System error calibration for time division multiple access inter-satellite payload of new-generation Beidou satellites

Abstract

The new-generation Beidou satellites constellation consists of 2 inclined geosynchronous orbit (IGSO) satellites and 3 medium orbit (MEO) satellites. The inter-satellite ranging payloads onboard provide the constellation with autonomous navigation capability. Each satellite navigates using the rest of the satellites in the constellation. The satellites perform two-way time division multiple access (TDMA) inter-satellite link (ISL) ranging using pseudo random codes. For some reasons, the global system of Beidou navigation satellite system (BDS) will still depend on its regional station net, which is not able to observe medium orbit satellites for the whole section. The ISL ranges also make it possible for BDS to obtain clock and orbit observables when the satellites cannot be seen by its limited regional stations. While ranging, the system errors of TDMA payloads on new-generation Beidou satellites must be considered, which are hard to calibrate on the ground and will affect the accuracy of inter-satellite time synchronization and orbit determination. In this paper, a calibration method of inter-satellite system error is proposed, and the application of ISL ranges on satellite-ground time synchronization is discussed. Firstly, the using strategy of ISL clock offset is discussed. The satellite-ground part obtained by L-band two-way satellite time frequency transfer (TWSTFT) is introduced and the satellite-satellite part obtained by inter-satellite link is modeled to obtain the clock and orbit observables. Broadcast ephemeris is used to decouple the inter-satellite clock offset and inter-satellite range, and the observation equations are provided. Secondly, the L-Band clock offset is used to calibrate the combined system error of each inter-satellite payload. By comparing inter-satellite clock offsets of a pair of satellites obtained by ISL with satellite-ground clock offsets of the same two satellites obtained by TWSTFT, a combination of signal transmitting delay and signal receiving delay is calibrated using least-squares estimation. The combined system error of one inter-satellite payload is fixed to solve the rank lack problem. The corrected clock offsets of ISL are then combined with clock offsets of TWSTFT to determine the satellite-ground clock offsets and calculate the predicting clock offset parameters while the satellites are out of the regional station net. The result shows that the accuracy of ISL clock offsets can reach 0.25 ns while the accuracy of TWSTFT clock offsets is 0.5 ns. The proposed method can calibrate the combined system errors and improve the accuracy of inter-satellite time synchronization. The standard deviations of a 14-day time series of combined inter-satellite system errors are less than 0.3 ns. And the calibrated ISL clock parameters are consistent with that of the L-band TWSTFT. The results of medium orbit satellite are quite remarkable: the monitoring section length increase more than 40% of the whole section length. At the beginning of the regional station net section, predicting error of satellite M1S is improved from 3.59 to 0.86 ns (RMS), predicting error of satellite M2S is improved from 1.94 to 0.57 ns (RMS). Taking into account all these results, we may reasonably come to the conclusion that inter-satellite link is a high accuracy measurement and it can improve the accuracy of clock offset prediction.