Abstract
The accuracy of underwater acoustic positioning is greatly influenced by both systematic error and gross error. Aiming at these problems, the paper proposes a robust zero-difference Kalman filter based on the random walk model and the equivalent gain matrix. The proposed algorithm takes systematic error as a random walk process, and estimates it together with the position parameters by using zero-difference Kalman filter. In addition, the equivalent gain matrix based on the robust estimation of Huber function is constructed to resist the influence of gross error. The proposed algorithm is verified by the simulation experiment and a real one for underwater acoustic positioning. The results demonstrate that the robust zero-difference Kalman filter can control both the effects of systematic error and gross error without amplifying the influence of the observation random noise, which is obviously superior to the zero-difference least squares (LS), the single-difference LS and zero-difference Kalman filter in underwater acoustic positioning.
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References
Yoerger DR, Jakuba MV, Bradley AM et al (2007) Techniques for deep sea near bottom survey using an autonomous underwater vehicle[J]. Int J Robot Res 26(1):41–54
Stutters L, Liu H, Tiltman C et al (2008) Navigation technologies for autonomous underwater vehicles[J]. IEEE Trans Syst Man Cybernet Part C (Applications and Reviews) 38(4):581–589
Yang Y, Xu T, Xue S (2018) Progresses and prospects in developing marine geodetic datum and marine navigation of China[J]. J Geodesy Geoinf Sci 1(1):17–25
Frankenthal S (1984) Beam-intensity calculations with uncertain sound speed profiles[J]. J Acoust Soc Am 76(1):198–204
Leonard J, Bennett AA, Smith CM, Feder HJS (1998) Autonomous underwater vehicle navigation. MIT Marine Robotics Laboratory Technical memorandum 98–1
Erol-Kantarci M, Mouftah HT, Oktug S (2011) Localization techniques for underwater acoustic sensor networks[J]. IEEE Commun Surv Tut 13(3):487–502
Averbakh VS, Bogolyubov BN, Dubovoi YA et al (2002) Application of hydroacoustic radiators for the generation of seismic waves[J]. Acoust Phys 48(2):121–127
Sun SB, Yu SN, Shi ZB, Fu J, Zhao CH (2018) A novel single-beacon navigation method for group AUVs based on SIMO model [J]. IEEE Access 99:1–1
Xu PL, Ando M, Tadokoro K (2005) Precise, three-dimensional seafloor geodetic deformation measurements using difference techniques[J]. Earth Planets Space 57:795–808
Zhao S, Wang ZJ, Wu SY et al (2017) A ship-board acoustic difference positioning method based on selection weight iteration[J]. Oil Geophys Prospect 52(6):1150–1155
Zhao JH, Zou YJ, Zhang HM et al (2016) A new method for absolute datum transfer in seafloor control network measurement[J]. J Mar Sci Technol 21(2):216–226
Yan WS, Wei C, Cui RX (2015) Moving long baseline positioning algorithm with uncertain sound speed[J]. J Mech Sci Technol 29(9):3995–4002
Paziewski J, Wielgosz P (2015) Accounting for Galileo–GPS inter-system biases in precise satellite positioning[J]. J Geodesy 89(1):81–93
Zhou JW (1989) Classical error theory and robust estimation[J]. J Surve Mapping 18(02):115–120
Yang Y, Song L, Xu T (2002) Robust estimator for correlated observations based on bifactor equivalent weights[J]. J Geodesy 76(6–7):353–358
Xu PL (2005) Sign-constrained robust least squares, subjective breakdown point and the effect of weights of observations on robustness[J]. J Geodesy 79(1–3):146–159
Wang J, Xu C, Wang J (2008) Applications of robust kalman filtering schemes in GNSS navigation. Proceedings of the International Symposium on GPS/GNSS. Yokohama, Japan, pp 308–316
Yang C, Shi WZ, Chen W (2019) Robust M-M unscented Kalman filtering for GPS/IMU navigation[J]. J Geodesy Geodynamics 93:1093–1194
Yang YX, He H, Xu G (2001) Adaptively robust filtering for kinematic geodetic positioning[J]. J Geodesy 75(2–3):109–116
Wang JT, Xu TH, Wang ZJ (2020) Adaptive robust unscented Kalman filter for AUV acoustic navigation[J]. Sensors 20(1):60. https://doi.org/10.3390/s20010060
Gagnon K, Chadwell CD, Norabuena E (2005) Measuring the onset of locking in the Peru-Chile trench with GPS and acoustic measurements[J]. Nature 434(7030):205–208
Chadwell CD (2003) Shipboard towers for Global Positioning System antennas[J]. Ocean Eng 30(12):1467–1487
Spiess FN, Chadwell CD, Hildebrand JA et al (1998) Precise GPS/Acoustic positioning of seafloor reference points for tectonic studies[J]. Phys Earth Planet Interiors 108(2):101–112
Yi CH, Ren WJ, Chai W (2009) Analysis on error of secondary acoustic positioning system[J]. Oil Geophys Prospect 44(2):136–139
Maybeck PS (1979) Stochastic models, estimation and control[J], vol 1. Academic Press, Inc., Cambridge, pp 1–16
Goad CC, Chadwell CD (1993) Investigation for improving GPS orbits using a discrete sequential estimator and stochastic models of selected physical processes[R]. Goddard Space Flight Center, Greenbelt, p 42
Huber PJ (1964) Robust estimation of a location parameter[J]. Ann Math Stat 35(1):73–101
Huber PJ (2011) Robust statistics[J]. J Am Stat Assoc 78(381):1248–1251
Yamada T, Ando M, Tadokoro K et al (2002) Error evaluation in acoustic positioning of a single transponder for seafloor crustal deformation measurements[J]. Earth Planets Space 54(9):871–882
Acknowledgements
The study was funded by National Key Research and Development Program of China (2016YFB0501701), National Natural Science Foundation of China (41931076, 41874032 and 41731069).
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Wang, J., Xu, T., Zhang, B. et al. Underwater acoustic positioning based on the robust zero-difference Kalman filter. J Mar Sci Technol 26, 734–749 (2021). https://doi.org/10.1007/s00773-020-00766-x
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DOI: https://doi.org/10.1007/s00773-020-00766-x