A two-stage Kalman filtering approach using GNSS and smartphone sensors for seismogeodetic applications

Recently, an enormous number of concepts have been introduced as new insights into seismogeodetic tools and algorithms. Integration of Global Navigation Satellite Systems (GNSS) with accelerometers is a well-known and widely used approach for estimating co-seismic displacements. In this study, we present a two-stage Kalman Filtering (TSKF) approach for seismogeodetic applications with low-cost accelerometers embedded in smartphones. The TSKF is initialized after a cost-effective and magnetometer-aided attitude estimation of accelerations in the sensor frame with respect to the local geodetic (topocentric) frame using the Singular Value Decomposition (SVD) method. In the first stage of TSKF, correlated noise processes in GNSS positions identified by the Allan Variance (AV) analysis are estimated with a linear Kalman Filter (LKF) and displacements are reflected in the innovation sequence of the LKF. In the second stage, the innovation sequence of the first stage LKF is integrated with the smartphone accelerations by a multi-rate Kalman Filter. The performance of TSKF was evaluated with harmonic motion and earthquake experiments using a single-axis shake table in a high multipath environment. Results of harmonic motion experiments showed that TSKF can produce mm-level amplitude deviations however the effect of phase shift decreases the performance and may cause mm to cm-level root mean square (RMS). On the other hand, the performance of the TSKF in earthquake experiments resulted in mm-level RMS values. In addition, comparisons of TSKF with an existing method i.e. the Multi-Rate Kalman Filter (MKF) show that TSKF may significantly increase the performance of displacement estimations.