi,ZHANG Xiangming,TANG Youmin. 2016. Comparison and combination of EAKF and SIR-PF in the Bayesian filter framework. Acta Oceanologica Sinica, 35(3):69－78 |
| Comparison and combination of EAKF and SIR-PF in the Bayesian filter framework |
| EnKF和SIR-PF在贝叶斯滤波框架下的比较和结合 |
| Received:May 15, 2015 Revised:September 25, 2015 |
| DOI：10.1007/s13131-015-0757-x |
| Key words:data assimilation ensemble adjustment Kalman filter particle filter Bayesian estimation ensemble adjustment Kalman particle filter |
| 中文关键词: 资料同化 集合卡尔曼滤波器 粒子滤波器 集合卡尔曼粒子滤波器 贝叶斯滤波 |
| 基金项目: |
| Author Name | Affiliation | E-mail | | SHEN Zheqi | State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou 310012, China | | | ZHANG Xiangming | State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou 310012, China | zhangxm@sio.org.cn | | TANG Youmin | State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou 310012, China
Environmental Science and Engineering, University of Northern British Columbia, Prince George V2N 4Z9, Canada | |
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| Abstract: |
| Bayesian estimation theory provides a general approach for the state estimate of linear or nonlinear and Gaussian or non-Gaussian systems. In this study, we first explore two Bayesian-based methods:ensemble adjustment Kalman filter (EAKF) and sequential importance resampling particle filter (SIR-PF), using a well-known nonlinear and non-Gaussian model (Lorenz '63 model). The EAKF, which is a deterministic scheme of the ensemble Kalman filter (EnKF), performs better than the classical (stochastic) EnKF in a general framework. Comparison between the SIR-PF and the EAKF reveals that the former outperforms the latter if ensemble size is so large that can avoid the filter degeneracy, and vice versa. The impact of the probability density functions and effective ensemble sizes on assimilation performances are also explored. On the basis of comparisons between the SIR-PF and the EAKF, a mixture filter, called ensemble adjustment Kalman particle filter (EAKPF), is proposed to combine their both merits. Similar to the ensemble Kalman particle filter, which combines the stochastic EnKF and SIR-PF analysis schemes with a tuning parameter, the new mixture filter essentially provides a continuous interpolation between the EAKF and SIR-PF. The same Lorenz '63 model is used as a testbed, showing that the EAKPF is able to overcome filter degeneracy while maintaining the non-Gaussian nature, and performs better than the EAKF given limited ensemble size. |
| 中文摘要: |
贝叶斯估计理论为非线性、非高斯系统的数据同化提供了一个统一的框架。在本文中,我们利用著名的洛伦茨吸引子(Lorenz'63)模式对两种基于贝叶斯滤波理论的数据同化方法——集合卡尔曼滤波器(EnKF)和重取样粒子滤波器(SIR-PF)——进行了较为全面的比较。比较的结果揭示了两种方法的优缺点:即当集合成员数目较多时,SIR-PF的同化效果优于EnKF;反之,则EnKF的表现较好。进一步地,我们使用统计方法分析了两者表现的差异和原因。
最近提出的一种集合卡尔曼粒子滤波器(EnKPF)通过使用一个可控的参数整合EnKF和SIR-PF的分析格式,可以结合两者的优点。本文在充分比较两种方法的前提下,重新阐释并改进了原有的EnKPF算法,使之适用于非线性的观测算子。通过使用相同的洛伦茨模式实验,我们揭示了EnKPF实质上提供了关于EnKF和SIR-PF的连续插值,使得后两者可以视为其特殊情况。并且,在集合成员数目有限的前提下,EnKPF可以在一定程度上避免滤波退化的发生,取得优于EnKF和SIR-PF的同化效果。 |
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