Unscented Kalman Filter–Based Fusion of GNSS, Accelerometer, and Rotation Sensors for Motion Tracking
Publication: Journal of Structural Engineering
Volume 150, Issue 7
Abstract
In this paper, we present an unscented Kalman filter (UKF) for fusion of information from an accelerometer, global navigation satellite system (GNSS) instrumentation, and rotational sensor recordings of structural motion. Seismic and structural motions do not only include translations, but further incorporate torsion and twisting of the ground and/or structural components. Accelerometer and GNSS positions are known to be prone to errors introduced by rotation, such as (1) gravitational leakage, (2) misorientation, and (3) antenna pole tilt. In alleviating such effects, we propose fusion of information from six component (6C) data—3C translation and 3C rotation—and demonstrate its applicability for motion tracking on a flexible pedestrian bridge. To simulate a variety of load effects, the bridge was subjected to various sources of excitation such as hammer impulses, jumping, twisting, and running, as well as a combination thereof named the “artificial coupled forcing.” The rotation errors of both the accelerometer and GNSS-estimated positions are corrected via a UKF-based fusion. We further identify the modal properties of the monitored bridge, excited by the different excitation sources, using a covariance driven stochastic subspace identification. The twisting of the bridge is shown to be a primary source of rotation errors. These errors ought to be corrected because their order of magnitude can be as large as the actual signal in the case of GNSS positions and up to 10% for accelerometer sensors. We compare the proposed UKF-based fusion for 6C motion tracking against a simplified linear Kalman filter and demonstrate the potential of the former for real-time, broadband, rotation-free displacement, velocity, and rotations tracking.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All seismic data used in this paper are discoverable and openly accessible at the SED Seismic Network datacenter and on EIDA, under network code 9E (SED at ETH Zurich 2014]. The station code for Aaresteg is AUST, and positions are indicated by the location code using the same convention used in this paper (e.g., “ME”). Channel codes HG* and HJ* indicate acceleration and rotational channels, respectively. Note that the BlueSeis data has not been deramped. The geodetic data is located in a Zenodo folder (Rossi et al. 2023a).
Acknowledgments
Pascal Graf from the ELAB team at SED has been indispensable in managing the instrumentation at Aaresteg. The use of the blueSeis-3A was only possible due to Donat Fäh, the Swiss National Science Foundation project 200020_175475/1, and ETH Zürich. This study is funded by the Swiss National Science Foundation within the project 200021_188599. Collaboration from John Clinton is possible in part thanks to the Real-time Earthquake Risk Reduction for a Resilient Europe “RISE” project funded from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 821115. Opinions expressed in this paper solely reflect the authors’ view; the EU is not responsible for any use that may be made of information it contains.
References
Alfakih, M., M. Keche, and H. Benoudnine. 2021. “A Kalman-filter-based fusion method for accurate urban localization.” IET Commun. 15 (5): 653–663. https://doi.org/10.1049/cmu2.12096.
Bernauer, F., et al. 2021. “Rotation, strain, and translation sensors performance tests with active seismic sources.” Sensors 21 (1): 264. https://doi.org/10.3390/s21010264.
Bernauer, F., J. Wassermann, F. Guattari, A. Frenois, A. Bigueur, A. Gaillot, E. de Toldi, D. Ponceau, U. Schreiber, and H. Igel. 2018. “BlueSeis3A: Full characterization of a 3C broadband rotational seismometer.” Seismol. Res. Lett. 89 (2A): 620–629. https://doi.org/10.1785/0220170143.
Bernauer, F., J. Wassermann, and H. Igel. 2012. “Rotational sensors-a comparison of different sensor types.” J. Seismolog. 16 (4): 595–602. https://doi.org/10.1007/s10950-012-9286-7.
Bernauer, F., J. Wassermann, and H. Igel. 2020. “Dynamic tilt correction using direct rotational motion measurements.” Seismol. Res. Lett. 91 (5): 2872–2880. https://doi.org/10.1785/0220200132.
Bock, Y., D. Melgar, and B. W. Crowell. 2011. “Real-time strong-motion broadband displacements from collocated GPS and accelerometers.” Bull. Seismol. Soc. Am. 101 (6): 2904–2925. https://doi.org/10.1785/0120110007.
Boehm, J., A. Niell, P. Tregoning, and H. Schuh. 2006. “Global mapping function (GMF): A new empirical mapping function based on numerical weather model data.” Geophys. Res. Lett. 33 (7): L07304. https://doi.org/10.1029/2005GL025546.
