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首页> 外文期刊>Journal of Computational Physics >Mathematical strategies for filtering complex systems: Regularly spaced sparse observations
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Mathematical strategies for filtering complex systems: Regularly spaced sparse observations

机译：过滤复杂系统的数学策略：规则分布的稀疏观测

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Real time filtering of noisy turbulent signals through sparse observations on a regularly spaced mesh is a notoriously difficult and important prototype filtering problem. Simpler off-line test criteria are proposed here as guidelines for filter performance for these stiff multi-scale filtering problems in the context of linear stochastic partial differential equations with turbulent solutions. Filtering turbulent solutions of the stochastically forced dissipative advection equation through sparse observations is developed as a stringent test bed for filter performance with sparse regular observations. The standard ensemble transform Kalman filter (ETKF) has poor skill on the test bed and even suffers from filter divergence, surprisingly, at observable times with resonant mean forcing and a decaying energy spectrum in the partially observed signal. Systematic alternative filtering strategies are developed here including the Fourier Domain Kalman Filter (FDKF) and various reduced filters called Strongly Damped Approximate Filter (SDAF), Variance Strongly Damped Approximate Filter (VSDAF), and Reduced Fourier Domain Kalman Filter (RFDKF) which operate only on the primary Fourier modes associated with the sparse observation mesh while nevertheless, incorporating into the approximate filter various features of the interaction with the remaining modes. It is shown below that these much cheaper alternative filters have significant skill on the test bed of turbulent solutions which exceeds ETKF and in various regimes often exceeds FDKF, provided that the approximate filters are guided by the off-line test criteria. The skill of the various approximate filters depends on the energy spectrum of the turbulent signal and the observation time relative to the decorrelation time of the turbulence at a given spatial scale in a precise fashion elucidated here. (C) 2008 Elsevier Inc. All rights reserved.
机译：通过在规则间隔的网格上进行稀疏观测来对嘈杂的湍流信号进行实时滤波是众所周知的困难且重要的原型滤波问题。本文提出了更简单的离线测试准则，作为在带有湍流解的线性随机偏微分方程的背景下，这些刚性多尺度滤波问题的滤波器性能的准则。通过稀疏观测来滤除随机强迫耗散对流方程的湍流解，作为针对具有稀疏常规观测的过滤器性能的严格测试平台。标准的合奏变换卡尔曼滤波器（ETKF）在测试台上的技能很差，甚至出现滤波器发散的问题，令人惊讶的是，在可观测的时间，谐振平均强迫和部分观测到的信号的能谱衰减。这里开发了系统的替代滤波策略，包括仅工作的傅立叶域卡尔曼滤波器（FDKF）和各种简化滤波器，分别称为强阻尼近似滤波器（SDAF），方差强阻尼近似滤波器（VSDAF）和简化傅立叶域卡尔曼滤波器（RFDKF）然而，在与稀疏观测网格相关的主要傅里叶模式上，将与剩余模式相互作用的各种特征合并到近似滤波器中。如下所示，这些便宜得多的替代过滤器在湍流溶液的测试床上具有显着的技能，该条件超过了ETKF，并且在各种情况下经常超过FDKF，前提是近似过滤器受离线测试标准的指导。各种近似滤波器的技巧取决于在给定的空间尺度上以精确的方式阐明了湍流信号的能谱和相对于湍流去相关时间的观察时间。 （C）2008 Elsevier Inc.保留所有权利。

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