Multi-reference-station based relative positioning method and impact analysis of the biases in priori baseline vectors

In order to improve the reliability of the single-reference-station based relative positioning solutions over short baselines, the multi-reference-station based relative positioning method was explored. A priori baseline information between the reference stations was integrated into the observable model, thus giving the functional and stochastic models of the multi-reference-station based relative positioning. Based on that, the closed-form formula of the ambiguity dilution of precision for the positioning was derived so that the influence of the number of reference stations on the float ambiguity precision was revealed. Then the impacts of the biases in the a priori baseline information on the integer ambiguity resolution were analyzed theoretically. It show that the integer ambiguity resolution could barely be influenced on the condition that the bias is less than 5 cm. The multi-reference-station based relative positioning method was validated with both the simulated and real data sets. The numerical results show that, increasing the number of reference stations not only improves the single-frequency ambiguity resolution success rate and convergence rate, but also restrains the biases in the a priori baseline information. For example, the ambiguity resolution success rate is still larger than 92% even when the biases of the baseline components attain 4 cm in the field tests. This contribution provides the theoretical foundation for the fast and imprecise calibration between the multiple-reference-station in special scenarios.