Improved Linear Direct Solution for Asynchronous Radio Network Localization (RNL)

The linear least square solution is frequently used in the field of localization. Compared to nonlinear solvers, this solution is more affected by noise but able to provide a position estimation without knowing any starting condition. The linear least square solution is able to minimize Gaussian noise by solving an overdetermined equation with the Moore-Penrose pseudoinverse. Unfortunately, this solution fails in the case of non-Gaussian noise. This publication presents a direct solution using prefiltered data for the LPM (RNL) equation. The input used for linear position estimation will not be the raw data but data filtered over time and for this reason this solution will be called the direct solution. It will be shown that the symmetrical direct solution presented is superior to the non-symmetrical direct solution and in particular to the non-prefiltered linear least square solution.