用可能性理论改进卡尔曼滤波，更好处理知识不足带来的不确定性
Redesigning the ensemble Kalman filter with a dedicated model of epistemic uncertainty
- 用可能性理论建模认知不确定性，替代传统概率假设
- 小样本下表现更优，甚至在随机不确定性场景中超越标准滤波器
- 适合高不确定性、数据稀缺的实际系统建模
在不确定性量化领域，如何串行融合时间观测信息是一个普遍问题。传统概率框架下的滤波方法常难以刻画源于知识不足的认知不确定性。本文提出一种可能性的集成卡尔曼滤波器，用于此类场景，并分析其性质。基于可能性理论描述认知不确定性具有哲学上的合理性，且能为标准集成卡尔曼滤波中的常见启发式方法提供严谨解释。该方法在小样本条件下表现出强鲁棒性，即使在真实随机不确定性下，也可在相同样本量下优于传统集成卡尔曼滤波器。
原文摘要 · Abstract (English)
The problem of incorporating information from observations received serially in time is widespread in the field of uncertainty quantification. Within a probabilistic framework, such problems can be addressed using standard filtering techniques. However, in many real-world problems, some (or all) of the uncertainty is epistemic, arising from a lack of knowledge, and is difficult to model probabilistically. This paper introduces a possibilistic ensemble Kalman filter designed for this setting and characterizes some of its properties. Using possibility theory to describe epistemic uncertainty is appealing from a philosophical perspective, and it is easy to justify certain heuristics often employed in standard ensemble Kalman filters as principled approaches to capturing uncertainty within it. The possibilistic approach motivates a robust mechanism for characterizing uncertainty which shows good performance with small sample sizes, and can outperform standard ensemble Kalman filters at given sample size, even when dealing with genuinely aleatoric uncertainty.
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