Böse, M., T. H. Heaton, and E. Hauksson. 2012. “Real-time finite fault rupture detector (FinDer) for large earthquakes.” Geophys. J. Int. 191 (2): 803–812. https://doi.org/10.1111/j.1365-246X.2012.05657.x.
Chatzi, E. N., and A. W. Smyth. 2009. “The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing.” Struct. Control Health Monit. 16 (1): 99–123. https://doi.org/10.1002/stc.290.
Chen, Y., P. Guéguen, K. H. Chen, C.-J. Lin, C.-S. Ku, W.-G. Huang, B.-S. Huang, and K.-C. Chen. 2023. “Dynamic characteristics of TAIPEI 101 skyscraper from rotational and translation seismometers.” Bull. Seismol. Soc. Am. 113 (2): 690–709. https://doi.org/10.1785/0120220147.
Chiu, H. C., F. J. Wu, C. J. Lin, H. C. Huang, and C. C. Liu. 2012. “Effects of rotation motions on strong-motion data.” J. Seismolog. 16 (4): 829–838. https://doi.org/10.1007/s10950-012-9301-z.
Clinton, J. F., S. C. Bradford, T. H. Heaton, and J. Favela. 2006. “The observed wander of the natural frequencies in a structure.” Bull. Seismol. Soc. Am. 96 (1): 237–257. https://doi.org/10.1785/0120050052.
Crawford, W. C., and S. C. Webb. 2000. “Identifying and removing tilt noise from low-frequency (\textless0.1 Hz) seafloor vertical seismic data.” Bull. Seismol. Soc. Am. 90 (4): 952–963. https://doi.org/10.1785/0119990121.
Cua, G. 2005. “Creating the virtual seismologist: Developments in ground motion characterization and seismic early warning.” Ph.D. thesis, Dept. of Engineering and Applied Science, California Institute of Technology. https://doi.org/10.7907/M926-J956.
Dahmen, N., R. Hohensinn, and J. Clinton. 2020. “Comparison and combination of GNSS and strong-motion observations: A case study of the 2016 Mw 7.0 Kumamoto earthquake.” Bull. Seismol. Soc. Am. 110 (6): 2647–2660. https://doi.org/10.1785/0120200135.
Dong, S., Z. Li, F. Hu, Z. Yu, and X. Chen. 2023. “TraceNet: An effective deep-learning-based method for baseline correction of near-field acceleration records.” Seismol. Res. Lett. 94 (3): 1656–1669. https://doi.org/10.1785/0220220272.
Farrar, C. R., and K. Worden. 2012. Structural health monitoring. Hoboken, NJ: Wiley.
Farrell, W. 1969. “A gyroscopic seismometer: Measurements during the Borrego earthquake.” Bull. Seismol. Soc. Am. 59 (3): 1239–1245. https://doi.org/10.1785/BSSA0590031239.
Ge, M., G. Gendt, M. Rothacher, C. Shi, and J. Liu. 2008. “Resolution of GPS carrier-phase ambiguities in precise point positioning (PPP) with daily observations.” J. Geod. 82 (7): 389–399. https://doi.org/10.1007/s00190-007-0187-4.
Geng, J., X. Chen, Y. Pan, S. Mao, C. Li, J. Zhou, and K. Zhang. 2019a. “PRIDE PPP-AR: An open-source software for GPS PPP ambiguity resolution.” GPS Solutions 23 (4): 91. https://doi.org/10.1007/s10291-019-0888-1.
Geng, J., Q. Wen, Q. Chen, and H. Chang. 2019b. “Six-degree-of-freedom broadband seismogeodesy by combining collocated high-rate GNSS, accelerometers, and gyroscopes.” Geophys. Res. Lett. 46 (2): 708–716. https://doi.org/10.1029/2018GL081398.
Graizer, V. 1979. “Determination of the true ground displacement by using strong motion records.” Izv. Earth Phys. 15 (12): 875–885.
Graizer, V. M. 1991. “Inertial seismometry methods.” Izv. Earth Phys. 27 (1): 51–61.
Graizer, V. M. 2005. “Effect of tilt on strong motion data processing.” Soil Dyn. Earthquake Eng. 25 (3): 197–204. https://doi.org/10.1016/j.soildyn.2004.10.008.
Guéguen, P., F. Guattari, C. Aubert, and T. Laudat. 2021. “Comparing direct observation of torsion with array-derived rotation in civil engineering structures.” Sensors 21 (142): 1–17. https://doi.org/10.3390/s21010142.
