Global robust estimation and its application to GPS positioning

Least-squares adjustment yields the most likely solution for a set of redundant data provided the mathematical model is correct and there are only random errors in the observations. When systematic or gross errors affect observations or the model does not accurately represent reality, i.e. when a systematic error affects the model, then least-squares performs very sensitive to these undesirable errors and may yield an unacceptable solution. Robust estimation was developed to obtain a least-affected solution in these cases of gross or systematic error appearance whereas a solution very close to the least-squares solution is obtained when only random errors are present. However, the fashion in which robust estimation is usually computed (by means of iteratively reweighed least-squares) undermines its potentialities. We propose to substitute the easy but not so reliable classic scheme by a global optimization procedure so as to recover all the robust estimation potential. We will show the advantages of applying the method to GPS positioning: a prior successful research for coping with the ionospheric delay of single frequency observations and, besides, an innovative application for avoiding signal multipath.