Robust Elliptic Localization Using Worst-Case Formulation and Convex Approximation

Recent years have seen a rapid growth in research on elliptic localization, due to its widespread usage in systems such as multiple-input multiple-output radar and multistatic sonar. However, most of the algorithms are devised under line-of-sight propagation, while a number of those existing non-line-of-sight (NLOS) mitigation schemes for elliptic localization are highly case-dependent. This paper addresses the problem of elliptic localization in adverse environments without assumptions about distribution/statistics of errors and NLOS status. To achieve robustness towards NLOS bias, we resort to the worst-case least squares formulation which requires only a bound on the errors. We then apply certain approximations to the resultant intractable constrained minimax optimization problem, and finally relax it into a readily solvable convex optimization problem. Simulation results show that our method can outperform several existing non-robust approaches in terms of positioning accuracy, and achieve comparable performance to a robust estimator with a lower computational cost.