Häberling, S., M. Rothacher, Y. Zhang, J. F. Clinton, and A. Geiger. 2015. “Assessment of high-rate GPS using a single-axis shake table.” J. Geod. 89 (7): 697–709. https://doi.org/10.1007/s00190-015-0808-2.
Haque, M. E., M. F. M. Zain, M. Hannan, M. Jamil, and M. Asikuzzaman. 2015. “Real time prototype to measure structural acceleration and tilt of high-rise building.” Prz. Elektrotech. 1 (2): 179–184. https://doi.org/10.15199/48.2015.02.40.
Hart, G. C., and C. Rojahn. 1979. “A decision-theory methodology for the selection of buildings for strong-motion instrumentation.” Earthquake Eng. Struct. Dyn. 7 (6): 579–586. https://doi.org/10.1002/eqe.4290070607.
Hohensinn, R., R. Stauffer, M. F. Glaner, I. D. Herrera Pinzón, E. Vuadens, Y. Rossi, J. Clinton, and M. Rothacher. 2022. “Low-Cost GNSS and real-time PPP: Assessing the precision of the u-blox ZED-F9P for kinematic monitoring applications.” Remote Sens. 14 (20): 5100. https://doi.org/10.3390/rs14205100.
Igel, H., A. Cochard, J. Wassermann, A. Flaws, U. Schreiber, A. Velikoseltsev, and N. Pham Dinh. 2007. “Broad-band observations of earthquake-induced rotational ground motions.” Geophys. J. Int. 168 (1): 182–196. https://doi.org/10.1111/j.1365-246X.2006.03146.x.
Igel, H., U. Schreiber, A. Flaws, B. Schuberth, A. Velikoseltsev, and A. Cochard. 2005. “Rotational motions induced by the M8.1 Tokachi-oki earthquake, September 25, 2003.” Geophys. Res. Lett. 32 (8): 1–5. https://doi.org/10.1029/2004GL022336.
Izgi, G., E. P. S. Eibl, S. Donner, and F. Bernauer. 2021. “Performance test of the rotational sensor blueSeis-3A in a huddle test in Fürstenfeldbruck.” Sensors 21 (9): 3170. https://doi.org/10.3390/s21093170.
Janusz, P., V. Perron, C. Knellwolf, and D. Fäh. 2022. “Combining earthquake ground motion and ambient vibration recordings to evaluate a local high-resolution amplification model—Insight from the Lucerne area, Switzerland.” Front. Earth Sci. 10 (May): 885724. https://doi.org/10.3389/feart.2022.885724.
Jekeli, C. 2001. Inertial navigation systems with geodetic applications. Berlin: DE GRUYTER.
Julier, S., and J. Uhlmann. 2004. “Unscented filtering and nonlinear estimation.” Proc. IEEE 92 (3): 401–422. https://doi.org/10.1109/JPROC.2003.823141.
Julier, S., J. Uhlmann, and H. Durrant-Whyte. 1995. “A new approach for filtering nonlinear systems.” In Vol. 3 of Proc., 1995 American Control Conf. ACC’95, 1628–1632. Seattle: American Autom Control Council. http://ieeexplore.ieee.org/document/529783/.
Liao, C.-M., F. Bernauer, H. Igel, C. Hadziioannou, and E. Niederleithinger. 2022. “Real-time bridge monitoring using ultrasonic techniques combined with six-component (6-C) measurements.” e-J. Nondestr. Test. 27 (9): 1–10. https://doi.org/10.58286/27184.
Limongelli, M. P., and M. Çelebi. 2019. Seismic structural health monitoring: From theory to successful applications. 1st ed. Cham, Switzerland: Springer.
Lin, C.-J., H.-P. Huang, C.-C. Liu, and H.-C. Chiu. 2010. “Application of rotational sensors to correcting rotation-induced effects on accelerometers.” Bull. Seismol. Soc. Am. 100 (2): 585–597. https://doi.org/10.1785/0120090123.
Lin, C.-J., C.-S. Ku, T.-C. Chi, B.-S. Huang, H.-H. Huang, and C.-C. Liu. 2022. “Correcting the background tilt signal of the horizontal seismometer using a rotation sensor.” Seismol. Res. Lett. 93 (3): 1564–1572. https://doi.org/10.1785/0220210185.
Lindner, F., J. Wassermann, M. C. Schmidt-Aursch, K. U. Schreiber, and H. Igel. 2017. “Seafloor ground rotation observations: Potential for improving signal-to-noise ratio on horizontal OBS components.” Seismol. Res. Lett. 88 (1): 32–38. https://doi.org/10.1785/0220160051.
