Fully and optimally use the redundancy in a TWSTFT network for accurate time transfer

Two-way Satellite Time and Frequency transfer (TWSTFT) is a primary technique for UTC generation [1]. Only the direct link, the so called UTC link between a Lab(k) and PTB, is used for UTC generation. The numerous redundant links are measured but never used. The concept of the TWSTFT network time transfer has been discussed by several authors [2,3,4,10]. [5,6] are examples of the very first use of redundancy (Triangle Closure Calibration) in the TW network for the time link calibrations. It is based on using all the direct UTC and redundant links (Fig. 1) and the hypothesis that the TWSTFT measurement errors obey the normal distribution with an homogeneous distribution over the whole network. However [7,8] proved that the hypothesis may not be held. Considerable biases exist, such as the diurnals, which cannot be fully averaged out by increasing the measurement quantity or eliminated in a simple least square (LSQ) network adjustment [3]. The maximised gains in uncertainty depend on the optimal use of the redundancy in the TWSTFT network but the maximum number of the measurements to be used. We first discussed the weak points of the equal-weight network time transfer and then proposed our solutions: (1) Weighting each link according to its uncertainty estimate; (2) Using the GPSPPP to strengthen or replace the errored TWSTFT links in the network adjustment. Obviously, unequal weighting is necessary; (3) The above solutions can be extended to use all types of observations, such as the TWOTFT (Two-Way Optical fibre Time and Frequency Transfer) etc. The global network adjustment takes the link measurement to establish its observation equation. Therefore, there are theoretically not limits in the types and the numbers of the observations (GPS, GLONASS, GALILEO, BEIDOU, TWOTFT, TWSTFT/SDR [13] etc.) on any baseline in the network T/F transfer. Such all the redundancy is used. This is called the multi-technique network T/F transfer [9].