非线性扩展与共制 Kalman 过滤器的对比: Gaussian 变形和双制组合过滤器 (A comparison of nonlinear extensions to the ensemble Kalman filter: Gaussian Anamorphosis and Two-Step Ensemble Filters)

Ensemble Kalman filters are based on a Gaussian assumption, which can limit their performance in some non-Gaussian settings. This paper reviews two nonlinear, non-Gaussian extensions of the Ensemble Kalman Filter: Gaussian anamorphosis (GA) methods and two-step updates, of which the rank histogram filter (RHF) is a prototypical example. GA-EnKF methods apply univariate transforms to the state and observation variables to make their distribution more Gaussian before applying an EnKF. The two-step methods use a scalar Bayesian update for the first step, followed by linear regression for the second step. The connection of the two-step framework to the full Bayesian problem is made, which opens the door to more advanced two-step methods in the full Bayesian setting. A new method for the first part of the two-step framework is proposed, with a similar form to the RHF but a different motivation, called the `improved RHF' (iRHF). A suite of experiments with the Lorenz-`96 model demonstrate situations where the GA-EnKF methods are similar to EnKF, and where they outperform EnKF. The experiments also strongly support the accuracy of the RHF and iRHF filters for nonlinear and non-Gaussian observations; these methods uniformly beat the EnKF and GA-EnKF methods in the experiments reported here. The new iRHF method is only more accurate than RHF at small ensemble sizes in the experiments reported here.

翻译：GA-EnKF方法基于一个高斯假设,它可以限制其在某些非加西安环境中的性能。本文回顾了Ensemble Kalman过滤器的两个非线性、非加西安扩展部分:Gaussian 变形(GA) 方法和两步更新,其中一级直方图过滤器(RHF)是一个原型例子。GA-EnKF方法将单向状态和观察变量转换,使其在应用 EnKF 之前的性能更加优于高斯。两步方法为第一步使用Salar Bayesian更新,随后是第二步的线性回归。将两步框架与整个巴伊西安问题连接起来,这为整个巴伊西亚环境中更先进的两步方法打开了大门。提出了两步框架第一部分的新方法,其形式与RHF相似,但有不同的动机,即“简化RHF”(iRCF) 第一步,其尺寸为“简化的RHF(iRHF) ” 和“EK” 实验中较精确的IF 方法,其中的iRC-F 和“GA-F 演示方法也报告了这里的精度。

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