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Du et al. Satell Navig (2021) 2:3 Page 9 of 22

It has been shown that availability of multi-frequency and DSC—as mentioned earlier. To achieve fxed-
signals can enhance cycle slip detection (Dai et al. ambiguity PPP solutions, one should carefully choose
2009; El-Mowafy and Deo 2015; Zhang and Li 2016). the corresponding PPP-AR products.
Tis is because there are more geometry-free combi-
nations, which can help in identifying the signal fre- To explore interoperability of the various PPP-AR
quency (and hence the carrier-phase measurement) products, Seepersad and Bisnath (2016) developed
on which the cycle slip has occurred. For single-fre- a transformation matrix to allow users to trans-
quency PPP based on GRAPHIC combinations, small form the IRC and FCB products to the DSC format.
cycle slips may be hard to identify due to the high Teir method also enabled multiple AR solutions to
noise level. To overcome these difculties, Banville improve the reliability of the user solution, especially
and Langley (2012) and Carcanague (2012) have pro- in cases of interruptions in specifc PPP-AR prod-
posed algorithms for cycle slip detection/repair using ucts. Tough their method is feasible, diferences in
time-diferenced carrier-phase observations and a satellite antenna conventions and/or in the satellite
geometry-based method. yaw attitude models can still cause AR failure with
the transformed products (Seepersad 2018).
As there are various causes for cycle slips, and they
are highly dependent on the local environment, it Unfortunately, PPP service providers seldom reveal
is extremely difcult to characterise the prior prob- the detailed conventions and models adopted in
ability of cycle slips. It may be easier to evaluate the their network solutions, and sometimes the correc-
probability of undetected cycle slips after a detection tions are not clearly defned (Seepersad and Bisnath
and repair procedure using a specifc method. 2016). It also should be noted that the potential faults
caused by incompatibility or inconsistency depend
User on users themselves. Once introduced, such faults
will continuous to exist until their removal.
• Incompatibility or inconsistency. PPP processing
should be consistent and compatible with the con- • Incorrect fxed ambiguity. Ambiguities fxed to wrong
ventions followed by the product generation pro- integer values will introduce large errors into the
cesses. Mixing the orbits generated by one AC with PPP-AR solutions. To check whether the resolved
the clocks from another will introduce position- ambiguities are correct, an ambiguity validation pro-
ing errors because of correlations in the computa- cedure is needed. Tere are several ambiguity vali-
tion of the orbit and clock corrections (Zumberge dation methods, e.g. the ratio-test, F-test, t test, dif-
et al. 1997). Te data type, as well as the transmitter ference test and integer aperture estimation and its
antenna (PCO and PCV) and attitude models, used variants, which are all in the framework of hypoth-
in PPP processing should also be consistent with esis test theory (Euler and Schafrin 1991; Frei and
the ones to which the products refer (Kouba et al. Beutler 1990; Han 1997; Teunissen 2003, 2005a, b;
2017; Montenbruck et al. 2015). Inconsistency of Tiberius and De Jonge 1995; Verhagen 2005; Wang
the geodetic reference frame among station coor- et al. 1998). However, no single approach is totally
dinates, EOPs, satellite/receiver PCV, satellite orbit reliable in all situations, and further improvements
products, and the coordinate and time systems need to be explored (Li et al. 2013; Verhagen 2004;
of diferent GNSSs can also introduce additional Verhagen and Teunissen 2013; Yu et al. 2017).
errors, as mentioned earlier. In contrast to other threats in observations, incorrect
fxed ambiguity is a solution domain failure caused
Since PPP-AR algorithms are complex and do not by the correlation between the estimator and param-
have a standard methodology, users will possibly face eter (between ambiguities and other parameters). It
the risks of inconsistency when using publicly avail- should be treated separately in the integrity monitor-
able orbit, clock, and other products. It is important ing procedure. In fact, ambiguity validation is a sepa-
that the user-end adopts the algorithms and models rate integrity monitoring or quality control proce-
consistent with those adopted for the computations dure of integer ambiguity estimates.
of the biases and corrections at the network-end.
“Mixing” of diferent conventions may lead to incor- • Communications problem. Errors may occur over the
rect AR or even positioning failure (Seepersad and communication link that transmits real-time correc-
Bisnath 2016). For example, there are three diferent tions, causing erroneous data, data loss, or high data
commonly used PPP-AR models—UPD/FCB, IRC latency. Short-term prediction of real-time correc-