一种改进的Kushner-Stratonovich（EnKS）非线性滤波器：非迭代和迭代形式的加性粒子更新
An Ensemble Kushner-Stratonovich (EnKS) Nonlinear Filter: Additive Particle Updates in Non-Iterative and Iterative Forms
摘要：
尽管廉价的计算资源使得蒙特卡罗模拟更快，但粒子滤波在揭示基于有限时间序列数据的动态系统的不精确已知的模型参数或建模误差的准确统计信息方面的潜在益处尚未完全实现。一个主要的数值瓶颈沉淀这种性能不佳，特别是对于高维系统，是渐进的粒子dedication由于重量崩溃，目前的工作的目的是解决这个问题，通过添加剂的取代基于重量的更新。因此，在非线性滤波问题的背景下，一个新的添加剂粒子更新计划，在其非迭代和迭代形式，提出了基于操纵的创新积分的Kushner-Stratonovich方程。用于非线性和大维度动力系统的识别的数值证据表明，与大多数现有滤波器相比，EnKS的非迭代版本具有实质性的优越性能。成本更高的迭代版本，虽然概念上优雅，大多数情况下似乎影响其非迭代对应的重建精度的边际改善。在所报告的数值比较中，突出的是也使用添加剂更新的包围卡尔曼滤波器（EnKF）的变体，尽管具有卡尔曼滤波器的许多固有限制。
英文摘要：
Despite the cheap availability of computing resources enabling faster Monte Carlo simulations, the potential benefits of particle filtering in revealing accurate statistical information on the imprecisely known model parameters or modeling errors of dynamical systems, based on limited time series data, have not been quite realized. A major numerical bottleneck precipitating this under-performance, especially for higher dimensional systems, is the progressive particle impoverishment owing to weight collapse and the aim of the current work is to address this problem by replacing weight-based updates through additive ones. Thus, in the context of nonlinear filtering problems, a novel additive particle update scheme, in its non-iterative and iterative forms, is proposed based on manipulations of the innovation integral in the governing Kushner-Stratonovich equation. Numerical evidence for the identification of nonlinear and large dimensional dynamical systems indicates a substantively superior performance of the non- iterative version of the EnKS vis-à-vis most existing filters. The costlier iterative version, though conceptually elegant, mostly appears to effect a marginal improvement in the reconstruction accuracy over its non-iterative counterpart. Prominent in the reported numerical comparisons are variants of the Ensemble Kalman Filter (EnKF) that also use additive updates, albeit with many inherent limitations of a Kalman filter.
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