PPP models and performances from single-to quad-frequency BDS observations

Nowadays,China BeiDou Navigation Satellite System(BDS)has been developed well and provided global services with highly precise positioning,navigation and timing(PNT)as well as unique short-message communication,particularly global system(BDS-3)with higher precision multi-frequency signals.The precise point positioning(PPP)can provide the precise position,receiver clock,and zenith tropospheric delay(ZTD)with a stand-alone receiver compared to the traditional double differenced relative positioning mode,which has been widely used in PNT,geodesy,meteorology and so on.However,it has a lot of challenges for multi-frequency BDS PPP with different strategies and more unknown parameters.In this paper,the detailed PPP models using the single-,dual-,triple-,and quad-frequency BDS observations are presented and evaluated.Firstly,BDS system and PPP method are introduced.Secondly,the stochastic models of time delay bias in BDS-2/BDS-3 PPP including the neglection,random constant,random walk and white noise are presented.Then,three single-frequency,four dual-frequency,four triple-frequency and four quad-frequency BDS PPP models are provided.Finally,the BDS PPP models progress and performances including theoretical comparison of the models,positioning performances,precise time and frequency transfer,ZTD,inter-frequency bias(IFB)and differential code bias(DCB)are presented and evaluated as well as future challenges.The results show that the multi-frequency BDS observations will greatly improve the PPP performances.