Abstract: In this paper four numerical methods for solving the overdetermined system of nonlinear equations  are introduced.The Enumeration method and the Monte Carlo method are improved and combined into a  Monte Carlo-Enumeration method.These numerical methods are applied to solve the over determined system  of nonlinear equations which established at the base of the technology for positioning with the shadow of sun,advantages and disadvantages of each algorithm is analyzed according to the results of numerical experiments.At last,the computing time and accuracy of each algorithm are compared with numerical examples,the effiiency of each method and the high efficiency of Monte Carlo-Enumeration method are verified. 

Key words: Overdetermined system of nonlinear equations, Enumeration method, Genetic algorithm, Monte Carlo method, MATLAB