Summary The accuracy and sampling rate of a coseismic displacement and velocity waveform can be improved by fusing Global Navigation Satellite System (GNSS) and strong motion (SM) sensor data with a multi-rate Kalman filter. However, many studies have shown that the noise in GNSS coseismic waveforms includes colored noise, and it is challenging to obtain proper GNSS and SM fusion results if the GNSS colored noise is not accurately represented. In this paper, we propose a colored noise multi-rate Kalman filter, which uses a stochastic model for modeling the GNSS colored noise to achieve an accurate fusion of data from GNSS and SM for different sampling rates. In addition, we also propose an estimation method for the multi-rate Kalman filter stochastic model under colored noise to achieve the optimal adaptive fusion of GNSS and SM data. After the reliability of the proposed method was confirmed using Monte Carlo simulations and earthquake engineering data tests, the proposed method was applied to data collected from the 2019 Mw 7.1 Ridgecrest earthquake and 2016 Mw 7.8 Kaikoura earthquake. The test results show that the proposed method can effectively fuse GNSS and SM data and accurately obtain broadband coseismic displacement and velocity waveforms.

中文翻译：

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自适应有色噪声多速率卡尔曼滤波器及其在同震变形中的应用

总结 通过将全球导航卫星系统 (GNSS) 和强震 (SM) 传感器数据与多速率卡尔曼滤波器融合，可以提高同震位移和速度波形的精度和采样率。然而，许多研究表明GNSS同震波形中的噪声包括有色噪声，如果不能准确表示GNSS有色噪声，则很难获得正确的GNSS和SM融合结果。在本文中，我们提出了一种有色噪声多速率卡尔曼滤波器，它使用随机模型对 GNSS 有色噪声进行建模，以实现不同采样率下 GNSS 和 SM 数据的准确融合。此外，我们还提出了一种有色噪声下多速率卡尔曼滤波随机模型的估计方法，以实现GNSS和SM数据的最优自适应融合。在使用蒙特卡罗模拟和地震工程数据测试确认所提出方法的可靠性后，将所提出的方法应用于从 2019 Mw 7.1 Ridgecrest 地震和 2016 Mw 7.8 Kaikoura 地震收集的数据。测试结果表明，该方法能够有效融合GNSS和SM数据，准确获取宽带同震位移和速度波形。