基于遗传算法的GPS病态方程的解算

Solutions of ill-conditioned GPS equations based on genetic algorithms

为准确解算仅有少数几个历元的GPS载波相位观测数据的病态定位方程,将GPS快速定位的病态法方程求解问题转化为一个函数优化问题,应用遗传算法求解病态方程,避免了法方程的求逆运算,从而可以得到参数的近似最优解。实验表明,通过设计合适的适应度函数、确定合理的初始种群范围并选择合适的遗传算法运行参数,可使GPS快速定位病态方程参数浮点解的精度得到大大提高,接近参数正确值,有利于快速固定模糊度。该成果对于缩短GPS定位时间、提高GPS定位精度具有一定的意义。

In order to achieve accurate solutions of ill-conditioned GPS equations with a few observational epochs, the ill-conditioned normal equations of GPS rapid positioning was transformed as a function optimization problem. Then genetic algorithm was used to calculate parameter solutions, which avoided the inversion of coefficient matrix of normal equations. Experiments show that the precision of parameter float solutions of ill-conditioned GPS equations can be greatly improved by designing appropriate fitness function, determining rational range of initial population and appropriate control parameters of genetic algorithms. The result is of significance in reducing GPS positioning time and improving positioning precision.