摘要
在卫星导航定位系统中,在精度因子计算和采用最小二乘法进行定位求解时,传统上采用测量矩阵直接求逆方法来进行.为了克服矩阵求逆带来的计算量大和数值稳定性差的不足,利用测量矩阵的对称正定性,提出了一种基于矩阵UTDU分解的定位解算和精度因子计算方法.改进方法具有严格的数学理论基础,保证了方法的正确性和有效性.数值分析结果表明,相对直接求逆的传统方法而言,在定位解算时,该方法能降低约60%的运算量,而在精度因子计算中,约能降低36%的运算量.且改进方法能大大降低求解矩阵的条件数,提高了求解的数值稳定性.
In satellite navigation system,the traditional algorithm of solving dilution of precision（DOP） and satellite positioning based on least square method is the direct matrix inverse（DMI） method.In order to overcome the disadvantages of high computational burden and poor numerical stability of traditional DMI method,an improved method of satellite positioning and DOP was presented based on the matrix UTDU decomposition,which made use of the symmetric and positive definite performance of the measurement matrix.The correctness and validity of the new method can be guaranteed by the strict mathematical theory.The numerical results show that,in comparison with the traditional DMI method,the reduction of operational volume of positioning is about 60% and that of solving DOP is about 36% by the proposed method.At the same time,the condition number of the solving matrix of the improved method has reduced considerably after decomposition and the numerical stability is significantly improved.
出处
《北京航空航天大学学报》
EI
CAS
CSCD
北大核心
2011年第4期472-477,共6页
Journal of Beijing University of Aeronautics and Astronautics
基金
国防科工局航天民用专项资助项目
北京市重点学科基金资助项目(XK100070525)
关键词
卫星导航
最小二乘
解算
精度因子
矩阵分解
satellite navigation
least square
solutions
dilution of precision（DOP）
matrix decomposition
