Convex Relaxation for Maximum-Likelihood Network Localization Using Distance and Direction Data

A reliable and accurate positioning technology is crucial for a large variety of wireless services and applications. High-resolution estimates of distance and direction data are available in most current and emerging wireless systems. Combining these two sensing modalities can improve the estimation performance and identifiability of the localization problem. However, the problem of cooperative localization using joint distance and direction estimates is still a largely unexplored problem. A novel convex relaxation of the maximum likelihood (ML) estimator for this problem called Semidefinite Programming Hybrid Localization (SDHL) algorithm is proposed in this paper. Numerical results are presented showing that the localization error is significantly reduced in almost every simulation scenario compared to the state of the art. This improvement in localization performance is due to the close approximation of the ML estimator.