Research On Solving Ill-conditioned Equation Based On Improved GA In GPS Coordinate Transformation

In recent years, Global Position System (GPS) technology develops rapidly and becomes more and more consummate. It has been widely used in many fields and created gigantic economic value and social value. The observation results using GPS are the coordinates or coordinate differences in World Geodetic System (WGS-84), but in practical using the coordinates of floor points system in national coordinate system or in local independent coordinate system are required. So in order to use GPS coordinate, we need to calculate the geodetic coordinate transformation parameters and transform the coordinates in WGS-84 that get from GPS observation to the coordinates of national coordinate or local independent coordinate which we need in practical engineering. The traditional way is using the least-squares method to get the transformation results by processing the normal equation group, but the accuracy of the results may be not very high and even they are unreliable for erroneous accumulation in Gauss melt process or the condition that the normal equation group is ill-conditioned, which can not satisfy the need of the practical application. Genetic algorithms have certain superiority in processing ill-conditioned problem. Therefore, exploring to use the genetic algorithms to get transformation parameters particularly in the condition that the normal equation group is ill-conditioned has the important research significance.In this paper, it firstly introduces some basic knowledge about GPS coordinate transformation and several transformation models in GPS coordinate transformation, in this foundation it analyzes the reason which the ill-conditioned questions produce and presents some traditional methods of processing ill-conditioned questions. Then it introduces elementary knowledge about genetic algorithms and its basic principle, discusses the existent deficiency of simple genetic algorithms and some improved ways to the simple genetic algorithms. At last, using the improved genetic algorithms realizes solving the ill-conditioned problems with several examples, and gets the wanted results after comparing with other traditional ways. Thus the improved genetic algorithms have confirmed the feasibility and the validity in processing the ill-conditioned questions.