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Li et al. Satell Navig (2021) 2:1 Page 12 of 14

performances of the multi-GNSS PPP/S-VINS solu-
tion were comprehensively evaluated with respect to
the stand-alone S-VINS positioning, the S-VINS aided
multi-GNSS PPP positioning, and the triple integrated
system positioning.
The GNSS outage simulation test demonstrates
that the S-VINS can achieve a slower degradation in
positioning accuracy than the INS-only. The statis-
tical analysis of the complete GNSS outages for 50 s
shows that the average RMS of position drifts for
S-VINS is 0.80, 1.16, and 0.12 m with an improve-
ment of 74.4%, 61.8%, 20.0% in north, east, and up
components, respectively, compared with the INS-
only mode. Furthermore, more than 90% of the pre-
dicted position differences is at centimeter level
during one-second GNSS outages. According to the
results of the vehicle-borne experiment, the accu-
rate predicted positions from S-VINS can assist PPP
to improve the overall positioning performance. The
maximum position error of the stand-alone PPP
(GPS + GLONASS + BDS) solution is reduced from
(5.36, − 19.14, − 44.99) m to (2.00, − 2.78, − 3.13) m
Fig. 10 Accuracy comparison of the multi-GNSS PPP/S-VINS solution, compared with the results of the aiding of S-VINS in
multi-GNSS PPP/INS (LC) solution, and multi-GNSS PPP/INS (TC) east, north, and up components, respectively. Besides,
solution in a GNSS-challenged environment the improvements of 3D positioning accuracy for the
unaided PPP solution are 49.0% for GPS, 40.3% for
GPS + GLONASS, 45.6% for GPS + BDS, and 51.2%
still largely impacted by the PPP performance due to the for GPS + GLONASS + BDS. Due to the improvement
location-based information fusion. In addition, the major in the positioning accuracy of the S-VINS aided PPP
improvement of PPP is in vertical component while the solution, better positioning results can participate
horizontal components obtain a modest improvement in the graph optimization for global fusion. The sta-
with the aiding of S-VINS. In conclusion, the multi- tistics shows that that the RMSs of position errors of
GNSS PPP/S-VINS solution achieves a higher position- the multi-GNSS PPP/S-VINS solution are 0.88, 1.47,
ing accuracy and availability compared with multi-GNSS/ and 0.96 m with an improvement of 7.4%, 6.4%, and
INS solutions in such GNSS-challenged environment. 27.3% in east, north, and up components, respectively,
compared with the S-VINS aided PPP (GPS + GLO-
Conclusion NASS + BDS) solution. Moreover, the multi-GNSS
To improve the positioning performance in GNSS- PPP/S-VINS solution improves 3D positioning accu-
challenged environments, an optimization-based racy by 60.6% and 41.8% compared with the LC multi-
semi-tightly coupled multi-sensor fusion framework of GNSS PPP/INS solution and the TC multi-GNSS PPP/
multi-GNSS PPP/S-VINS was developed and validated INS solution, respectively.
in this study. Based on the GNSS outage simulation In conclusion, the positioning performance of the
test and the vehicle-borne experiment, the positioning PPP solution can be signifcantly improved with the

Table 5 RMS of position diferences for S-VINS solution, multi-GNSS PPP/S-VINS solution, LC multi-GNSS PPP/INS
solution, and TC multi-GNSS PPP/INS solution (unit: m)
RMS in diferent directions RMS in diferent directions RMS in diferent directions RMS in diferent directions
for S‑VINS for Multi‑GNSS for Multi‑GNSS for Multi‑GNSS
PPP/S‑VINS PPP/INS (LC) PPP/INS (TC)
E N U E N U E N U E N U

12.75 6.23 0.53 0.88 1.47 0.96 3.48 1.18 3.36 0.62 0.53 3.27