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

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.