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An Adaptive Loose Integration Method for High-Rate GNSS and Strong Motion with Colored Noise.

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Title: An Adaptive Loose Integration Method for High-Rate GNSS and Strong Motion with Colored Noise.
Authors: Fan, Shijie1 (AUTHOR), Wang, Chuan1,2 (AUTHOR), Zang, Jianfei1,3 (AUTHOR) jianfeizang@upc.edu.cn, Mu, Chunlin2,4 (AUTHOR), Yang, Zhengyi1 (AUTHOR), Chen, Guanxu2,3 (AUTHOR), Xu, Caijun3,4 (AUTHOR)
Source: Remote Sensing. Jun2026, Vol. 18 Issue 12, p1932. 21p.
Subjects: Kalman filtering, Shaking table tests, Global Positioning System, Ground motion, Measurement errors, Random noise theory
Abstract: Highlights: What are the main findings? A novel two-step loose integration method is proposed to jointly mitigate high-rate GNSS colored noise and strong-motion baseline shift. Colored noise in high-rate GNSS is suppressed by using a colored-noise-based Kalman filter with an adaptive strategy. What are the implications of the main findings? The proposed method improves the accuracy and stability of coseismic displacement estimation, achieving an approximately 21% RMSE reduction compared with the KFb solution in the shake table experiment. Validations using a shake table experiment and three real earthquake cases demonstrate that the method effectively suppresses GNSS low-frequency colored noise and SM baseline shift, enabling more reliable broadband coseismic displacement. Integration of high-rate Global Navigation Satellite Systems (GNSS) with strong motion (SM) sensors enables accurate broadband coseismic displacements, which are critical for earthquake early warning and rapid source inversion. However, GNSS colored noise and SM baseline shift can degrade the accuracy and stability of the integrated displacements. In this study, we propose a novel loose integration approach where a two-step Kalman filter (KF) is used. In the first step, the high-rate GNSS displacements without colored noise are estimated using an adaptive KF that parameterizes the colored noise. Then, the denoised high-rate GNSS displacements are integrated with SM in the second KF where the baseline shift in SM is parameterized as a random walk process. The effectiveness of the proposed method was validated with co-located high-rate GNSS and strong motion data collected from a shake table experiment, the 2010 Mw 7.2 El Mayor-Cucapah earthquake, the 2016 Mw 7.8 Kaikōura earthquake, and the 2019 Mw 7.1 Ridgecrest earthquake. The results show that the proposed method achieves an RMSE of 1.1 mm, a 21% improvement over the KFb solution when shake table recordings are used as the reference. Application to three real earthquake cases demonstrates that the method effectively mitigates low-frequency GNSS noise and SM baseline shift, resulting in more accurate and stable coseismic displacement estimates. [ABSTRACT FROM AUTHOR]
Copyright of Remote Sensing is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: An Adaptive Loose Integration Method for High-Rate GNSS and Strong Motion with Colored Noise.
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  Data: <searchLink fieldCode="AR" term="%22Fan%2C+Shijie%22">Fan, Shijie</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wang%2C+Chuan%22">Wang, Chuan</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zang%2C+Jianfei%22">Zang, Jianfei</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)<i> jianfeizang@upc.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Mu%2C+Chunlin%22">Mu, Chunlin</searchLink><relatesTo>2,4</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Yang%2C+Zhengyi%22">Yang, Zhengyi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Chen%2C+Guanxu%22">Chen, Guanxu</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Xu%2C+Caijun%22">Xu, Caijun</searchLink><relatesTo>3,4</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Remote+Sensing%22">Remote Sensing</searchLink>. Jun2026, Vol. 18 Issue 12, p1932. 21p.
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  Data: <searchLink fieldCode="DE" term="%22Kalman+filtering%22">Kalman filtering</searchLink><br /><searchLink fieldCode="DE" term="%22Shaking+table+tests%22">Shaking table tests</searchLink><br /><searchLink fieldCode="DE" term="%22Global+Positioning+System%22">Global Positioning System</searchLink><br /><searchLink fieldCode="DE" term="%22Ground+motion%22">Ground motion</searchLink><br /><searchLink fieldCode="DE" term="%22Measurement+errors%22">Measurement errors</searchLink><br /><searchLink fieldCode="DE" term="%22Random+noise+theory%22">Random noise theory</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: Highlights: What are the main findings? A novel two-step loose integration method is proposed to jointly mitigate high-rate GNSS colored noise and strong-motion baseline shift. Colored noise in high-rate GNSS is suppressed by using a colored-noise-based Kalman filter with an adaptive strategy. What are the implications of the main findings? The proposed method improves the accuracy and stability of coseismic displacement estimation, achieving an approximately 21% RMSE reduction compared with the KFb solution in the shake table experiment. Validations using a shake table experiment and three real earthquake cases demonstrate that the method effectively suppresses GNSS low-frequency colored noise and SM baseline shift, enabling more reliable broadband coseismic displacement. Integration of high-rate Global Navigation Satellite Systems (GNSS) with strong motion (SM) sensors enables accurate broadband coseismic displacements, which are critical for earthquake early warning and rapid source inversion. However, GNSS colored noise and SM baseline shift can degrade the accuracy and stability of the integrated displacements. In this study, we propose a novel loose integration approach where a two-step Kalman filter (KF) is used. In the first step, the high-rate GNSS displacements without colored noise are estimated using an adaptive KF that parameterizes the colored noise. Then, the denoised high-rate GNSS displacements are integrated with SM in the second KF where the baseline shift in SM is parameterized as a random walk process. The effectiveness of the proposed method was validated with co-located high-rate GNSS and strong motion data collected from a shake table experiment, the 2010 Mw 7.2 El Mayor-Cucapah earthquake, the 2016 Mw 7.8 Kaikōura earthquake, and the 2019 Mw 7.1 Ridgecrest earthquake. The results show that the proposed method achieves an RMSE of 1.1 mm, a 21% improvement over the KFb solution when shake table recordings are used as the reference. Application to three real earthquake cases demonstrates that the method effectively mitigates low-frequency GNSS noise and SM baseline shift, resulting in more accurate and stable coseismic displacement estimates. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Remote Sensing is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.3390/rs18121932
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      – Code: eng
        Text: English
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        PageCount: 21
        StartPage: 1932
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      – SubjectFull: Kalman filtering
        Type: general
      – SubjectFull: Shaking table tests
        Type: general
      – SubjectFull: Global Positioning System
        Type: general
      – SubjectFull: Ground motion
        Type: general
      – SubjectFull: Measurement errors
        Type: general
      – SubjectFull: Random noise theory
        Type: general
    Titles:
      – TitleFull: An Adaptive Loose Integration Method for High-Rate GNSS and Strong Motion with Colored Noise.
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            NameFull: Fan, Shijie
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              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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