Integration of GNSS and Strong Motion Accelerometer based on Robust Adaptive Recursive Noise Kalman Filter by Variational Bayesian Approximations

Global Navigation Satellite System (GNSS) allows for precise monitoring of ground displacements, offering accuracies ranging from millimeters to centimeters, and sample rates varying between 1Hz and 50Hz. However, the GNSS observation signal is susceptible to the presence of a complex seismic environment with vegetation cover and strong external dynamic interference, in which case its accuracy and reliability cannot meet the requirements of coseismic deformation monitoring. Strong motion (SM) accelerometers, as a kind of inertial sensor, are capable of recording middle-rate to high-rate ground accelerations without electromagnetic signal interference and demonstrate stable working performance. An accurate displacement series can be obtained by combining GNSS and SM accelerometers. Usually, a Kalman filter is employed to merge GNSS displacements and SM acceleration data, using priori fixed noise values for both datasets. However, due to the time-varying errors introduced by the aforementioned disturbances, employing fixed noise for GNSS displacements is inappropriate. In this study, a recursive noise Kalman filter using variational Bayesian approximations is employed. The GNSS displacement noise covariances' sufficient statistics are adaptively estimated through iterative processes. Additionally, robust equivalent weight functions and adaptive factor scaling based on predicted residuals are incorporated into the estimation process to mitigate outliers. The proposed method's performance is validated through a shake table experiment. In standard shake table test, it shows an accuracy enhancement of up to 21% compared to the conventional Kalman filter, achieving a correlation coefficient (CC) of 0.97. When outliers are introduced into GNSS displacement data, the proposed method yields up to 49% greater accuracy than the Kalman filter, with a CC of 0.96 relative to references.