Application of Genetic Algorithm to Solve Ill-Conditioned Equations for GPS Rapid Positioning

The normal equations of GPS single frequency rapid positioning are seriously ill-conditioned because of a few observational epochs,which causes the inversion of coefficient matrix of normal equations unstable.We converted the ill-conditioned normal equations of GPS rapid positioning into a function optimization problem,and used genetic algorithm to calculate parameters solutions,which avoided the inversion of coefficient matrix of normal equations and could approximately acquire best solutions.A method was developed,which use MSEM(mean square error matrix) matrix of biased estimation to determine the ambiguity search space and use GA(enetic algorithm) method combining with Lambda method to fix integer ambiguities.Experiment shows that the method can correctly fix integer ambiguities with a few several epochs.