Configuration Analysis of Two-Dimensional Resection Networks
Publication: Journal of Surveying Engineering
Volume 142, Issue 4
Abstract
The optimal configuration of a resection network plays an important role in the precision analysis of free stations. The two conditions of the optimal configuration for distance-only resection networks were derived. Based on the two conditions, the regular sector configuration was proposed, and the character of the optimal configuration was determined. Furthermore, the geometric dilution of precision (GDOP) for a generic direction resection network with n known points was deduced. The conclusion was reached that A-D-E-optimality cannot be simultaneously achieved in the direction resection network. The pursuit of only the lowest GDOP is impractical in engineering, whereas the E-optimality criterion is suitable in such a situation, as shown by cases with three known points. There are typically two E-optimal configurations for a three-known-point direction resection network, and the regular pattern was explored. Finally, the configuration of a heterogeneous resection network was analyzed. An in-depth understanding of the resection network configuration is provided, which is beneficial for developing an initial guess for the optimal resection network configuration in practice.
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Acknowledgments
The authors thank the editor and anonymous reviewers for their time, effort, and helpful comments. The work described in this paper is supported by the National Natural Science Foundation of China (Project No. 51378512).
References
Amiri-Simkooei, A. (2004). “A new method for second order design of geodetic networks: Aiming at high reliability.” Surv. Rev., 37(293), 552–560.
Amiri-Simkooei, A. R., Asgari, J., Zangeneh-Nejad, F., and Zaminpardaz, S. (2012). “Basic concepts of optimization and design of geodetic networks.” J. Surv. Eng., 172–183.
Berné, J. L., and Baselga, S. (2004). “First-order design of geodetic networks using the simulated annealing method.” J. Geod., 78(1), 47–54.
Bishop, A. N., Fidan, B., Anderson, B. D. O., Doğançay, K., and Pathirana, P. N. (2010). “Optimality analysis of sensor-target localization geometries.” Automatica, 46(3), 479–492.
Blewitt, G. (2000). “Geodetic network optimization for geophysical parameters.” Geophys. Res. Lett., 27(22), 3615–3618.
Chang, Y. M., Chen, C. H., and Chen, C. S. (1996). “Optimal observation design of a surveying network using artificial neural network.” Geomat Res. Australas., 64(Jun), 1–16.
Chen, C. S. (2015). “Weighted geometric dilution of precision calculations with matrix multiplication.” Sensors, 15(1), 803–817.
Dare, P., and Saleh, H. (2000). “GPS network design: Logistics solution using optimal and near-optimal methods.” J. Geod., 74(6), 467–478.
Gerasimeko, M. D. (1997). “First order design of the deformation networks with the minimal number of geodetic points and their optimal allocation.” Far East Math Rep., 4, 86–94.
Gerasimenko, M. D., Shestakov, N. V., and Kato, T. (2000). “On optimal geodetic network design for fault-mechanics studies.” Earth Planets Space, 52(11), 985–987.
Grafarend, E. W. (1974). “Optimization of geodetic networks.” Boll. Geod. Sci. Aff., 33(4), 351–406.
Grafarend, E. W., and Sanso, F., eds. (1985). Optimization and design of geodetic networks, Springer Verlag, Berlin.
Howell, K. B. (2001). Principles of fourier analysis, CRC Press, Boca Raton, FL.
Hsu, D. Y. (1994). “Relations between dilutions of precision and volume of the tetrahedron formed by four satellites.” Proc., IEEE Position Location and Navigation Symp., IEEE, New York, NY, 669–676.
Isaacs, J. T., Klein, D. J., and Hespanha, J. P. (2009). “Optimal sensor placement for time difference of arrival localization.” Proc., 48th IEEE Conf. on Decision and Control, IEEE, New York, NY, 7878–7884.
Johnson, H. O., and Wyatt, F. K. (1994). “Geodetic network design for fault-mechanics studies.” Manuscr. Geodaet., 19(5), 309–323.
Kaplan, E. D., and Hegarty, C. J. (2006). Understanding GPS: Principles and applications, Artech House Press, Boston.
Kihara, M., and Okada, T. (1984). “A satellite selection method and accuracy for the global positioning system.” Navig., 31(1), 8–20.
Langley, R. B. (1999). “Dilution of precision.” GPS World, 10(5), 52–59.
Levanon, N. (2000). “Lowest GDOP in 2-D scenarios.” IEEE Proc. Radar Sonar Navig., 147(3), 149–155.
Massatt, P., and Rudnick, K. (1990). “Geometric formulas for dilution of precision calculations.” Navig., 37(4), 379–391.
Moreno-Salinas, D., Pascoal, A. M., and Aranda, J. (2011). “Optimal sensor placement for underwater positioning with uncertainty in the target location.” Proc., 2011 IEEE Int. Conf. on Robotics and Automation, IEEE, New York, NY, 2308–2314.
Sairo, H. D., Akopian, D., and Takala, J. (2003). “Weighted dilution of precision as quality measure in satellite positioning.” IEEE Proc. Radar Sonar Navig., 150(6), 430–436.
Seemkooei, A. A. (2001a). “Comparison of reliability and geometrical strength criteria in geodetic networks.” J. Geod., 75(4), 227–233.
Seemkooei, A. (2001b). “Strategy for designing geodetic network with high reliability and geometrical strength.” J. Surv. Eng., 104–117.
Ucinsky, D. (2005). Optimal measurement methods for distributed parameter system identification, CRC Press, Boca Raton, FL.
Xue, S., Yang, Y., Dang, Y., and Chen, W. (2014). “Dynamic positioning configuration and its first-order optimization.” J. Geod., 88(2), 127–143.
Yarlagadda, R., Ali, I.,Al-Dhahir, N., and Hershey, J. (2000). “Gps gdop metric.” IEE Proc. Radar Sonar Navig., 147(5), 259–264.
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© 2016 American Society of Civil Engineers.
History
Received: Jan 7, 2015
Accepted: Mar 15, 2016
Published online: Apr 14, 2016
Discussion open until: Sep 14, 2016
Published in print: Nov 1, 2016
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