A Theoretical Framework for Collaborative Estimation of Distances Among GNSS Users

In the field of Global Satellite Navigation System (GNSS), modern mass-market receivers are able to provide raw measurements, thus representing a valuable resource for the design of new navigation algorithms. Among these devices, a considerable amount of smartphones allows to gather such measurements before they are processed to compute the positioning solution. In parallel, they provide natively ubiquitous connectivity within low-latency cellular networks. This framework has enabled the implementation of novel paradigms of positioning including networked GNSS positioning. Navigation algorithms exploiting relative positioning have been widely investigated in the last years and many kinds of shareable data have been integrated within collaborative approaches (e.g. GNSS navigation data, relative distance, relative heading). The present work investigates geometrical impairments in the computation of pairwise ranges (i.e. Inter-Agent Range) through the exchange of GNSS-only measurements between a pair of GNSS receivers in short baseline scenario. Although Inter-Agent Range technique acts similarly to code-pseudorange single differences, it exploits the angle obtained from the joint observation of a common satellite by two collaborating receivers. A statistical characterization of the output measurements is provided along with the evaluation of optimal and suboptimal geometrical conditions. A mathematical model for collaborative systems is formulated and compared with a collection of realistic simulation results for the validation. Raw and corrected measurements were compared, thus highlighting a remarkable advantage of the latter in terms of biases. The results confirm the suitability of the presented model for the optimization of collaborative and differential GNSS applications.