提出自适应筛选方法，动态确定状态子空间维度以控制误差。
Filtering with Randomised Observations: Sequential Learning of Relevant Subspace Properties and Accuracy Analysis
- 基于随机观测设计自适应学习机制，动态选择有效子空间。
- 理论证明了观测随机性对追踪误差的上限约束。
- 适合需要高效滤波与误差可控的复杂系统建模场景。
状态估计融合观测数据与数学模型，在众多应用中至关重要，通常采用滤波方法如集合卡尔曼滤波。本文研究在固定、随机及自适应部分观测下的连续集合卡尔曼滤波信号追踪性能。建立了观测算子随机性下期望信号追踪误差的严格界。此外，提出一种序列学习方案，通过权衡观测复杂度与估计精度，自适应确定确保滤波误差有界的最小状态子空间维数。该方法不仅实现误差控制，还系统性地识别出与滤波相关的底层动力学子空间大小。
原文摘要 · Abstract (English)
State estimation that combines observational data with mathematical models is central to many applications and is commonly addressed through filtering methods, such as ensemble Kalman filters. In this article, we examine the signal-tracking performance of a continuous ensemble Kalman filtering under fixed, randomised, and adaptively varying partial observations. Rigorous bounds are established for the expected signal-tracking error relative to the randomness of the observation operator. In addition, we propose a sequential learning scheme that adaptively determines the dimension of a state subspace sufficient to ensure bounded filtering error, by balancing observation complexity with estimation accuracy. Beyond error control, the adaptive scheme provides a systematic approach to identifying the appropriate size of the filter-relevant subspace of the underlying dynamics.
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