论文标题
标量集合卡尔曼滤波器中通胀的明确概率推导，以实现有限的集合收敛
An Explicit Probabilistic Derivation of Inflation in a Scalar Ensemble Kalman Filter for Finite Step, Finite Ensemble Convergence
论文作者
论文摘要
本文使用一种概率方法来分析集合滤波器解决方案的收敛到最简单的设置，即标量案例，因为它允许我们建立在标量概率分布和非元素功能的丰富文献上。为此，我们介绍了赤骨标量教学合奏Kalman Filter（SpenKF）。我们表明，在整体大小的渐近情况下，SPENKF的分析均值和方差估计值的期望值会收敛到真正的Kalman滤波器的期望值，并且在每个时间时刻，两者的方差都倾向于零。我们还表明，当合奏是有限的，并将时间带到无限时，整体在互补情况下会收敛。此外，我们表明，可以利用有限汇合的有限时间案例，差异通货膨胀和平均校正来胁迫SPENKF融合到其标量KALMAN滤波器对应物中。然后，我们将此框架应用于分析扰动的观察结果，并解释为什么扰动观察结果集合Kalman过滤器表现不佳。
This paper uses a probabilistic approach to analyze the converge of an ensemble Kalman filter solution to an exact Kalman filter solution in the simplest possible setting, the scalar case, as it allows us to build upon a rich literature of scalar probability distributions and non-elementary functions. To this end we introduce the bare-bones Scalar Pedagogical Ensemble Kalman Filter (SPEnKF). We show that in the asymptotic case of ensemble size, the expected value of both the analysis mean and variance estimate of the SPEnKF converges to that of the true Kalman filter, and that the variances of both tend towards zero, at each time moment. We also show that the ensemble converges in probability in the complementary case, when the ensemble is finite, and time is taken to infinity. Moreover, we show that in the finite-ensemble, finite-time case, variance inflation and mean correction can be leveraged to coerce the SPEnKF converge to its scalar Kalman filter counterpart. We then apply this framework to analyze perturbed observations and explain why perturbed observations ensemble Kalman filters underperform their deterministic counterparts.
