基于HouseHold变换的全球卫星导航

Algebraic Solution of GPS Equations Based on HouseHold Transformation

摘要:

研究传统最小二乘和卡尔曼滤波方法求解GNSS(Global Navigation Satellite System)观测方程时接收机钟差参数的处理策略，将失效的接收机钟差参数通过矩阵变换的方式消除.针对计算机截断误差可能会造成卡尔曼滤波结果发散的现象，将HouseHold变换用于GNSS观测方程参数求解中，根据其建立的正交矩阵的特性，导出求解公式.结果表明，该方法在理论上可消除计算机截断误差的影响，且在储存空间上仅为传统方法的一半，可有效节约计算机资源.

关键词:全球卫星导航系统; 最小二乘; 卡尔曼滤波; Household变换

Abstract:

Processing strategy of receiver clock error offset in least squares and Kalman filtering method for global navigation satellite system (GNSS) solution is mentioned. Disabled clock error offsets will be eliminated through matrix transformation. Due to the fact that Kalman filter algorithm is sensitive to computer foundoff, HouseHold transformation is put in GNSS parameter solution. According to the properties of its initial reflective matrix, this method is proved to be effectively. It is found that the computer roundoff can be eliminated, which is more elegant in theory. Plus, the solution using HouseHold transformation is more space saving and efficient.

Key words:global navigation satellite system(GNSS); least squares; Kalman filter; HouseHold transformation