Preliminary Results of the Sign-Constrained Robust Least Squares Method in a Leveling Network

摘要

The method of least squares yields the most likely solution for a set of redundant observation data provided that both functional and stochastic model are correct and only random errors affect the observations. However, the method of least squares is very sensitive to model errors and gross errors. Therefore, spatial data analysis must be performed using rigorous robust statistical procedures to reduce bad effects of outlying observations on parameter estimation. A newly introduced robust estimation method, sign constrained robust least squares, may be applied to geodetic networks. Nevertheless, the implementation of the method may require a good computational technique. In this study, we propose the use of the shuffled frog leaping algorithm which is an evolutionary optimization algorithm to solve sign-constrained robust least squares estimation problem in a geodetic network. The constraints in the optimization problem can be dealt with penalty function approach. The practical results are given in a leveling network.