基于多参数正则化的空间坐标转换与精度分析  

SPATIAL COORDINATE TRANSFORMATION BASED ON MULTIPLE PARAMETER REGULARIZATION AND ITS ACCURACY ANALYSIS

作　　者：陈正宇[1] 刘春[1] 

机构地区：[1]同济大学测量与国土信息工程系,上海200092

出　　处：《大地测量与地球动力学》2008年第1期92-95,共4页Journal of Geodesy and Geodynamics

基　　金：国家自然科学基金(40501061)

摘　　要：三维坐标转换广泛应用于测绘内业计算中,其转换参数直接影响到转换点的精度。采用Bursa模型通过3个以上的公共点利用最小二乘法求取转换参数时,其中的系数矩阵严重病态,使求得的转换参数在公共点范围之外并不可靠。提出了基于Morozov偏差原理的Tikhonov正则化方法,考虑平移量、旋转角和尺度的多正则化参数的计算模型。模拟实验精度分析表明:多参数正则化求得的转换参数较最小二乘和单参数正则化,可以更好地提高外推精度和稳定性。Three-dimensional coordinate transformation is widely used in indoor computation for surveying and mapping. The transformated parameters may directly influence the accuracy of transformationed points. These parameters can be obtained with least square by at least three common points under Bursa model. Because of the ill-posed coefficient matrix, the obtain parameters is uncertain. In order to improve the accuracy and reliability, we put forward a transformation model considering translation, rotation and scale parameters by Tikhonov multiple parameter regularization based on Morozov bias principle. The simulated examples verify that the accuracy of the transformed coordinates in peripheral area and its stability can be significantly improved by multiple parameter regularizatlon.

关 键 词：正则化 坐标转换 最小二乘 不适定问题 外推精度 

分 类 号：P226.3[天文地球—大地测量学与测量工程]