一次范数最小稳健估计在高程混合网中的应用

目的探讨如何获得高程混合网高精度的平差结果。方法结合高程混合网的模拟计算,分别采用下面4种方法平差,即:第1种,不考虑三角高程测量中折光系数影响的最小二乘法;第2种,考虑三角高程测量中折光系数影响的最小二乘法;第3种,不考虑三角高程测量中折光系数影响的一次范数最小稳健估计;第4种,考虑三角高程测量中折光系数影响的一次范数最小稳健估计。结果上述第2种方法比第1种方法精度高,第3种方法与第4种方法精度相当,且均高于第1种方法和第2种方法。对于一次范数最小稳健估计,权函数中常数c越小,平差结果的精度越高。结论在高程混合网中,上述4种方法中,第3种方法是最佳的,因为它精度最高,同时野外工作量最小。在按一次范数最小稳健估计计算时,应根据需要和实际,选择尽量小的c值。

Application of the first order minimum norm robust estimation in height mixed nets

Aim In height mixed nets.To discuss how the best method of surveying estimate is obtained.Methods Four methods are used in the imitation example of height mixed nets.These four methods are as follows:the first method is least squares estimation without considering refraction coefficient of triangulated height surveying;the sencond is least squares estimation with considering refraction coefficient of triangulated height surveying;the third is first order minimum norm robust estimation without considering refraction coefficient of triangulated height surveying;and the fourth is first order minimum norm robust estimation with considering refraction coefficient of triangulated height surveying.Results The precision of the second method is higher than that of the first one,and the precision of the third and the fourth method is almost equal and higher than that of the first method and the second method.When first order minimum norm robust estimation is applied,the smaller the value of c of weight function is,the higher the precision of survering estimate.Conclusion In height mixed nets,the third method among these four is the highest in precision and smallest in outdoor work.When first order minimum norm robust estimation is applied,the value of c should be as small as possible according to necessity and reality.