Lognormal and Mixed Gaussian–Lognormal Kalman Filters
Lognormal and Mixed Gaussian–Lognormal Kalman Filters
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对数正态和混合高斯 - 对数正态卡尔曼滤波器
DOI：
10.1175/mwr-d-22-0072.1
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发表时间：
2023
影响因子：
3.2
通讯作者：
Van Loon, Senne
中科院分区：
文献类型：
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作者：
Fletcher, Steven J.;Zupanski, Milija;Goodliff, Michael R.;Kliewer, Anton J.;Jones, Andrew S.;Forsythe, John M.;Wu, Ting-Chi;Hossen, Md. Jakir;Van Loon, Senne
本文给出了卡尔曼滤波方程的两种新形式的推导；第一个是纯对数正态分布随机变量，而第二组卡尔曼滤波方程将用于高斯和对数正态分布随机变量的组合。我们表明，其外观与基于高斯的方程相似，但分析状态是多元中位数而不是平均值。我们还展示了具有对数正态误差的Lorenz 1963模型的混合分布卡尔曼滤波器的结果，并将其与传统的基于高斯的扩展卡尔曼滤波器的分析结果进行了比较，并表明在某些情况下，新方法产生了更准确的结果。
In this paper we present the derivation of two new forms of the Kalman filter equations; the first is for a pure lognormally distributed random variable, while the second set of Kalman filter equations will be for a combination of Gaussian and lognormally distributed random variables. We show that the appearance is similar to that of the Gaussian-based equations, but that the analysis state is a multivariate median and not the mean. We also show results of the mixed distribution Kalman filter with the Lorenz 1963 model with lognormal errors for the background and observations of thezcomponent, and compare them to analysis results from a traditional Gaussian-based extended Kalman filter and show that under certain circumstances the new approach produces more accurate results.