病态总体最小二乘模型的正则化算法  

REGULARIZED TOTAL LEAST-SQUARES SOLUTION TO ILL-POSED ERROR-IN-VARIABLE MODEL

作　　者：袁振超[1] 沈云中[1,2] 周泽波[1] 

机构地区：[1]同济大学测量与国土信息工程系,上海200092 [2]国家测绘局现代工程测量重点实验室,上海200092

出　　处：《大地测量与地球动力学》2009年第2期131-134,共4页Journal of Geodesy and Geodynamics

基　　金：自然自然科学基金(40674003,40874016)

摘　　要：当线性观测方程的观测向量与设计矩阵均包含随机误差时,需要采用总体最小二乘法进行参数估计,但传统的总体最小二乘无法处理病态问题,需要进行正则化处理。根据Tikhonov正则化原理,导出了等权总体最小二乘正则化解法的计算公式,并提出了用数值方法估计正则化解方差-协方差阵的方法。采用第一类Fredholm积分方程的算例验证了正则化总体最小二乘算法。结果表明:采用的设计矩阵和常数项向量都含有观测误差时,该算法能明显改善估值的精度。Total least-squares method is preferrable to estimate the parameters in the linear observation models when both the observaion and designed matrix are contaminated by random errors. However, the conventional total least-squares solution cannot deal with the ill-posed problems, so the regularization algorithm must be used in this case. The formulas of regularized total least-squares solution based on Tikhonov regularization criterion are derived and the variance-covariance matrices of the estimated parameters are computed by numerical method. Finally, a simulated example is investigated to verify the regularized total least squares solution by use of the Fredholm integration equation of the first kind. The result shows that the accuracy of estimates is significantly improved with this regularized algorithm.

关 键 词：总体最小二乘算法 病态模型 TIKHONOV正则化 设计矩阵 随机误差 

分 类 号：P207[天文地球—测绘科学与技术]