Abstract
Geodesy utilizes state of the art data collection techniques such as GPS (Global Positioning System) to acquire locations of points. Traditionally, the coordinates of these points are estimated using the Least Squares (LS) method. Nevertheless, Robust Estimation (RE) yields more accurate results than LS method in the presence of blunders (gross errors) among the data set. For example, the Least Trimmed Squares (LTS) method and the Least Median Squares (LMS) method can be used for this purpose. The first method aims to minimize the sum of the squared residuals by trimming away observations with large residuals. On the other hand, the second method involves the minimization of the median of the squared residuals. Both methods can be implemented using an optimization method, i.e., Artificial Bee Colony (ABC) algorithm. The ABC algorithm is a swarm intelligence (a branch of artificial intelligence) technique that can be used for the solution of minimization or maximization problems. In this paper, using the LTS and LMS methods for GPS data by employing the ABC, a new approach is put forward. Firstly, some discussions about the theoretical principals of RE and ABC are given. Then, a numerical example is used to demonstrate the validity of the proposed approach. Numerical results show that application of the robust estimation to GPS data can easily be carried out by ABC and this approach helps to enhance the reliability of geospatial data for any application of geodesy.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baselga S (2007) Global optimization solution of robust estimation. J Surv Eng 133(3):123–128
Baselga S, Garcia-Asenjo L (2008a) GNSS differential positioning by robust estimation. J Surv Eng 134(1):21–25
Baselga S, Garcia-Asenjo L (2008b) Global robust estimation and its application to GPS positioning. Comput Math Appl 56(3):709–714
Baselga S, Garcia-Asenjo L (2008c) Multipath mitigation by global robust estimation. J Navig 61(3):385–392
Berber M, Hekimoglu S (2003) What is the reliability of conventional outlier detection and robust estimation in trilateration networks? Surv Rev 37(290):308–318
Elbeltagi E, Hegazy T, Grierson D (2005) Comparison among five evolutionary-based optimization algorithm. Adv Eng Inform 19(1):43–53
Elbeltagi E, Hegazy T, Grierson D (2007) A modified shuffled frog-leaping optimization algorithm: applications to project management. Struct Infrastruct Eng 3(1):53–60
Ghilani CD, Wolf PR (2006) Adjustment computations: spatial data analysis. John Wiley & Sons Inc., New Jersey
Huber PJ (1964) Robust estimation of a location parameter. Ann Math Stat 35(2):73–101
Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical Report-TR06, Erciyes University, Engineering Faculty, Computer Engineering Department
Karaboga D, Akay B (2009) A comparative study of Artificial Bee Colony algorithm. Appl Math Comput 214:108–132
Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39(3):459–471
Karaboga D, Basturk B (2008) On the performance of Artificial Bee Colony (ABC) algorithm. Appl Soft Comput 8(1):687–697
Koch KR (1999) Parameter estimation and hypothesis testing in linear models, 2nd edn. Springer, Berlin
Rousseeuw PJ (1984) Least median of squares regression. J Am Stat Assoc 79(388):871–880
Xu P (2005) Sign-constrained robust least squares, subjective breakdown point and the effects of weights of observations on robustness. J Geodesy Berlin 79(1–3):146–159
Yang XS (2008) Nature-inspired metaheuristic algorithms. Luniver Press, UK
Yetkin M (2013) Metaheuristic optimisation approach for designing reliable and robust geodetic networks. Surv Rev 45(329):136–140
Yetkin M, Berber M (2013) Application of the sign-constrained robust least squares method to surveying networks. J Surv Eng 139(1):59–65
Yetkin M, Inal C (2011) L1 norm minimization in GPS networks. Surv Rev 43(323):523–532
Yetkin M, Inal C, Yigit C (2009) Use of the particle swarm optimization for second order design of leveling networks. J Appl Geodesy 3:171–178
Zhang H, Mei C (2011) Local least absolute deviation estimation of spatially varying coefficient models: robust geographically weighted regression approaches. Int J Geogr Inf Sci 25(9):1467–1489
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by: H. A. Babaie
Rights and permissions
About this article
Cite this article
Yetkin, M., Berber, M. Implementation of robust estimation in GPS networks using the Artificial Bee Colony algorithm. Earth Sci Inform 7, 39–46 (2014). https://doi.org/10.1007/s12145-013-0131-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12145-013-0131-5