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A non-Gaussian Bayesian filter for sequential data assimilation with non-intrusive polynomial chaos expansion
International Journal for Numerical Methods in Engineering ( IF 2.7 ) Pub Date : 2021-09-12 , DOI: 10.1002/nme.6827
Srikanth Avasarala 1 , Deepak Subramani 1
Affiliation  

Non-Gaussian data assimilation is vital for several applications with nonlinear dynamical systems, including geosciences, socio-economics, infectious disease modeling, and autonomous navigation. Widespread adoption of non-Gaussian data assimilation requires easy-to-implement schemes. We develop, implement, and apply an efficient nonlinear non-Gaussian data assimilation scheme using non-intrusive stochastic collocation-based polynomial chaos expansion (PCE) and Gaussian mixture model (GMM) priors fit to the state's uncertainty. First, we represent the uncertainty in a dynamical system using PCE and propagate it using the stochastic collocation method until an assimilation time. Then, we convert the polynomial basis prior to its equivalent Karhunen–Loeve (KL) form, fit a GMM in the subspace and perform a Bayesian filtering step. Thereafter, the posterior polynomial basis is recovered from the posterior GMM in the KL form, and uncertainty propagation is continued using the stochastic collocation method. The derivation and new equations required for the above conversions are presented. We apply the new scheme to an illustrative population growth dynamics application and a complex fluid flow problem for demonstrating its capabilities. In both cases, our filter accurately captures the non-Gaussian statistics compared to the polynomial chaos-ensemble Kalman filter and the polynomial chaos-error subspace statistical estimation filter.

中文翻译:

用于具有非侵入式多项式混沌扩展的顺序数据同化的非高斯贝叶斯滤波器

非高斯数据同化对于非线性动力系统的多种应用至关重要,包括地球科学、社会经济学、传染病建模和自主导航。非高斯数据同化的广泛采用需要易于实施的方案。我们使用基于非侵入式随机搭配的多项式混沌展开 (PCE) 和适合状态不确定性的高斯混合模型 (GMM) 先验来开发、实施和应用高效的非线性非高斯数据同化方案。首先,我们使用 PCE 表示动态系统中的不确定性,并使用随机搭配方法传播它直到同化时间。然后,我们将多项式基转换为其等效的 Karhunen-Loeve (KL) 形式,在子空间中拟合 GMM 并执行贝叶斯过滤步骤。此后,从KL形式的后验GMM中恢复后验多项式基,并使用随机搭配方法继续不确定性传播。给出了上述转换所需的推导和新方程。我们将新方案应用于说明性的人口增长动态应用和复杂的流体流动问题,以展示其功能。在这两种情况下,与多项式混沌集成卡尔曼滤波器和多项式混沌误差子空间统计估计滤波器相比,我们的滤波器准确地捕获了非高斯统计。我们将新方案应用于说明性的人口增长动态应用和复杂的流体流动问题,以展示其功能。在这两种情况下,与多项式混沌集成卡尔曼滤波器和多项式混沌误差子空间统计估计滤波器相比,我们的滤波器准确地捕获了非高斯统计。我们将新方案应用于说明性的人口增长动态应用和复杂的流体流动问题,以展示其功能。在这两种情况下,与多项式混沌集成卡尔曼滤波器和多项式混沌误差子空间统计估计滤波器相比,我们的滤波器准确地捕获了非高斯统计。
更新日期:2021-11-12
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