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Du et al. Satell Navig (2021) 2:3 Page 8 of 22

end (Dach et al. 2006; El-Mowafy et al. 2016). Tey or ambiguity fxing, and the resultant unreliability of
are assumed to be constant during short-to-medium ambiguity fxing (Henkel et al. 2016; Seepersad and
observing periods, but may vary slowly or abruptly Bisnath 2015).
in various situations including receiver or antenna
replacement, satellite component switching or acti- Multipath/NLOS is environment-dependent and
vation, thermal variation of receiver or satellite (dur- is especially severe in dense urban areas where tall
ing eclipse season), aging and so on (Imparato et al. buildings refect, difract and/or block the GNSS sig-
2018b). nals (Groves et al. 2013; van Nee 1995). Furthermore,
low-cost GNSS receivers may sufer from larger mul-
• Incorrect phase biases. Tese biases are also fre- tipath and NLOS errors than geodetic-grade receiv-
quency-dependent and system-dependent, and are ers due to their poor multipath/NLOS suppression
relative values (between satellites and receivers). (Murrian et al. 2016; Pesyna et al. 2014) and low-
Similar to code biases, phase biases are considered quality antennas, challenging their use in high pre-
stable, although short-term variations have been cision positioning for ITS. Terefore, quality control
observed due to ambient temperature efects (Zhang and stochastic modelling are very important in PPP
et al. 2017). In fact, the factors leading to code bias processing when using low-cost devices (Bisnath
variations can also afect phase biases. Network gen- et al. 2018). A comprehensive overview of multipath
erated phase biases may be either not reliable or not and NLOS characteristics and their mitigation can be
fully available due to network-end errors. Mismodel- found in Imparato et al. (2018b).
ling of the hardware delay, i.e. biases in the estimated
UPDs/FCBs, IRCs or DSCs, will be absorbed into the • Cycle slips. Tere are fve main causes for cycle
estimated ambiguity terms, causing incorrect fxed- slips: signal obstruction, low signal-to-noise ratio,
PPP solutions, or even failure in ambiguity fxing receiver software faults (Hofmann-Wellenhof et al.
(Geng et al. 2012). Cheng, et al. (2017) proposed a 2001), receiver dynamics (Julien 2005), and high
quality control and reliability analysis procedure for level of ionospheric disturbance (Cai et al. 2012).
their own FCB and IRC estimation to achieve reliable Cycle slips are more likely to occur in dense urban
PPP-AR. Teir detector for FCB was able to detect environments, especially for receivers mounted on
small phase outliers (larger than 0.4 cycles) and the a moving vehicle. As a result, ITS applications are
undetectable outliers had insignifcant impact on easily afected by cycle slips. Cycle slips are a major
estimated FCBs. challenge for PPP processing for both foat-PPP
and PPP-AR solutions. Unfxed or incorrectly fxed
cycle slips can result in the need for re-initialisation
and reconvergence of ambiguity parameters or lead
Work environment to incorrect ambiguity estimation. Consequently,
the reliability, continuity and availability of the
• Multipath and NLOS. Code multipath may cause navigation system may not meet the performance
range errors of up to 150 m for L1, while NLOS requirements of ITS.
errors can be up to several kilometres (Groves et al.
2013). Te dual-frequency IF combinations will fur- A number of algorithms for cycle slip detection and
ther amplify these efects. Carrier-phase multipath correction which apply to standalone GNSS position-
is much lower (about two orders of magnitude) than ing have been proposed. Real-time dual-frequency
those of code observations. Te maximum carrier- cycle slip correction algorithms are typically based
phase multipath error is frequency-dependent and on a time-diferenced geometry-free combination
amounts to 1/4 cycle (Georgiadou and Kleusberg (Banville et al. 2010; Kim and Langley 2001; Zhang
1988; Braasch 1992). NLOS carrier-phase error is and Li 2012). Tis kind of measurement combination
within half a cycle (modulo one carrier cycle) (Groves is sensitive to the temporal variation of ionospheric
et al. 2013). Since the accuracy of PPP depends on delay, receiver phase wind-up, and multipath. Tus,
the carrier-phase observations, the impact of code ionospheric variations and other parameters should
multipath on PPP can be down weighted and is not be estimated along with the integer cycle slips. In
as severe as that for code-only positioning tech- addition, an integer validation procedure is needed to
niques. Te major adverse efect of code multipath is determine the correct number of integer cycle slips
the longer time needed for the solution convergence (Zhang and Li 2016).