非线性映射图像集的随机近似及其在滤波中的应用
Randomized Approximations of the Image Set of Nonlinear Mappings with Applications to Filtering
AI总结：
本文提出基于场景设计的随机算法近似非线性映射的图像集，引入最小体积近似以保证低违反概率，并开发新的随机预测-校正滤波器，扩展了高斯和集值滤波器并借鉴现代工具如粒子滤波。
摘要：
本文旨在双方面：第一部分利用近期场景设计结果，开发随机算法近似非线性映射的图像集，即通过非线性函数将集合映射为可能有噪声的集合。我们引入最小体积近似，其特点是保证低违反概率，即允许图像集中的某些点不在近似集合中，但该概率保持在预设阈值以下。第二部分将此思想用于开发新的随机预测-校正滤波器。这些滤波器是高斯和集值滤波器的自然扩展和接近，并与粒子滤波等现代工具有相似之处。
英文摘要：
The aim of this paper is twofold: In the first part, we leverage recent results on scenario design to develop randomized algorithmsfor approximating the image set of a nonlinear mapping, that is, a (possibly noisy) mapping of a set via a nonlinear function.We introduce minimum-volume approximations which have the characteristic of guaranteeing a low probability of violation, i.e.,we admit for a probability that some points in the image set are not contained in the approximating set,but this probability is kept below a pre-specified threshold.In the second part of the paper, this idea is then exploited to develop a new family of randomized prediction-corrector filters.These filters represent a natural extension and rapprochement of Gaussian and set-valued filters,and bear similarities with modern tools such as particle filters.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
