A new algorithm for a multi-baseline solution based on the equivalence principle

A new algorithm of a multi-baseline solution (MBS) based on the equivalence principle for precise relative positioning is proposed in this paper. The objective of the solution is to keep the observations independent when eliminating the satellite and receiver's clock errors. The equivalent differenced observation equations are developed through the equivalent transform. Because of the high-dimension characteristics of the MBS ambiguity, a modified partial ambiguity resolution of the MBS (PAR-MBS) strategy is developed to determine an ambiguity subset. Compared with the traditional single-baseline solution (SBS), the zero and short baseline experiments are carried out to validate and evaluate the proposed algorithm. The results show that the MBS can enhance the strength of the relative positioning model and improve positioning accuracy and availability. The PAR-MBS can shorten the convergence time for the epoch to first fix by on average 41.7% with all 80 observation segments. Moreover, the difference of the positioning errors between the MBS and SBS is indistinguishable for the 45 and 60 min schemes. However, for the 30 min scheme, there is a significant performance improvement by approximately 11%, 10% and 14% in the N, E, and U components, respectively. The closure errors of the repeated baselines and triangle closed loops can also deliver similar results for the 45 and 60 min schemes; however, for the 30 min scheme, there is a remarkable performance improvement by approximately 48%, 59%, and 12%, and 54%, 65%, and 10% in the N, E, and U components, respectively.

Automated summary

This paper proposes a new algorithm for precise relative positioning based on the equivalence principle. The algorithm aims to maintain observation independence while eliminating clock errors. A modified PAR-MBS strategy is developed for high-dimension MBS ambiguity, which shows significant performance improvement in reducing convergence time and positioning errors, especially for the 30 minute scheme.