In this presentation we consider the problem of delimiting the region of all possible target locations, given minimal knowledge on the underlying noise distribution. In concrete, we only assume that the noise is supported on a known ellipsoid which reflects two assumption on the problem: (1) range measurements are, in general, correlated but with bounded errors and (2) measurements are non-negative (almost surely) as they represent physical distances. The set of target localizations can also be seen as a tight majorizer of the set of Maximum-Likelihood (ML) estimates with arbitrary noise densities. We construct a superset of the aforementioned region through convex relaxations that use Linear Fractional Representations (LFRs), a well-known technique in robust control. Our method uses LFRs to model and re-parametrize the uncertainty vector in the additive data model. We compare our method with a standard semidefinite relaxation and, for low noise regimes, our supersets double the accuracy of the benchmark. For moderate to high noise regimes our method still improves the benchmark but the benefit tends to be less significant, as both supersets tend to have the same size (area).
João Domingos received a M.S. degree in Electrical and Computer Engineering from Instituto Superior Técnico, Technical University of Lisbon, Lisbon, Portugal, in 2018. His master thesis on Distributed Control won the Luís Vidigal Award for the best master thesis at Instituto Superior Técnico (IST) in the scientific areas of Electrical and Computer Engineering. After his thesis, João went to Carnegie Mellon University, Pittsburgh, USA, where he worked on Graph Signal Processing (GSP). He is currently working towards his Ph.D. degree in Electrical and Computer Engineering, at Instituto Superior Técnico, Lisbon, Portugal. His research interests include Optimization, Signal Processing, Robust Statistics and Distributed Computation.