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Shinghal and Bisnath Satell Navig (2021) 2:10 Page 8 of 17

observable using the blue and red box graph. Te num- measurement noises, σ 2 , σ 2 of the C/A-code and
L1/L5
C/A
bers on the right indicate the duration in terms of sec- carrier-phase measurements, respectively, at zenith is
onds or epochs. Te blue boxes signify the presence of directly proportional to the square of the pseudorange
the observable, while the red boxes indicate the absence chip length, C/A or carrier wavelength, and inversely
of the observable. Te L5 carrier-phase measurements proportional to the C/N (Braasch and van Dierendonck
0
are the most afected, followed by the L1 carrier-phase 1999). Unlike geodetic receivers, an elevation angle-
measurements, and the presence of all four observa- based weighing strategy is not justifed for smartphone
bles decreased from 90% in low multipath static envi- GNSS measurements, as smartphones receive signals
ronments to just 47% in medium multipath kinematic from all directions and have varying orientations due to
environments and 20% in high multipath scenarios. Te use. (Paziewski et al. 2019; Banville et al. 2019). A C/N -
0
smartphone antenna is not as sensitive to tracking the based stochastic model had been suggested by Banville
L5 signal as compared to the L1 signal (Wanninger and et al. (2019) where the parameters used to compute the
Heßelbarth 2020), which explains the frequent phase- standard deviation of the code and carrier-phase meas-
loss-of-lock and consequent data gaps afecting the L5 urements were estimated from the flter residuals. Tis
carrier-phase measurements the most. Tese data gaps in model was adapted to assign measurement weights based
any particular observable lead to the rejection of the sat- on multipath noise, chipping-length or wavelength and
ellite in the processing. And subsequently, after satellite C/N Since measurement prediction is carried out, espe-
0.
rejections due to missing observables or large residuals, cially for the missing carrier-phase measurements, the
the count of useable satellites falls to below the minimum prediction error (1 m) was incorporated into this weigh-
requirement resulting in no solution. ing factor. Te C/N -based stochastic model is as follows
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Figure 8 compares the count of actual satellites avail- (Banville et al. 2019):
able versus useable satellites after rejection for the driv-
1
ing dataset, with the solution gap portions identifed with σ = a + b × 10 − × C/N 0 (1)
10
2
black arrows.
On average, 11 satellites were tracked, but only 5 could where a is the RMS of pseudorange multipath noise for
be processed after rejections due to large residual mag- code measurements, while it is limited to the 1 m wave-
nitude, low elevation angle or C/N value, or missing length for carrier-phase (compensated for prediction
0
measurements. Several epochs only had 3 to 4 satellites error); b is the pseudorange chipping length of C/A-code
available for processing with all 4 measurements present. (293 m for L1 measurements and 29.3 m for L5 code
measurements) or carrier-phase wavelength for code and
carrier parameters, respectively.
C/N ‑based stochastic model
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Measurement weighting of parameters is another Static scenario assessment
important aspect in PPP processing and since C/N is Figure 9 compares the 2D and 3D RMS positioning accu-
0
a key quality indicator in assessing smartphone GNSS racy and convergence time for the static mannequin
measurements, this ratio can be employed in stochas- dataset after employing three diferent measurements
tic modeling (Braasch and van Dierendonck 1999). Te

Fig. 8 Satellites tracked versus satellites processed in a kinematic medium multipath scenario