Mariani, S., and A. Ghisi. 2007. “Unscented Kalman filtering for nonlinear structural dynamics.” Nonlinear Dyn. 49 (1–2): 131–150. https://doi.org/10.1007/s11071-006-9118-9.
Martakis, P., Y. Reuland, M. Imesch, and E. Chatzi. 2022. “Reducing uncertainty in seismic assessment of multiple masonry buildings based on monitored demolitions.” Bull. Earthquake Eng. 20 (9): 4441–4482. https://doi.org/10.1007/s10518-022-01369-0.
Martakis, P., Y. Reuland, A. Stavridis, and E. Chatzi. 2023. “Fusing damage-sensitive features and domain adaptation towards robust damage classification in real buildings.” Soil Dyn. Earthquake Eng. 166 (Mar): 107739. https://doi.org/10.1016/j.soildyn.2022.107739.
Melgar, D., Y. Bock, D. Sanchez, and B. W. Crowell. 2013. “On robust and reliable automated baseline corrections for strong motion seismology.” J. Geophys. Res. Solid Earth 118 (3): 1177–1187. https://doi.org/10.1002/jgrb.50135.
Murray-Bergquist, L., F. Bernauer, and H. Igel. 2021. “Characterization of six-degree-of-freedom sensors for building health monitoring.” Sensors 21 (11): 3732. https://doi.org/10.3390/s21113732.
Nayeri, R. D., S. F. Masri, R. G. Ghanem, and R. L. Nigbor. 2008. “A novel approach for the structural identification and monitoring of a full-scale 17-story building based on ambient vibration measurements.” Smart Mater. Struct. 17 (2): 025006. https://doi.org/10.1088/0964-1726/17/2/025006.
Panzera, F., P. Bergamo, and D. Fäh. 2021. “Canonical correlation analysis based on site- response proxies to predict site-specific amplification functions in Switzerland.” Bull. Seismol. Soc. Am. 111 (4): 1905–1920. https://doi.org/10.1785/0120200326.
Paziewski, J., R. Sieradzki, and R. Baryla. 2018. “Multi-GNSS high-rate RTK, PPP and novel direct phase observation processing method: Application to precise dynamic displacement detection.” Meas. Sci. Technol. 29 (3): 035002. https://doi.org/10.1088/1361-6501/aa9ec2.
Rajaduraimanickam, K., J. Shanmugam, and G. Anitha. 2005. “ADDR-GPS data fusion using Kalman filter algorithm.” In Vol. 2 of Proc., 24th Digital Avionics Systems Conf., New York: IEEE. http://ieeexplore.ieee.org/document/1563447/.
Rauch, H. E., F. Tung, and C. T. Striebel. 1965. “Maximum likelihood estimates of linear dynamic systems.” AIAA J. 3 (8): 1445–1450. https://doi.org/10.2514/3.3166.
Reuland, Y., A. Abi, R. A. Jaoude, P. Lestuzzi, and I. F. C. Smith. 2017. “Usefulness of ambient-vibration measurements for seismic assessment of existing structures.” In Proc., 4th Int. Conf. on Smart Monitoring, Assessment and Rehabilitation of Civil Structures. Winnipeg, MB, Canada: International Society for Structural Health Monitoring of Intelligent Infrastructure.
Reynders, E., J. Houbrechts, and G. De Roeck. 2012. “Fully automated (operational) modal analysis.” Mech. Syst. Sig. Process. 29 (May): 228–250. https://doi.org/10.1016/j.ymssp.2012.01.007.
Rossi, Y., J. Clinton, and P. Graf. 2023a. GNSS data of ambient vibrations and artificial excitations of the Aaresteg bridge. Geneva: Zenodo.
Rossi, Y., K. Tatsis, M. Awadaljeed, K. Arbogast, E. Chatzi, M. Rothacher, and J. Clinton. 2021. “Kalman filter-based fusion of collocated acceleration, GNSS and rotation data for 6C motion tracking.” Sensors 21 (4): 1543. https://doi.org/10.3390/s21041543.
Rossi, Y., K. Tatsis, J. Clinton, E. Chatzi, and M. Rothacher. 2023b. “A new paradigm for structural characterization, including rotational measurements at a single site.” Bull. Seismol. Soc. Am. 113 (6): 2249–2274. https://doi.org/10.1785/0120230026.
