基于Oja流的线性时变系统Kalman-Bucy滤波器低秩近似
On the Oja-Flow-Based Low-Rank Approximation of Kalman-Bucy Filters for Linear Time-Varying Systems
AI总结：
该研究针对线性时变系统，通过分析Oja主成分流提出低秩Kalman-Bucy滤波框架，利用结构化假设简化子空间跟踪，为低秩滤波提供理论支撑并经数值实验验证。
AI中文摘要：
本文通过对Oja主成分流的跟踪分析，研究线性时变系统的低秩Kalman-Bucy滤波框架。在关于特征空间及其时变的结构化假设下，我们表明通过调整流的参数，Oja流可保持在时变主导子空间的邻域内，无需精确跟踪该子空间。这些限制性假设确定了一类可处理的线性时变系统，并为低秩滤波提供了理论基础，数值实验也验证了这一点。
英文摘要：
This paper studies a low-rank Kalman-Bucy filtering framework for linear time-varying systems through the tracking analysis of Oja's principal component flow. Under structured assumptions on the eigenspaces and their time variation, we show that the Oja flow can remain in a neighborhood of the time-varying dominant subspace by tuning a parameter of the flow, rather than tracking it exactly. These restrictive assumptions identify a tractable class of linear time-varying systems and provide a theoretical basis for low-rank filtering, as illustrated by a numerical experiment.
