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Du et al. Satell Navig (2021) 2:3 Page 12 of 22

carrier-phase observation residuals for monitoring sta- large variances, which is impractical for PPP (Teunis-
tions to validate orbit and clock corrections, regional sen 1990; Wieser 2004), and thus may not be sensitive to
tropospheric corrections, and regional ionospheric some faults in the dynamic model (see Appendix–Exam-
corrections (Weinbach et al. 2018). A two-step integ- ple 2). On the other hand, snapshot PLs cannot protect
rity monitoring procedure, i.e. pre-broadcast and post- against the undetected faults in historical observations or
broadcast integrity monitoring, is adopted to detect and in the predicted states.
fag out-of-tolerance corrections and to generate timely Additionally, as discussed previously, the traditional
alarms to users. Te integrity information is provided as RAIM methods cannot handle multiple faults correctly,
Quality Indicators (QI) with the correction data; how- which have a high probability when carrier-phase meas-
ever, how to calculate PLs using QIs was not mentioned. urements are used, especially for multiple GNSS constel-
Tere is little literature that discusses the quality control lations. In contrast to the above research, Gunning et al.
procedures which can be used to check the integrity of (2018) adopted the well-founded models of ARAIM for
PPP corrections, e.g. FCB/IRC estimation (Cheng et al. civil aviation for PPP integrity monitoring. Tey applied
2017), orbit and clock corrections (El-Mowafy 2018), and an ARAIM-like methodology and algorithms of both
the combined corrections of satellite clocks, ionospheric residual-based (Chi-square) and solution-separation test
parameters and ambiguity solutions (Khodabandeh et al. statistics to determine the PLs in PPP, enabling initial
2019). Tese quality control procedures can perform integrity monitoring for a foat-PPP position solution.
FDE and the analysis of diferent faults, as well as their Teir method (or a similar one) was later evaluated with
impacts on the PPP solutions. IGS tracking data, fight data and driving data, using GPS
Current user-level integrity algorithms for PPP are broadcast ephemeris and real-time corrections, including
still very preliminary, hence not well-accepted in mod- SBAS corrections (Gunning et al. 2019a, b; Norman et al.
els and methods. Te Spanish company GMV devel- 2019; Phelts et al. 2020). However, a bank of parallel fl-
oped their own integrity concept for their PPP solution, ters was used, as in Brenner (1996), for the Kalman flter
known as magicPPP (Romay and Lainez 2012; Navarro to account for historical faults, based on an assumption
et al. 2015). Teir integrity concept was a little diferent that all faults will exist continuously for a period of time.
from that developed in the aviation feld as they were Such a method has a high computational cost. More
not restricted to system-level only or user-level only importantly, the nominal error model and threat model
integrity, but focused on “most favourable combination are very preliminary for complex urban environments. To
of signifcant indicators” which they assess (Romay and provide PLs for PPP in challenging environments, Blanch
Lainez 2012). In the PPP-Wizard software developed by et al. (2020) refned the threat model and accordingly
CNES, two FDE mechanisms are implemented, namely adapted the FDE algorithm, considering the efect of
“Simple FDE” with post-ft residuals screened one by Kalman fltering time updates, to address potential faults
one against empirical thresholds and “Advanced FDE” in urban and suburban areas.
testing all the combinations of observations to fnd one
with all post-ft residuals below the threshold values Open research issues on PPP vulnerabilities
(Laurichesse and Privat 2015). Te software can also and integrity for ITS applications
provide an integrity indicator for each solution. How- Tere are many problems to be addressed for PPP integ-
ever, the FDE methods and the integrity indicator in rity in ITS applications. One of the prerequisite issues
PPP-Wizard are not statistically sound (for example is the determination and standardisation of specifc
P , i.e. the probability of false alert is not specifed) integrity requirements for various ITS applications and
FA
(see Appendix–Example 1). diferent levels of automation, without which the cor-
Jokinen et al. (2011, 2013) and Seepersad and Bisnath responding integrity monitoring methods cannot be
(2013) adopted the traditional RAIM algorithms in PPP properly evaluated. Another challenging problem is
processing to enable FDE and PL computation. Tey that stochastic models of diferent errors must be clari-
directly performed snapshot RAIM at each separate fed, e.g. ambiguity errors, non-Gaussian range errors, as
epoch even though Kalman flters were used. On the one well as the error correlations amongst the measurements
hand, the fault detection statistics used by them were the and over time (Bryant 2016, 2019). It is also important,
weighted sum of squares of post-ft measurement residu- though challenging, to develop a representative threat
als. Tis kind of test is based on the assumption that the model for integrity risk evaluation and PL computation
dynamic model is absent or predicted states have very (Gunning et al. 2018). Te threat model, which is a list of