Abstract: Distance observations play a very key role in surveying,of which the related observation model is nonlinear.Because of the complexity of nonlinear problems,observation equations may have a non-unique solution,particularly when the equation is ill-conditioned,the solutions of the equation may become more complex.In view of this problem,the paper uses the direct method and Gauss-Newton method and closed-form of Newton method to solve ill-conditioning,testing the their performances and local convergence of three methods.The result shows that the closed-form of Newton method has the best local convergence.In the experiment,the direct method and Gauss-Newton method can get two solutions,while the closed-form of Newton method can get three solutions two of which are the same with the solutions of direct method and Gauss-Newton method,but,the search total solutions are the best local optimum.

Key words: distance observation, non-linear models, multiple solutions, iterative method