Distributionally Robust Radio Frequency Localization

We consider the problem of estimating the location of an RF-device using observations such as received signal strengths, generated according to an uncertain distribution from a set of transmitters with known locations. We present a distributionally robust formulation of the localization problem that explicitly takes into account the uncertainty in the distribution that generates the observations. We identify the structure of the robust solution and demonstrate how to construct the optimization problem so that it is easily computed, and always yields the optimal solution. We show that the robust estimate outperforms traditional methods in the presence of modeling errors, while remaining close to the traditional estimate when the modeling is exact. This suggests that the formulation presented here is an attractive option in applications where we use a model that may not be an exact fit to our environment or if changes in our environment have induced errors in an empirically derived model.