Abstract
This paper addresses the common issue of locating an Underwater Vehicle. Usually, the positioning of a vehicle is based on the propagation of electromagnetic waves, using systems such as the Global Positioning System. However, water, and particularly salty water, makes the use of electromagnetic waves impractical due to the attenuation caused by the high conductivity of the medium. Hence, the most reliable way to transmit information underwater is by using sound waves and many technologies have emerged to solve the positioning problem in this way. Technologies such as Long BaseLine (LBL), Short BaseLine (SBL) and Ultra-Short BaseLine (USBL) are the most frequently used underwater. These technologies are based on the use of multiple emitters in the case of LBL and SBL, or multiple receivers in the case of USBL. This paper describes a way of finding a vehicle location, on-board, based on the measurement at the vehicle by a single receiver of the phase of an acoustic sine wave transmitted from a single emitter that is at a fixed and known location. The method also uses other proprioceptive measurements: vehicle’s velocity and heading. An algorithm based on contractors and bisections scatters the solution space searching for all possible solutions (positions in this case) to the set of equations. Moreover, this paper introduces the Time Constraint Satisfaction Problem. Indeed, the proposed algorithm does not compute the solutions from measurements at a single point in time, rather it uses a set of measurements taken over a time window and stored in a buffer. As a result, the location is not only known at the latest instant but the past locations can be tracked back over the length of the chosen time window.
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References
Araya, I., Neveu, B., Trombettoni, G.: Exploiting common subexpressions in numerical C. In: Stuckey, P. J. (ed.) Principles and Practice of Constraint Programming, vol. 5202. In: Lecture Notes in Computer Science, pp. 342–357. Springer, Berlin (2008)
Aubry C., Desmare R., Jaulin L.: Loop detection of mobile robots using interval analysis. Automatica 49(2), 463–470 (2013)
Benhamou, F., Goualard, F., Granvilliers, L., Puget, J.-F.: Revising hull and box consistency. In: International Conference on Logic Programming, Citeseer (1999)
Chabert G., Jaulin L.: Contractor Programming. Artif. Intell. 173, 1079–1100 (2009)
Drevelle, V., Bonnifait, P.: Localization confidence domains via set inversion on short-term trajectory. IEEE Trans. Robot. 29(5), 1244–1256 (2013)
Galton I.: Analog-input digital phase-locked loops for precise frequency and phase demodulation. IEEE Trans. Circuits Syst. II Analog Digit. Signal Process. 42(10), 621–630 (1995)
Gordon N., Sanjeev Arulampalam M., Maskell S., Clapp T.: A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans. Signal Process. 50(2), 174–188 (2002)
Guyonneau, R., Lagrange, S., Hardouin, L., Lucidarme, P., et al.: Interval analysis for kidnapping problem using range sensors. In: SWIM’11 Small Workshop on Interval Methods (2011)
Jaulin L.: A nonlinear set-membership approach for the localization and map building of an underwater robot using interval constraint propagation. IEEE Trans. Robot. 25(1), 88–98 (2009)
Jaulin L.: Robust set membership state estimation; application to underwater robotics. Automatica 45(1), 202–206 (2009)
Jaulin, L.: Solving set-valued constraint satisfaction problems. In: SCAN 2010, Lyon, France (2010)
Jaulin L., Walter E.: Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis. Math. Comput. Simul. 35(2), 123–137 (1993)
Kieffer, M., Jaulin, L., Walter E.: Guaranteed recursive nonlinear state estimation using interval analysis. In: Proceedings of the 37th IEEE Conference on Decision and Control, pp. 3966–3971, Tampa (1998)
Lindsey W.C., Chie C.M.: A survey of digital phase-locked loops. Proc. IEEE 69(4), 410–431 (1981)
Marzullo, K.A.: Maintaining the time in a distributed system: an example of a loosely-coupled distributed service (synchronization, fault-tolerance, debugging). PhD thesis (1984)
Meizel D., Leveque O., Jaulin L., Walter E.: Initial localization by set inversion. IEEE Trans. Robot. Autom. 18(6), 966–971 (2002)
Opderbecke, J.: At-sea calibration of a USBL underwater vehicle positioning system. In: MTS/IEEE Conference Proceedings, OCEANS ’97, vol 1, pp. 721–726 (1997)
Smith, S.M., Kronen, D.: Experimental results of an inexpensive short baseline acoustic positioning system for auv navigation. In: MTS/IEEE Conference Proceedings, OCEANS ’97, vol. 1, pp. 714–720 (1997)
Vickery, K.: Acoustic positioning systems: a practical overview of current systems. In: Proceedings of the Workshop on Autonomous Underwater Vehicles, 1998, AUV’98, pp. 5–17, IEEE (1998)
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Ibn Seddik, M.S., Jaulin, L. & Grimsdale, J. Phase Based Localization for Underwater Vehicles Using Interval Analysis. Math.Comput.Sci. 8, 495–502 (2014). https://doi.org/10.1007/s11786-014-0197-6
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DOI: https://doi.org/10.1007/s11786-014-0197-6
Keywords
- Interval analysis
- Acoustic localization
- Underwater localization
- GPS
- USBL
- LBL
- Time constraint satisfaction problem
- TCSP
- Constraint satisfaction
- CSP
- Contractor
- Sequential Monte Carlo
- Particle filters