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采用岭估计法处理加权总体最小二乘平差的病态性问题,推导了相应的求解公式及均方误差评定精度的方法,定义了病态加权总体最小二乘平差中的模型参数分辨矩阵,并讨论了岭参数的含义及其作用,给出了确定病态加权总体最小二乘岭估计中岭参数的岭迹法、广义交叉核实法和L曲线法。算例计算了普通最小二乘、普通总体最小二乘的结果,并比较了三种确定岭参数的方法在处理病态加权最小二乘岭估计和病态加权总体最小二乘岭估计中的优缺点。
The ill-posed problem of weighted total least square adjustment was solved by using ridge estimation method, and the corresponding solution formulas and the mean square error evaluation accuracy were deduced. The model parameter discernibility matrix in ill-conditioned weighted least square adjustment was defined. The meanings and functions of the ridge parameters are discussed. The ridge trace method, the generalized cross validation method and the L curve method for determining the ridge parameters in the pathological weighted total least square ridge estimation are given. An example is given to calculate the results of ordinary least squares and general least squares, and the advantages and disadvantages of three methods of determining the ridge parameters are compared in dealing with pathological weighted least square ridge estimates and ill - weighted total least square ridge estimates.