Some numerical aspects of nonlinear estimation

Given a nonlinear estimation problem, it is well-known that one algorithm might produce a solution where another algorithm might fail. What is less well-known is that when both algorithms do produce solutions, one of the solutions might be more accurate than the other. In particular, one might give several accurate digits, while the other gives no accurate digits. Possible sources of the phenomenon are presented, including step-length, stopping rule, convergence criterion and method of derivative calculation. Additionally, practical advice for using nonlinear solvers is offered.