Accurate geolocation in the presence of outliers using linear programming

Precise geolocation have attracted considerable interest in the engineering literature. Almost all previous publications consider small measurement errors. In this paper we discuss geolocation in the presence of outliers, where several measurements are severely corrupted while other measurements are reasonably accurate. It is known that Maximum Likelihood or Least Squares provide poor results under these conditions. We demonstrate how using the ℓ₁ norm and linear programming we can detect the outliers and use only the good measurements for providing the final location estimate. Moreover, we provide bounds on the number of outliers that can be detected and eliminated.