基于镜像变换的GPS坐标变换方法研究

解算GPS坐标系和国家坐标系间的转换参数,传统方法是最小二乘法和高斯约化相结合,通过解算由误差方程组推导出的法方程组,间接求出结果。该方法有两个缺陷:一是精度不高;二是“病态”矩阵带来的不稳定问题。采用最小二乘法和镜像变换相结合的方式直接解算误差方程组,不需解算法方程组,不但提高了解算精度,而且避免了“病态”法方程组问题。

Research on GPS Coordinate Transformation Based on Householder Reflection

Traditional Gauss Method of Reduction suffers two flaws in evaluating the transformation parameters between GPS coordinate system and state coordinate system:lower precision caused by the accumulated error in the deduction from observation equations to normal equations and instability in the case of ill-conditioned normal equations carrying at times.This paper introduces a novel method that combines Least Square Method with Householder Reflection.Instead of solving normal equations,this method deals with observation equations directly,which surmounts the primary shortcoming of Gauss method that is lower in precision and instable in result.Experimental results show that the new method is more robust and superior in comparison with the traditional method.