Galileo Multi-frequency Observation Combination Method Based on Minimum Noise Coefficients

Classic multi-frequency combination is mainly to build a long wavelength combination and eliminate the ionospheric delay combination, and the combined noise factor is greater than 1. On the basis of un-differenced and un-combining observations, this paper proposes a general real coefficient combination based on the principle of minimum noise coefficients. The combined noise coefficient is less than 1, which can be applied to any multi-frequency observation combination. According to the frequency of each signal frequency of Galileo, we give the optimal combination of Galileo multi-frequency noise coefficients and the effect of theoretical improving accuracy. Compared with single frequency observation, the optimal combination of dual frequency triple frequency, four frequency and five frequency improve the observation accuracy by 40%, 49%,54% and 59% respectively. It is verified by the observation of the actual Galileo three frequency E1, E5A and E5b signals, the optimal combination of dual frequency and triple frequency improves the observation accuracy by 52% and 62% respectively compared with single frequency observation. According to the actual measurements, the observation accuracy improvement of minimum noise coefficients combination is basically consistent with the theoretical analysis. Finally, we analyze the equivalence between the minimum noise combination and the un-differenced un-combining observations, the results show that the minimum noise combination is an optimal weight model of un-differenced un-combining observations, which the optimization criterion is the minimum observation noise.