zonotopic混合滤波器
The Zonotopic Mixture Filter
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中文总结 AI 辅助
本文提出zonotopic混合噪声模型，推导对应zonotopic混合滤波器，结合概率与有界噪声框架，通过数值示例验证其优势。
中文摘要 AI 辅助
状态估计通常可表述为概率框架或未知有界框架。前者需要完全指定噪声分布，通常具有无界支撑；后者可得到带保证的包围集，不包含概率权重。为衔接这两种噪声描述，本文提出zonotopic混合噪声模型：噪声通过按固定概率从有限集合中抽取一个zonotope，再从该zonotope中取任意元素生成。针对该噪声模型，本文推导了zonotopic混合滤波器，其在模式历史上传播一组zonotopic卡尔曼滤波器，丢弃被数据证伪的历史，并按相对概率对幸存历史加权。所得状态包围集具有保证的覆盖概率，对所有与边界兼容的噪声实现均有效，且贪婪混合约简方案在保持统计保证的同时，使表示易于处理。数值示例说明了所提方法及其相对于相关状态估计方法的潜在优势。
英文摘要
State estimation is commonly posed in either a probabilistic or an unknown-but-bounded framework. The former requires a fully specified noise distribution, typically with unbounded support, while the latter yields guaranteed enclosures that carry no probabilistic weighting. Bridging these noise descriptions, this paper proposes a zonotopic mixture noise model, in which the noise is generated by drawing a zonotope from a finite collection according to fixed probabilities and then realizing an arbitrary element of it. For this noise model, we derive the zonotopic mixture filter, which propagates a bank of zonotopic Kalman filters over mode histories, discards the histories falsified by the data, and weights the surviving ones by their relative probability. The resulting state enclosures yield guaranteed coverage probabilities and remain valid for every noise realization compatible with the bounds, and a greedy mixture reduction scheme preserves these statistical guarantees while keeping the representation tractable. Numerical examples illustrate the proposed approach and its potential benefits over related state estimation methods.
