Title: Robust Localization Using Range Measurements with Unknown and Bounded Errors,
Abstract: Cooperative geolocation has attracted significant research interests in
recent years. A large number of localization algorithms rely on the
availability of statistical knowledge of measurement errors, which is often
difficult to obtain in practice. Compared with the statistical knowledge of
measurement errors, it can often be easier to obtain the measurement error
bound. This work investigates a localization problem assuming unknown
measurement error distribution except for a bound on the error. We first
formulate this localization problem as an optimization problem to minimize the
worst-case estimation error, which is shown to be a non-convex optimization
problem. Then, relaxation is applied to transform it into a convex one.
Furthermore, we propose a distributed algorithm to solve the problem, which
will converge in a few iterations. Simulation results show that the proposed
algorithms are more robust to large measurement errors than existing algorithms
in the literature. Geometrical analysis providing additional insights is also
provided.