Correlated Self-born Weighted Cons-truction And Robustness In Adjust-ment Of Leveling Network

Robust estimation method can effectively eliminate or weaken theinfluence of the observed value of gross errors on the result of parameterestimation. However, different robust estimation methods show differentrobustness in the adjustment of leveling network. Among them, the robustestimation method based on M estimation is the most widely used method ofrobust estimation. The construction of the equivalent weight is the core of therobust estimation method based on M estimation. Domestic and overseasscholars have done many researches about how to construct equivalent weightand put forward the corresponding varieties of robust estimation methods.Commonly used robust estimation methods use the true error estimates ofthe least squares method to construct the equivalent weight of the observedvalue. Self-born weighted least squares method (SBWLS) was put forward bythe Yong-hui Ge and it makes full use of the effective information about theconditions of equation, which the true error estimate of independent observations shall meet, to construct the equivalent weight of the observed value,namely using multiple true error estimates to construct the self-born weight.Yong-hui ge and others showed that in the adjustment of leveling network,self-born weighted least squares method had better robustness and effectivenessthan common robust estimation methods through the simulation experiment.This paper, based on self-born weighted least squares method, studies howto structure the correlated self-born weight and the robustness of the correlatedself-born weighted least squares method (CSBWLS) in the adjustment ofleveling network(Function model is linear form), confirming a method ofstructuring the correlated self-born weight. In the calculation, it is found thatwhether the observations contain gross errors or not, some of the main diagonalelements of the correlated self-born weight are negative. The situation leads tonon convergence of the iterative calculation. Therefore introducing the limitingfactor, to make the results of the correlated self-born weight more practicaland effective.When observations do not contain gross errors, with the simulationexperiments of four leveling networks with different numbers of observations,by comparing robustness related to CSBWLS method, SBWLS method and13kinds of commonly used robust estimation methods with the least squaresmethod, the results show that compared with the LS method they have someaccuracy losses, but the influence of the parameter estimation results is notserious. With nine observations and four undetermined points of leveling networksand with different numbers of gross errors and different values of gross errorsare taken as examples, to compare robustness related to CSBWLS method withSBWLS method. The result shows that, in this situation, when observationscontain gross errors, CSBWLS method is more effective.The paper exploits a MATLAB program to study the correlated self-bornweighted least squares method in the adjustment of leveling network. It canbalance both the leveling networks and the simulation experiments of levelingnetworks. In the simulation experiments, the observations can contain none ofgross errors and one or more of the gross errors.