A Theoretical Study on the Benefits of Integrating GNSS and Collaborative Relative Ranges

Previous research contributions addressed the definition of a Cramer Rao Lower Bound (CRLB) as a theoretical tool to investigate the performance of unbiased position estimators for deterministic non linear systems. Moving from such theoretical findings, this work aims at investigating the CRLB of hybrid estimators integrating auxiliary measurements obtained from the combination of satellite-based range measurements shared among pairs of connected receivers. The study is conceived to inspect the benefits of this GNSS-based collaborative positioning approach in terms of precision improvement. The analysis of such a theoretical limit aims at identifying when the use of cooperative ranges is beneficial despite of their correlation with the individual measurements, according to the geometry of satellites and terrestrial agents w.r.t. a target agent. The theoretical analysis is validated by simulation by demonstrating when the collaborative measurements increases the precision of the position estimates. The study practically provides a methodology for the selection of the best cooperating agents in multi-agent frameworks.