Implementation of robust estimation in GPS networks using the Artificial Bee Colony algorithm

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.