矩阵奇异值分解与广义岭估计及其在测量中的应用

APPLICATION OF SINGULAR VALUE DECOMPOSITIONAND GENERALIZED RIDGE ESTIMATION IN SURVEYING

在测量等许多工程领域中，存在因函数模型结构差即设计矩阵病态、致使未知数的最小二乘估计偏差太大且不稳定的问题，因此，研究了使用矩阵奇异值分解和广义岭估计进行数据处理的方法。首先，简述了矩阵奇异值分解及广义岭估计的理论与性质；然后，重点比较研究了它们解算病态方程的思想、途径、对关键问题的处理、适应范围、工作量大小等；最后，通过摄影测量算例验证了所得结果。并且指出，奇异值分解方法应用于病态方程的参数解算，是一种易于操作、效果更好的方法，有重要的应用价值。

The methods of data processing in surveying were studied with Singular Value Decomposition(SVD) and Generalized Ridge Estimation(GRE) under the circumstances that the multicollinearity among the columns of the coefficient matrix makes deviation of estimator too great by least squares adjustment. The theory and their properties of SVD and GRE were narrated, then a comparison between these two methods in the thoughts, ways, key problems, amount of work, applicable limits of solving illconditioned equation series was made. At last a photogrammetrical example was used to give the verification for the conclusion reached, and the SVD method solving illconditioned equation series was pointed out to be easy to handle and effective, therefore SVD method will be of great value to surveying work.