This manuscript derives locally weighted ensemble Kalman methods from the point of view of ensemble-based function approximation. This is done by using pointwise evaluations to build up a local linear or quadratic approximation of a function, tapering off the effect of distant particles via local weighting. This introduces a candidate method (the locally weighted Ensemble Kalman method for inversion) with the motivation of combining some of the strengths of the particle filter (ability to cope with nonlinear maps and non-Gaussian distributions) and the Ensemble Kalman filter (no filter degeneracy).

翻译：本文从基于集成的函数逼近视角推演了局部加权集成卡尔曼方法。通过利用逐点评估构建函数的局部线性或二次近似，并借助局部加权减弱远距离粒子的影响，从而提出一种候选方法（用于反问题的局部加权集成卡尔曼方法）。该方法的动机在于融合粒子滤波器（能够处理非线性映射和非高斯分布）与集成卡尔曼滤波器（无滤波退化）的部分优势。