On the use of two L1 norm minimization methods in geodetic networks

Document Type : Original Article

Author

Department of Geomatics Engineering, Faculty of Civil Engineering and Transportation, University of Isfahan, Isfahan, Iran

Abstract

L1 norm adjustment is a powerful technique to detect gross errors in geodetic observations. This paper
investigates the results of two formulations that provide the L1 norm adjustment of a linear functional model.
The usual method for implementation of the L1 norm adjustment leads to solving a linear programming (LP)
problem. The formulation of the L1 norm minimization is presented based on the LP problem for a rank
deficient linear(ized) system of equations. Then, an alternative technique is explained based on the least
squares residuals. The results are tested on both linear and non-linear functional models, which confirm the
efficiency of both formulations. The results also indicate that the L1 norm minimization, compared to the
weighted least squares method, is a robust technique for the detection of blunders in geodetic observations.
Finally, this contribution presents a data snooping procedure to the residuals obtained by the L1 norm
minimization method.

Keywords

Main Subjects

References

Amiri-Simkooei, A. (2003). Formulation of L 1 norm minimization in Gauss-Markov models. Journal of Surveying Engineering, 129(1), 37-43.
Baarda, W. (1968). A Testing procedijre for use in geodetic networks. Publication on Geodesy, New series 2, No. 5, Netherlands Geodetic Commission, Delft.
Bazaraa, M. S., Jarvis, J. J., & Sherali, H. D. (2011). Linear programming and network flows. John Wiley & Sons.
Chen, Y. Q. (1984). Analysis of deformation surveys-A generalized method. Tech. Report No. 94, Dept. of Surveying Engineering, University of New Brunswick.
Dantzig, G. B. (1963). Linear Programming and Extensions. Princeton landmarks in mathematics and physics. Princeton University Press, Princeton, N. J., 1963.
Kok, J. J. (1984). On data snooping and multiple outlier testing. US Department of Commerce, National Oceanic and Atmospheric Administration, National Ocean Service, Charting and Geodetic Services.
Krarup, T. (1980). Gotterdammerung over least squares adjustment. In Proc. 14th Congress of the International Society of Photogrammetry (Vol. 3, pp. 369-378).
Marshall, J., & Bethel, J. (1996). Basic concepts of L 1 norm minimization for surveying applications. Journal of surveying engineering, 122(4), 168-179.
Mikhail, E. M., & Ackermann, F. E. (1976). Observations and least squares. IEP-A dun-Donnelley Publisher.
Pope, A. J. (1976). The statistics of residuals and the detection of outliers (No. NOS-65-NGS-1), NOAA Tech. Report NOS 65 NGS 1, National Geodetic Survey, Rockville, Md.
Roos, C., Terlaky, T., & Vial, J. P. (1997). Theory and algorithms for linear optimization: an interior point approach. John Wiley & Son Ltd.
Secord, J. M. (1985). Implementation of a generalized method for the analysis of deformation surveys. Department of Surveying Engineering, University of New Brunswick.
Earth Observation and Geomatics Engineering
Volume 2, Issue 1
June 2018
Pages 1-8

Files

Share

How to cite

Statistics