Application of robust estimation in geodesy using the harmony search algorithm

Abstract

The modern era utilizes high-tech measurement techniques such as GNSS (global navigation satellite system) to determine the positions of points. Traditionally, the coordinates of these points are estimated using the least squares (LS) method. However, robust estimation yields ‘less-biased’ results than the LS method in the presence of errors in measurements. One robust estimation method is called the least median squares (LMS) method. This method involves the minimization of the median of the squared residuals and can be implemented using an optimization method, i.e. the harmony search algorithm (HSA). The HSA is a music-inspired metaheuristic optimization algorithm that can be used for minimization or maximization problems. In this study, using the LMS method for GNSS and levelling measurements by employing the HSA, a new approach is put forward. Initially, some discussions about the theoretical foundations of RE and HSA are given. Then, two numerical examples are provided to verify the success of the proposed approach.