Closed-form algorithms in mobile positioning: Myths and misconceptions

The iterative least squares method, or Gauss-Newton method, is a standard algorithm for solving general nonlinear systems of equations, but it is often said to be unsuited for mobile positioning with e.g. ranges or range differences or angle-of-arrival measurements. Instead, various closed-form methods have been proposed and are constantly being reinvented for the problem, claiming to outperform Gauss-Newton. We list some common conceptual and computation pitfalls for closedform solvers, and present an extensive comparison of different closed-form solvers against a properly implemented Gauss-Newton solver. We give all the algorithms in similar notations and implementable form and a couple of novel closed-form methods and implementation details. The Gauss-Newton method strengthened with a regularisation term is found to be as accurate as any of the closed-form methods, and to have comparable computation load, while being simpler to implement and avoiding most of the pitfalls.