论文标题
集合平方根过滤器的平均场限制 - 离散和连续时间
Mean field limit of Ensemble Square Root Filters -- discrete and continuous time
论文作者
论文摘要
考虑集合平方根滤波算法的类别，以部分观察到以独立测量噪声破坏的线性观测值的非线性马尔可夫信号的后验分布的数值近似。我们在离散时间和连续时间中分析了这些算法的渐近行为。我们确定集合成员水平上的限制均值过程，证明了混乱结果的相应传播，并根据整体规模得出相关的收敛速率。在连续的时间内，我们还确定了驱动平均场过程分布的随机部分微分方程，并与Kushner-Stratonovich方程进行比较。
Consider the class of Ensemble Square Root filtering algorithms for the numerical approximation of the posterior distribution of nonlinear Markovian signals partially observed with linear observations corrupted with independent measurement noise. We analyze the asymptotic behavior of these algorithms in the large ensemble limit both in discrete and continuous time. We identify limiting mean-field processes on the level of the ensemble members, prove corresponding propagation of chaos results and derive associated convergence rates in terms of the ensemble size. In continuous time we also identify the stochastic partial differential equation driving the distribution of the mean-field process and perform a comparison with the Kushner-Stratonovich equation.
