Study On Robustness Of Robust Estimation Methods Under The Condition Of Unequal Weighted Observations

Robust estimation methods have been widely used in the disciplines of surveying and mapping and related fields as they are put forward. Robust estimation is a theory based on the real, rather than the ideal, distribution of data. Robust estimation method can effectively eliminate or weaken the influence of gross errors on adjustment results. It mainly includes M estimation (generalized maximum likelihood estimation), L estimatoin (linear combination order statistic estimation) and R estimation (rank test estimation). Among them, the robust estimation method based on M estimator is the most widely used method.The selection of weight function is the core of the robust estimation method based on M estimator. Domestic and overseas scholars have done much research on how to select weight function and construct accordingly various robust estimation methods. However, different robust estimation methods have different abilities to eliminate or weaken the influence of gross errors on adjustment results.That is to say, the robustness of various robust estimation methods are different. Determine the robustness of various robust estimation methods, so that when gross errors are included in the observations, selecting relatively more effective parameter estimation methods to improve precision of the parameter values is of great practical significance.The robustness of robust estimation methods is difficult to be strictly proved theoretically. Breakdown point provides a powerful theoretical standard for analysising the overall robustness of robust estimation methods. But the breakdown point is only related to the robust estimation method itself. Two robust estimation methods with the same breakdown point can have different robustness. The robustness of robust estimation methods depends on robust estimation method itself, the specific parameter estimation problem and the number of observations, etc. Through the simulation experiment to study the robustness of robust estimation methods is an effective way.Three different forms of leveling and trilateration networks under the condition of unequal weighted observations with different numbers of observations (9,15and22), different numbers of gross errors (1-3) and different values of gross errors (5.0σ0and10.0σ0) are taken as examples, and simulation experiments are used to compare the robustness of SBWLS method and13frequently used robust estimation methods (Huber method, L1method, L1-L2method, Andrews method, Hampel method, Welsch method, Tukey method, Danish method, Fair method, German-McClure method, IGG scheme, IGGⅢ scheme and Cauchy method), and then determining the more effective relatively robust estimation methods applied to leveling and trilateration networks adjustment with unequal weighted observations. The results of simulation experiments show that when the unequal weighted observations contain gross errors, SBWLS method, L1method, Danish method, German-McClure method and IGGⅢ scheme have better robustness, and SBWLS method is the optimal parameter estimation method. They can more effectively eliminate or weaken the influence of gross errors on adjustment results than LS method and the other commonly used robust estimation methods. When the unequal weighted observations contain no gross errors, SBWLS method,1I method, Danish method, German-McClure method and IGGⅢ scheme have certain accuracy loss ralative to the LS method, and the accuracy loss of other commonly robust estimation methods is smaller. At this piont, the estimatoin efficiency of robust estimation methods is slightly lower, but it has no significant impact on adjustment calculation results. On the whole, when conducting leveling and trilateration networks adjustment with unequal weighted observations, SBWLS method, L1method, Danish method, German McClure method and IGGⅢ scheme are relatively more effective robust estimation methods, which SBWLS method is the most effective method presented in this paper.