The Feasible Combining Observation Models and Equivalence in Dual-Frequency Precise Point Positioning

Compared with differential positioning, the measurement noises of observation models in precise point positioning are larger; a good observation model can speed up convergence time. There are already a series of dual-frequency observation models in practice. But whether there is another one that has better performance than existing observation models. Furthermore, whether any two of observation models are equivalent is still a problem which is not solved systematically. The goal of this paper is to exhibit all feasible observation models and demonstrate the equivalence among the models. More specifically, by analyzing all possible clusters, all feasible dual-frequency observation models comprise the basic observation models and their reversible combining observation models. Subsequently, a set of theorems is proposed to systematically demonstrate whether all feasible observation models are equivalent or not. In single epoch, all feasible dual-frequency observation models are equivalent. But for multi-epoch iteration, any two of the reversible observation models are equivalent; any two of the irreversible observation models are unequivalent. Finally, the global positioning system experiments verify the theorems in the actual dual-frequency precise point positioning. In addition, the results show that the measurement noises in the observation models may reflect the performance of observation models, only when the observation models are unequivalent. These theorems are still valid in triple-frequency. Before the performance is evaluated by using the measurement noises in a new triple-frequency model, the equivalence between the model and others should be confirmed by using these theorems.