稀疏矩阵技术及其在天测与测地VLBI数据处理中的应用

介绍了稀疏矩阵的四种常见形式以及稀疏矩阵技术在天测与测地VLBI数据处理中的应用。推演了天测与测地VLBI数据综合解算中所用稀疏矩阵形式下待估参数求解和协方差矩阵估算的算法。通过对是否采用稀疏矩阵技术时方程求解 (乘法和加法 )运算对数的估算和比较 ,表明普通最小二乘方法的运算对数约为参数总数的 3次方 ,而采用稀疏矩阵技术时的运算对数近似与参数总数成线性关系 ,从而能够在现代空间对地观测技术的大样本数据处理中显著缩短计算时间。

SPARSE MATRIX TECHNOLOGY AND ITS APPLICATION IN ASTROMETRIC AND GEODETIC VLBI DATA ANALYSIS

Some ordinary forms of sparse matrix and the application of sparse matrix technology in astrometric and geodetic VLBI data analysis are introduced. The algorithm of parameter solution and the covariance matrix calculation in the astrometric and geodetic VLBI data reduction are deduced. Based on the estimation and comparison of the number of operations in solving the observation equations by using the sparse matrix technology and by a straightforward least square adjustment (LSQ), it was shown that the number of operations is approximately proportional to the cube of the total number of parameters for the straightforward LSQ solution, while it is about linearly proportional to the total number of parameters for the algorithms which remarkably decrease the computer time in the reduction of the modern space geodetic observations characterized by huge amount.