**A Method of Whole-Network Adjustment for Clock Offset Based on Satellite-Ground and Inter-Satellite Link Observations**

**Dongxia Wang 1,2, Rui Guo 2,\*, Li Liu 2, Hong Yuan 1, Xiaojie Li 2, Junyang Pan <sup>3</sup> and Chengpan Tang <sup>3</sup>**


**Abstract:** The inter-satellite link is an important technology to improve the accuracy of clock offset measurement and prediction for BeiDou Navigation Satellite System (BDS). At present, BDS measures clock offsets of invisible satellite mainly through the "one-hop" reduction mode based on the satellite-ground clock offset of the node visible satellite and the inter-satellite clock offset between the two satellites. However, there exists a systematic deviation caused by the node satellite reduction, and there is still a large room for improvement in clock offset measurement and prediction. Therefore, this paper firstly proposes a method of whole-network adjustment for clock offset based on the satellite-ground and inter-satellite two-way data. The least square method is used to realize the whole-network adjustment of clock offset based on the observations of two sources, and to obtain optimal estimates of different clock offset reduction. Secondly, the evaluation method combining internal and external symbols are proposed by the fitting residual, prediction error and clock offset closure error. Finally, experimental verification is completed based on BDS measured data. In comparison with the "one-hop" reduction method, the fitting residual and prediction error of the whole-network adjustment method reduces about 45.06% and 52.15%, respectively. In addition, inter-satellite station closure error and three-satellite closure error are reduced from 0.69 ns and 0.23 ns to about 0 ns. It can be seen that the accuracy of BDS time synchronization is significantly improved.

**Keywords:** BDS-3; satellite-ground and inter-satellite link; multi-source data; satellite clock offset; whole-network adjustment
