CASTELO: Convex Approximation based Solution To Elliptic Localization with Outliers

This short communication considers mitigating the negative effects of possibly unreliable path delay measurements acquired in non-line-of-sight (NLOS) environments on the positioning performance, a problem deserving further investigation within the expanding research area of elliptic localization. We present CASTELO, a Convex Approximation based Solution To Elliptic Localization with Outliers, to achieve such a goal. Our proposal corresponds to a mixed semidefinite (SD)/second-order cone (SOC) programming formulation derived from an error-mitigated nonlinear least squares (LS) location estimator, presenting itself as a remedy for the neglect of positivity of NLOS biases suffered by the majority of currently fashionable outlier-handling approaches. In terms of analytical discussions, we provide rationales supporting the incorporation of the SOC constraints, which serve to tighten the problem obtained after SD relaxation, and conduct a complexity analysis for the ultimate mixed SD/SOC programming formulation. Simulations are carried out to confirm the strong ability of CASTELO to attain reliable elliptic localization in the presence of NLOS outliers.