Improved linear direct solution for asynchronous radio network localization (RNL)

In the field of localization the linear least square solution is frequently used. This solution is compared to nonlinear solvers more effected by noise, but able to provide a position estimation without the knowledge of any starting condition. The linear least square solution is able to minimize Gaussian noise by solving an overdetermined equation with the MoorePenrose pseudoinverse. Unfortunately this solution fails if it comes to non Gaussian noise. This publication presents a direct solution which is able to use prefiltered data for the LPM (RNL) equation. The used input for the linear position estimation will not be the raw data but over the time filtered data, for this reason this solution will be called direct solution. It will be shown that the presented symmetrical direct solution is superior to non symmetrical direct solution and especially to the not prefiltered linear least square solution.