Table 1 Processing strategies in multi-constellation GNSS PPP

Signals and tracking modes processed

The tracking approaches for the bands are sorted in increasing order of selecting priority, and each tracking mode is represented by one letter

GPS L1/L2: C S L X W; L5: I Q X

GLONASS G1/G2: C P

Galileo E1/E6: C X; E5a/E5b/E5: I Q X

BDS-2 B1/B2/B3: I Q X

Sampling rate

30 s

Elevation cutoff

7°

Weighting

The a priori precisions for carrier-phase and code observations are 0.01 cycle and 0.6 m, respectively

Elevation-dependent factor: \(\left\{ {\begin{array}{*{20}l} 1 \hfill & {{{E}} > 30^\circ } \hfill \\ {2sin\, (E)} \hfill & {{{E}} \le 30^\circ } \hfill \\ \end{array} } \right.\), where E is the satellite elevation

Weight ratios: GPS:GLONASS:BDS:Galileo = 4:4:1:1 [11]

Phase center

Phase center offset/variation (PCO/PCV) for GNSS satellite antennas follows igs14_2056.atx, receiver antenna PCO/PCV corrections of BDS and Galileo satellites refer to GPS L1 frequency

Tropospheric delay

Zenith wet delay parameters are estimated for the stations at each epoch by a one-dimensional random walk process (spectral density is 0.015 m/hour), the Global Mapping Function (GMF) is applied [25]

Ionospheric delay

(1) PPP with raw observations: the ionospheric delay is estimated for each station-satellite pair as a one-dimensional random walk process, the corresponding spectral density is set as 0.5 TECU/min

(2) PPP with dual-frequency IF observations: the first order of ionospheric delay is eliminated and the higher order of ionospheric delay is ignored

Receiver/Satellite DCB

Satellite DCB are corrected by the DCB products issued by Chinese Academy of Sciences [26], the receiver DCB are estimated as constants in one day

Receiver clock

Solved at each epoch by a white noise process (spectral density is 900 m/s)

GPS time as a reference and estimating GLONASS/BDS/Galileo to GPS inter-system bias for each station

Receiver inter-frequency clock biases

The inter-frequency clock biases are lumped to DCB parameters and ignored

Satellite clock/orbits

Fixed to Wuhan University MGEX (WUM) precise orbit and clock products [27]

Tidal displacement

Corrected

Ambiguity resolution

No

BDS satellite-induced code bias

Corrected by elevation-dependent model [28]