标题： 一种用于高维非线性系统的改进数据同化方案 显示英文标题

标题： An Improved Data Assimilation Scheme for High Dimensional Nonlinear Systems

摘要： 非线性/非高斯滤波在生命科学的许多领域有着广泛的应用，其中动态可能是非线性的和/或不确定状态的概率密度函数是非高斯的。 在这种问题中，估计量的准确性高度依赖于后验概率密度函数（pdf）能够被多精确地近似。 在低维状态空间中，基于序贯重要性采样（SIS）的方法可以适当地近似后验pdf。 然而，对于更高维的问题，这些技术通常是不合适的，因为为了达到令人满意的估计，所需的粒子数会随着状态空间维度呈指数增长。 另一方面，由于贝叶斯更新步骤中粒子的变换，集合卡尔曼滤波（EnKF）及其变体更适合大规模问题。 研究表明，由于更新步骤中的高斯假设，后一类方法可能导致强非线性问题的次优解。 本文介绍了一种基于高斯和展开的新技术，在捕捉非高斯特征方面更加准确，同时对于高维问题所需的计算努力仍然合理。 我们通过几个例子，包括强非线性Lorenz模型，展示了该方法在非高斯过程中的性能。 结果显示，与EnKF相比，均方误差有显著改善，并且随着粒子数量的增加表现出理想的收敛行为。 显示英文摘要

摘要： Nonlinear/non-Gaussian filtering has broad applications in many areas of life sciences where either the dynamic is nonlinear and/or the probability density function of uncertain state is non-Gaussian. In such problems, the accuracy of the estimated quantities depends highly upon how accurately their posterior pdf can be approximated. In low dimensional state spaces, methods based on Sequential Importance Sampling (SIS) can suitably approximate the posterior pdf. For higher dimensional problems, however, these techniques are usually inappropriate since the required number of particles to achieve satisfactory estimates grows exponentially with the dimension of state space. On the other hand, ensemble Kalman filter (EnKF) and its variants are more suitable for large-scale problems due to transformation of particles in the Bayesian update step. It has been shown that the latter class of methods may lead to suboptimal solutions for strongly nonlinear problems due to the Gaussian assumption in the update step. In this paper, we introduce a new technique based on the Gaussian sum expansion which captures the non-Gaussian features more accurately while the required computational effort remains within reason for high dimensional problems. We demonstrate the performance of the method for non-Gaussian processes through several examples including the strongly nonlinear Lorenz models. Results show a remarkable improvement in the mean square error compared to EnKF, and a desirable convergence behavior as the number of particles increases.