使用和扩展Lomb-Scargle方法对不均采样数据的多变量频率和幅度估计
Martin Seilmayer1, Thomas Wondrak2, Ferran Garcia3
1Staatliche Studienakademie Bautzen, Duale Hochschule Sachsen, Löbauer Strasse 1, 02625 Bautzen, Germany.
Sensors (Basel, Switzerland)
|November 13, 2025
概括
一般化的Lomb-Scargle方法 (LSM) 准确地估计了不规则采样的多变量数据中的频率. 这种强大的技术改进了分析复杂数据集的传统方法,例如太阳活动和超声波测量.
科学领域:
- 数据科学数据科学数据科学
- 天文学 天文学
- 信号处理 信号处理
背景情况:
- 传统的光谱分析方法与不规则采样的数据作斗争,导致显著的偏差.
- 经典的Lomb-Scargle方法 (LSM) 对单变量,不均采样的时间序列有效.
- 将LSM扩展到多变量数据对于分析复杂的现实数据集至关重要.
研究的目的:
- 为了将Lomb-Scargle方法 (LSM) 对具有不规则采样的多变量数据集进行概括.
- 为了使复杂数据中的频率,相位和振幅向量的同时估计.
- 保持LSM的统计稳定性和抗噪能力.
主要方法:
- 重定了移动参数 τ,以保持三角形基础函数在 Rn. 中的直角性.
- 将一般化的LSM应用于随机抽取的2D太阳活动数据 (太阳黑子).
- 将一般化的LSM应用于3D超声速概况数据集,其中包括缺失值和时间动.
主要成果:
- 在太阳活动数据中成功确定了特征频率.
- 在超声波测量中实现了准确的速度估计,尽管数据不完美.
- 通过比较分析,与基于富里埃变换的方法相比,表现出优异的性能.
结论:
- 一般化的LSM提供了一个强大的和统计学上合理的方法,用于在多变量,不规则采样数据中的频率和振幅估计.
- 这种方法显著提高了复杂数据集的分析在诸如太阳物理和医学超声波等领域.
- 导出的置信区间和比较分析验证了该方法的有效性和可靠性.
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