Range and Bearing Data Fusion for Precise Convex Network Localization

Abstract

Hybrid localization in GNSS-challenged environments using measured ranges and angles is becoming increasingly popular, in particular with the advent of multimodal communication systems. Here, we address the hybrid network localization problem using ranges and bearings to jointly determine the positions of a number of agents through a single maximumlikelihood (ML) optimization problem that seamlessly fuses all the available pairwise range and angle measurements. We propose a tight convex surrogate to the ML estimator, we examine practical measures for the accuracy of the relaxation, and we comprehensively characterize its behavior in simulation. We found that our relaxation outperforms a state of the art SDP relaxation by one order of magnitude in terms of localization error, and is amenable to much more lightweight solution algorithms. I. INTRODUCTION Spatial awareness is a hallmark of contemporary real-world systems and applications, particularly when multiple agents collaborate to attain common goals. Location technologies are key for operation in GNSS-challenged environments, like underwater [1] or indoor [2] and city skyscraper areas [3], and also in many applications in wireless communications [4], sensor networks [5], IoT [6], medicine [7], [8], etc. Our work addresses the network localization problem [9], where multiple networked agents cooperate in sensing and computation to jointly estimate their unknown positions. Related work: There is a vast literature for range-based network localization, from multidimensional scaling [10], [11] to nonconvex ML estimation [12], [13], convexifications of ML problems [14]-[16], and other convex heuristics to match measured data to a data model [17], [18].Several current technologies not only give access to accurate distance measurements, but also provide angle information. These added measurements can improve the quality of estimates or reduce the amount of resources spent to obtain a reasonable localization precision. 5G is an especially noteworthy example where the value of hybrid measurements has been noted [4], [19], and information-theoretic bounds are available to characterize their impact [5], [20]. While the topic of single-source range/bearing localization is reasonably well covered in the technical literature, specific references addressing network localization algorithms for that data model