论文标题
中等非线性问题的杂交粒子质合滤波器
A hybrid particle-ensemble Kalman filter for problems with medium nonlinearity
论文作者
论文摘要
杂交粒子集合kalman滤波器是针对中等非高斯性问题的问题，即先验是非常非高斯但后部大约高斯的问题。例如，当非线性动力学产生非高斯预测时，这种情况会出现，但紧密的高斯可能性会导致几乎高斯的后部。混合过滤器首先考虑了可能性。首先，粒子滤波器与产生中间体的可能性的一个因素相吸收了，该因素接近高斯，然后集合卡尔曼过滤器与其余因子完成了同化。确定粒子滤波器避免崩溃的方式确定两个阶段之间的可能性如何分开，并且通过平均具有的随机正交转换破坏了粒子退化。该混合动力车以简单的二维（2D）问题和由Lorenz-'96模型动机的多尺度系统进行测试。在2D问题中，它的表现既优于纯粒子过滤器，又超出了纯集合卡尔曼滤波器，在多尺度的洛伦兹 - '96模型中，它显示出优于纯机组的卡尔曼滤波器，前提是集合尺寸足够大。
A hybrid particle ensemble Kalman filter is developed for problems with medium non-Gaussianity, i.e. problems where the prior is very non-Gaussian but the posterior is approximately Gaussian. Such situations arise, e.g., when nonlinear dynamics produce a non-Gaussian forecast but a tight Gaussian likelihood leads to a nearly-Gaussian posterior. The hybrid filter starts by factoring the likelihood. First the particle filter assimilates the observations with one factor of the likelihood to produce an intermediate prior that is close to Gaussian, and then the ensemble Kalman filter completes the assimilation with the remaining factor. How the likelihood gets split between the two stages is determined in such a way to ensure that the particle filter avoids collapse, and particle degeneracy is broken by a mean-preserving random orthogonal transformation. The hybrid is tested in a simple two-dimensional (2D) problem and a multiscale system of ODEs motivated by the Lorenz-`96 model. In the 2D problem it outperforms both a pure particle filter and a pure ensemble Kalman filter, and in the multiscale Lorenz-`96 model it is shown to outperform a pure ensemble Kalman filter, provided that the ensemble size is large enough.
