Page 40 - 卫星导航2021年第1-2合期

Du et al. Satell Navig (2021) 2:3 Page 7 of 22

bined solutions (Caissy et al. 2012; Guo et al. 2016). corrections as quasi-observations (El-Mowafy 2018),
Furthermore, the IGS products may sufer from sys- to overcome this kind of defciency.
tematic errors (Grifths and Ray 2013; Weiss et al.
2017). Although RTS products from IGS and the ACs • Satellite antenna PCOs and PCVs. Satellite PCO can
have been evaluated in many studies in recent years reach a few metres, and PCV centimetres, depending
(Hadas and Bosy 2015; Kazmierski et al. 2018; Zhang on the line-of-sight direction, signal frequency and
et al. 2018), the anomaly events and corresponding the satellite (Bilich and Mader 2010; Schmid et al.
failure rates have been rarely investigated. 2005). PCOs and PCVs are nominal errors which
can be modelled at the network-end, and are avail-
In addition to IGS and ACs, other institutes also pro- able from the IGS. However, the satellite PCO cannot
vide real-time products with comparable accuracies be well corrected for without reliable satellite atti-
(Ding et al. 2018; Fu et al. 2019), as well as some com- tude information, which is difcult to model during
panies which provide their commercial users with short periods of noon and midnight turns during the
real-time PPP services (Jokinen et al. 2018; Leandro eclipse period (Schmid et al. 2007).
et al. 2011; Liu 2018; Tobías et al. 2014). Apart from
satellite orbit and clock corrections, some of these • Receiver antenna PCOs and PCVs. Various phase
companies also provide global/regional ionospheric centre patterns exist for diferent antenna models,
corrections and/or regional tropospheric correc- manufacturing, radome designs and antenna installa-
tions. All these products are vulnerable to outliers or tions (Bilich and Mader 2010; Hatanaka et al. 2001).
failures. Take Trimble RTX corrections as an exam- To correct for these efects, mean absolute calibra-
ple, the probability of failure derived from historical tions of certain antenna types and models can be
and real-time data (with empirical overbound) is at determined using a specially designed feld robot
−6
the 1 × 10 (for GPS and Galileo orbit + clock and (Bilich and Mader 2010) or an anechoic chamber
−5
regional troposphere) to 1 × 10 (for GLONASS (Becker et al. 2010). Tere are nevertheless some
orbit + clock and regional ionosphere) level (Rodri- challenges, for example phase centre patterns may be
guez-Solano et al. 2019). not known for new antennas (i.e. uncalibrated equip-
ment); or integrated antenna-receiver units with-
Te performance degradation in orbit and/or clock out an external clock input; some antennas may be
products is due to various causes, such as unan- substantially diferent from the type mean; antenna
nounced thrusting events on GNSS satellites, phase centres of low-cost equipment may be insta-
unhealthy satellites (Caissy et al. 2012), changes of ble (Bilich and Mader, 2010; Murrian et al. 2016);
reference clock and Diferential Code Biases (DCB), etc. Tus, it is essential to have calibrations for non-
lack of broadcast almanac, and satellite modelling standard antenna models and installations, as well as
problems (Hadas and Bosy 2015). Meanwhile, the for new antenna types (Bilich and Mader, 2010).
quality of orbit and clock products can be afected
by tracking network errors, such as undetected cycle • Code bias estimation errors. Tese instrumental
slips, tropospheric mismodelling, errors in assumed delays include Time Group Delay (TGD) for single-
antenna heights, and the quality of the station-sat- frequency C/A users, DCB, Inter-System Bias (ISB)
ellite geometry (Zumberge et al. 1997). Similarly, when using multi-GNSS and Inter-Frequency Bias
tracking network errors can also afect regional (IFB) when using GLONASS, to name a few. Tey
ionospheric and tropospheric corrections. Tus, it are therefore either observation-type-dependent, fre-
is important to perform quality control or integrity quency-dependent, or system-dependent. Tey are
monitoring both at the network-end and at the user- all relative delays and contain satellite-dependent or
end. receiver-dependent parts (although sometimes they
are inseparable) (Villiger et al. 2016). Even though
It should be noted that for traditional real-time PPP PPP performance is partially tolerant to the errors in
processing, the observations are combined with orbit code observations, incorrect code biases can afect
and clock corrections. Accordingly, faulty correc- the convergence time of foat-PPP and reliable ambi-
tions will result in the exclusion of the corresponding guity fxing in PPP-AR (El-Mowafy et al. 2016; Kouba
observations (together with the corrections), degrad- et al. 2017).
ing the positioning results (El-Mowafy 2018). Some
methods were proposed, e.g. using orbit and clock Tese biases constitute the nominal errors and can
be either estimated at the user-end or the network-