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

However, neither empirical models nor efective methods integrity of the resolved ambiguity parameters, and the
exist to completely correct for these errors. To improve probability of wrong ambiguity fxing must be taken into
the positioning accuracy and integrity, it is necessary to account in the integrity risk budget.
carefully investigate all these error sources.
Tere are two approaches for PPP processing, namely Vulnerabilities and integrity fault analysis in PPP
foat-ambiguity PPP (foat-PPP) and fxed-ambiguity PPP To improve GNSS positioning performance, especially
(fxed-PPP) or PPP-AR. Both approaches can be imple- with respect to integrity, it is necessary to have a good
mented in real-time. Te major problem with the foat- knowledge of all potential threats and faults, or the so-
PPP technique is that it needs a longer time for the phase called failure modes (Bhatti and Ochieng 2007). Te
ambiguities to converge to their best estimates (for a analysis of failure modes can help identify GNSS integ-
flter-based solution) (Kouba and Héroux 2001). Moreo- rity requirements and develop a threat model as well as
ver, a re-initialisation process is needed once most of the prevent and/or protect against possible failures (van
satellite signals are lost. Such situations happen more fre- Dyke et al. 2003). Tere are many works published on
quently in urban environments. Te positioning accuracy the fault analysis of GNSS (Bhatti and Ochieng 2007;
of the kinematic foat-PPP solution after convergence van Dyke et al. 2003; Milner and Ochieng 2008; Ochieng
can reach the decimetre- to centimetre-level (Bisnath et al. 2003), but failure modes in the PPP technique are
and Gao 2009; Choy et al. 2017), which is high enough seldom discussed. In this paper the potential faults that
for ITS applications, when sufcient satellites with good need to be considered for PPP integrity (some of which
data quality are observed. However, the convergence/ are common for both PPP and SPS techniques) are inves-
reconvergence problem restricts the use of PPP for ITS tigated with two representative fault analysis methods:
applications. (1) Failure Modes and Efects Analysis (FMEA), and (2)
Te convergence period can be shortened by exploiting Fault Tree Analysis (FTA). A detailed discussion on some
the integer property of carrier-phase ambiguities through of the major threats is also presented, focusing on their
the application of AR techniques (Bisnath and Gao 2009; impacts on PPP.
Collins et al. 2010). To resolve the integer values of the
phase ambiguities, additional network-level satellite Integrity fault analysis
products are required. Tere are several alternate for- Failure Modes and Efects Analysis (FMEA)
mulations, such as Uncalibrated Phase Delays (UPD) or FMEA usually involves identifying all potential failure
Fractional-Cycle Biases (FCB), Integer Recovery Clocks modes with their causes and characteristics, impacts on
(IRC), Decoupled Satellite Clocks (DSC) (Collins 2008; users, probabilities of occurrence and/or corresponding
Bertiger et al. 2010; Ge et al. 2008; Laurichesse and Mer- mitigation methods (van Dyke et al. 2003; Milner and
cier 2007). PPP-AR can be further augmented with the Ochieng 2008). Te potential failure modes of the PPP
corrections derived from a regional RTK or Continu- algorithm are summarised in Table 1. Tey are com-
ously Operating Reference Station (CORS) network, a piled from existing literature (Bhatti and Ochieng 2007;
technique referred to as PPP-RTK or PPP-RA (PPP with Imparato et al. 2018b; Kouba et al. 2017; Martins 2014;
regional augmentation), where PPP provides rapid con- Ochieng et al. 2003; Tomas et al. 2011; Witchayangkoon
vergence to centimetre-level positioning accuracy (Geng 2000), and are categorised into fve groups: satellite and
et al. 2011; Li et al. 2011; Teunissen et al. 2010; Wüb- signal, medium (atmosphere), products (corrections),
bena et al. 2005). Te regional network is used not only work environment, and user. Te mathematical mod-
to estimate the parameters such as the satellite clock els for diferent types of failures, which were proposed
corrections and satellite phase biases, but also to inter- by Bhatti and Ochieng (2007), are listed in Table 2. Such
polate ionospheric (and sometimes tropospheric) delays models, although approximate, can help design and
(Teunissen et al. 2010; Wübbena et al. 2005; Shi et al. evaluate integrity monitoring algorithms in a simulation
2014). Te a priori knowledge of the ionosphere is the context (Bhatti and Ochieng 2007). Prior probabilities
key to rapid convergence (Choy et al. 2017). shown in Table 1, which are cited from the existing litera-
It should be noted that the accuracy and integrity of ture, are empirical assumptions or estimates, mainly sup-
the PPP solutions are only evaluated after convergence. ported by historical data, and they are subject to ongoing
Tis is because during solution convergence the system refnements.
cannot provide the required level of performance, i.e.
sub-metre accuracy and related integrity. Likewise, integ- Fault Tree Analysis (FTA)
rity monitoring for PPP-AR is only performed after fx- Te FTA is a risk analysis procedure that breaks
ing the ambiguities. However, an extra procedure, known down a failure event to lower-level events or factors
as ambiguity validation, is needed for monitoring of the to determine the probabilities of loss of integrity or