In this work, a method in order to jointly estimate
the position of the different User Equipments (UEs) and the
Relative Time Differences (RTDs) between base stations in UMTS
networks is proposed. This method is based on the hyperbolic
multilateration technique defined from the Time Differences
of Arrival (TDOAs) and the resolution of a nonlinear system
of equations. A comparative study between two well-known
iterative algorithms, Gauss-Newton and Levenberg-Marquardt,
is obtained by employing real data collected from drive tests
in urban and sub-urban areas. The accuracy of the obtained
results is mainly related to multipath errors associated with the
measurements carried out by UEs, and with errors introduced by
the numerical method. By considering that, it can be concluded
that Levenberg-Marquardt gives better results, providing faster
convergence, higher accuracy and more robustness, provided that
its parameters are properly optimized.
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