SED (Swiss Seismological Service) at ETH Zurich. 2014. Temporary deployments in Switzerland associated with building monitoring. Zürich, Switzerland: ETH Zurich.
Shin, E. H., and N. El-Sheimy. 2007. “Unscented Kalman filter and attitude errors of low-cost inertial navigation systems.” Navig. J. Inst. Navig. 54 (1): 1–9. https://doi.org/10.1002/j.2161-4296.2007.tb00390.x.
Simonelli, A., M. Desiderio, A. Govoni, G. De Luca, and A. Di Virgilio. 2021. “Monitoring local earthquakes in central Italy using 4C single station data.” Sensors 21 (13): 4297. https://doi.org/10.3390/s21134297.
St-Pierre, M., and D. Gingras. 2004. “Comparison between the unscented Kalman filter and the extended Kalman filter for the position estimation module of an integrated navigation information system.” In Proc., IEEE Intelligent Vehicles Symp., 831–835. New York: IEEE.
Suryanto, W., H. Igel, J. Wassermann, A. Cochard, B. Schuberth, D. Vollmer, F. Scherbaum, U. Schreiber, and A. Velikoseltsev. 2006. “First comparison of array-derived rotational ground motions with direct ring laser measurements.” Bull. Seismol. Soc. Am. 96 (6): 2059–2071. https://doi.org/10.1785/0120060004.
Tatsis, K. E., V. K. Dertimanis, and E. N. Chatzi. 2020. “Adaptive process and measurement noise identification for recursive Bayesian estimation.” In Model validation and uncertainty quantification, 361–364. Cham, Switzerland: Springer.
Tatsis, K. E., V. K. Dertimanis, and E. N. Chatzi. 2022. “Sequential Bayesian inference for uncertain nonlinear dynamic systems: A tutorial.” J. Struct. Dyn (1): 236–262. https://doi.org/10.25518/2684-6500.107.
Venkateswara, K., et al. 2017. “Subtracting tilt from a horizontal seismometer using a ground-rotation sensor.” Bull. Seismol. Soc. Am. 107 (2): 709–717. https://doi.org/10.1785/0120160310.
Wan, E., and R. Van Der Merwe. 2000. “The unscented Kalman filter for nonlinear estimation.” In Proc., IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symp. (Cat. No.00EX373), 153–158. New York: IEEE. http://ieeexplore.ieee.org/document/882463/.
Wassermann, J., F. Bernauer, B. Shiro, I. Johanson, F. Guattari, and H. Igel. 2020. “Six-axis ground motion measurements of caldera collapse at Kīlauea Volcano, Hawai’i: More data, more puzzles?” Geophys. Res. Lett. 47 (5): 1–7. https://doi.org/10.1029/2019GL085999.
Wu, M., and A. W. Smyth. 2007. “Application of the unscented Kalman filter for real-time nonlinear structural system identification.” Struct. Control Health Monit. 14 (7): 971–990. https://doi.org/10.1002/stc.186.
Xu, P., C. Shi, R. Fang, J. Liu, X. Niu, Q. Zhang, and T. Yanagidani. 2013. “High-rate precise point positioning (PPP) to measure seismic wave motions: An experimental comparison of GPS PPP with inertial measurement units.” J. Geod. 87 (4): 361–372. https://doi.org/10.1007/s00190-012-0606-z.
Xu, Z., R. Zhu, T. Zheng, and L. Yang. 2021. “The fusion of GPS and gyroscope based on Kalman filter.” In Proc., 2021 Int. Conf. on Intelligent Transportation, Big Data & Smart City (ICITBS), 205–208. New York: IEEE. https://ieeexplore.ieee.org/document/9525971/>(3).
Yu, B., L. Chen, and M. Fatin Fatihur Rahman. 2023. “Design of multi-sensor fusion positioning and navigation method based on federated Kalman filter for low-speed rotorcraft of atmospheric detection.” J. Phys. Conf. Ser. 2428 (1): 012031. https://doi.org/10.1088/1742-6596/2428/1/012031.
Zumberge, J. F., M. B. Heflin, D. C. Jefferson, M. M. Watkins, and F. H. Webb. 1997. “Precise point positioning for the efficient and robust analysis of GPS data from large networks.” J. Geophys. Res. Solid Earth 102 (B3): 5005–5017. https://doi.org/10.1029/96JB03860.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 150 • Issue 7 • July 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Jun 8, 2023
Accepted: Jan 23, 2024
Published online: May 6, 2024
Published in print: Jul 1, 2024
Discussion open until: Oct 6, 2024
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.