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Shinghal and Bisnath Satell Navig (2021) 2:10 Page 12 of 17

4 measurements is 2.8 and 2.6 m, respectively. Te cubic 100% continuous solution was obtained. Te RMS hori-
spline extrapolation yields an error of 3.5 m for the same. zontal positioning error decreases from 15.5 m to 8.4 m
Based on the analysis carried for a wide range of data, it and fnally to 5.8 m for the portion between epochs
was concluded that better prediction occurs with linear 1553–1953.
extrapolation using measurements from the previous two As seen, the prediction and C/N -based stochastic
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epochs. Tis result can be attributed to the large variabil- model improved the position availability and accuracy,
ity in the magnitude of code and carrier-phase measure- considerably. Te RTK solution for the same had an avail-
ments over successive epochs in a dynamic environment ability of 98% (1983/2021), suggesting the successful use
and hence, it is best to use measurements from a mini- of a similar prediction technique for it as well. Further,
mum number of past epochs to predict ahead. Te posi- several other datasets were tested for the same and the
tioning solution obtained with the application of this positioning accuracy was compared against the SPP, RTK
technique is investigated next. and internal positioning solution.

Kinematic scenario assessment Comparison of various positioning solutions
Suburban vehicle data collected on DOY 325, 2019 suf- Tis section compares the PPP positioning solution after
fered from frequent data gaps. Figure 14 shows the vehi- conditioning of raw measurements with the SPP, RTK
cle trajectory positioning accuracy and availability before and internal phone solutions. Both static and kinematic
the application of the C/N -based stochastic model and data have been compared and quantitative comparison
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measurement prediction techniques (Fig. 14a), after the results are tabulated.
implementation of the C/N -based stochastic model but
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no prediction (Fig. 14b), and after the application of the Static dataset
C/N -based stochastic model and the prediction strat- Most GNSS chips compute positioning solutions using
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egy (Fig. 14c). Te red ovals indicate periods of no solu- the SPP technique using the GPS L1 code measure-
tion and/or solution divergence. Te three solutions have ments. Hence, it is deemed necessary to test the posi-
been plotted together (Fig. 14d) and with the SwiftNav tioning accuracy of the SPP technique with PPP solution
PPP solution (Fig. 14e). obtained by the YorkU PPP engine. A static dataset was
Te objective of the analysis is to compare the overall chosen and a weighted, least-squares, epoch-by-epoch,
improvement in the horizontal positioning accuracy and GPS L1 code SPP solution was computed. Data collected
availability of the Xiaomi PPP solution with itself before on DOY 225, 2019, by attaching the phone to a tripod,
and after the implementation of the C/N -based stochas- was chosen since it represents the standard open sky,
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tic model and prediction technique using the Piksi PPP static positioning test. In degraded and difcult environ-
reference solution as shown in Fig. 15. ments, the SPP solution quality was expected to dete-
Notably, the phase centers of the SwiftNav antenna riorate, further. Figure 16 compares the two positioning
and the phone antenna were not aligned. Te SwiftNav solutions where the smooth and continuous PPP solution
antenna on the vehicle roof had better signal availability, converges to a horizontal positional accuracy of 1 m in
while the smartphone being inside the car had additional 9 min.
signal blockages, fewer tracked satellites, consider- Te RMS in the horizontal and vertical directions are
able missing carrier-phase measurements and multipath 22 cm and 35 cm, respectively, whereas the SPP solu-
afecting the code measurements. Despite these adversi- tion is scattered and irregular with a horizontal and ver-
ties, with the implementation of prediction and C/N - tical RMS of 2.0 m and 3.0 m, respectively, as shown in
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based stochastic model, a solution with 100% availability Table 8.
is achieved and the accuracy of the positioning solution
improved, especially over the region between epoch 1553 Kinematic dataset
and 1953 – highlighted in Fig. 14. Overall, there is a 64% Te kinematic dataset collected on DOY 85 was pro-
decrease in horizontal positioning standard deviation cessed in PPP mode after implementing the C/N -based
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and RMS error and a 1.3% increase in solution availability stochastic modeling and prediction technique and the
to 100% after the conditioning and prediction as shown solution is compared against RTK and internal smart-
in Table 7. phone solutions. It is expected that the internal solution
For the major outage between epochs 1553–1953, 23% was computed using SPP with the aid of measurements
(91/400) of epochs has no solution before the C/N - from internal sensors. Due to lack of internet connection,
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based stochastic model and prediction, which decreased the solution was not aided by measurements from cell
to 5% (21/400) after the stochastic model implementa- towers and hence, the positioning solution periodically
tion, while with both the conditioning and prediction, a showed drifts. Te RTK baseline, which matched the PPP