Analysis of Galileo five-frequency precise satellite clock estimation models and its effect on multi-frequency PPP

The Global Navigation Satellite System (GNSS) multi-frequency observations are widely used in positioning applications, while precise orbit determination and precise clock estimation (PCE) techniques typically employ dual-frequency undifferenced (UD) ionospheric-free (IF) observations from global networks. To fully utilize the multi-frequency GNSS observations for generating satellite products at the server-end, we develop some new five-frequency PCE models based on Galileo data, which are five-frequency uncombined FFUC model, FFIF0 model combining the E1/E5a, E1/E5b, E1/E5 and E1/E6 IF observables, FFIF1 model combining E1/E5a and E1/ E5a/E5b/E5/E6 IF observables, respectively. The traditional dual-frequency UD IF and triple-frequency PCE models are also introduced for comparison. The new multi-frequency PCE models can not only make full use of the modern GNSS multi-frequency observations, but also obtain satellite clock offsets and inter-frequency clock bias (IFCB) at the same time, which can better support multi-frequency precise point positioning (PPP) appli-cations. The multi-frequency models can improve the stability of GNSS satellite clock estimation, the precision of satellite clock offsets can be improved by 8-12% for triple-frequency models, and 19-27% for five-frequency PCE models compared with the traditional dual-frequency IF model. The PPP positioning accuracy using only multi -frequency satellite clock offsets can be improved by 7-18% for dual-frequency PPP, 8-15% for triple-frequency PPP, 4-16% for five-frequency PPP. The positioning accuracy can be further improved by 11-28% for triple -frequency PPP and 7-20% for five-frequency PPP. Therefore, the new multi-frequency PCE models are demonstrated to support PPP applications with better performance.