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

but also focusing on the multi-frequency observations (Li accurate local pose estimation, the errors still accumulate
et al. 2019b, 2020a, b). Briefy, the multi-frequency and over the time.
multi-GNSS based PPP is becoming increasingly fashion- To eliminate the accumulated errors of VINS, many
able for precise positioning services (Alkan and Öcalan researchers integrate the GNSS and VINS for realizing
2013; Guo et al. 2018), particularly in some new applica- a local accurate and global drift-free localization. Lynen
tions such as self-driving cars and unmanned aerial vehi- et al. (2013) proposed a basic multi-sensor fusion frame-
cles (Nie et al. 2019; Geng and Guo 2020). work to process delayed, relative, and absolute meas-
However, PPP fails in the cases of observation out- urements from diferent sensors. Mascaro et al. (2018)
ages or harsh signal environments (Zhang and Li 2012). proposed a decoupled optimization-based multi-sensor
Consequently, the Inertial Navigation System (INS) has fusion method, which is demonstrated to be more accu-
been utilized to assist PPP in GNSS-challenged envi- rate than other decoupled fusion strategies. Although
ronments in the last decades (Roesler and Martell 2009; some progress has been made with these methods in
Gao et al. 2017). Shin and Scherzinger (2009) demon- multi-sensor fusion navigation, they adopt the decoupled
strated that PPP/INS integration could realize a better way to integrate the GPS and VINS. In addition, only
accuracy and reliability of positioning in both open sky the GPS derived positions are utilized in their frame-
and GNSS blocked areas. Rabbou and El-Rabbany (2015) work rather than the GNSS raw observations with more
presented a tightly coupled multi-GNSS PPP/INS solu- available information. Vu et al. (2012) developed a multi-
tion and achieved the positioning accuracy at decimeter sensor fusion framework with diferential GPS (DGPS),
to centimeter-level when the measurement updates from vision, and INS, which can provide a lane-level vehicle
GNSS are available. Nevertheless, the performance of the navigation in GNSS open-sky conditions. Moreover, Li
GNSS/INS integration is degraded due to the rapid INS et al. (2019a) proposed a tightly coupled fusion solution
drift errors for the case of the long-term GNSS outages. of multi-GNSS Real-Time Kinematic (RTK)/INS/vision,
Favorable complementary properties of visual and iner- which can achieve centimeter-level positioning accuracy
tial measurements make them suitable for fusion. Tus, in GNSS degraded conditions. In the above two studies,
extensive applications based on a visual-inertial integra- the relative positioning methods were used to provide
tion were found in drones (Weiss et al. 2012) and self- the global locations, which requires additional GNSS
driving vehicles (Li and Mourikis 2012). Generally, the infrastructures such as reference stations and receivers
existing visual-inertial fusion methods can be classifed in comparison to PPP. Zhu (2019) proposed a new struc-
into the optimization-based (Yang and Shen 2017; Use- ture named Semi-Tightly Coupled (STC) integration,
nko et al. 2016) and the flter-based approaches (Bloesch which realized multi-sensor information fusion by the
et al. 2015; Tsotsos et al. 2015). A popular flter-based bidirectional location transfer and sharing in two sepa-
Visual-Inertial Odometry (VIO) algorithm was proposed rate navigation systems. Te STC not only combines the
by Mourikis and Roumeliotis (2007). In their approach, advantages of the Loosely Coupled (LC) integration and
a versatile measurement model was presented to express Tightly Coupled (TC) integration, but also overcomes
the geometric constrains among multiple-camera poses their main defciencies.
with a common view. In practice, the optimization- In this contribution, we present a graph-optimization
based approaches can provide higher accuracy than the based and semi-tight coupling framework of multi-GNSS
flter-based approaches given adequate computational PPP and S-VINS for improving the PPP performance in
resources (Delmerico and Scaramuzza 2018). Te prop- a GNSS-challenged environment and realizing a stable
erty of the re-linearization at each iteration contributes and accurate global positioning outputs in a complex
to the high accuracy of the optimization-based methods. driving environment. In addition to a GNSS outage simu-
Leutenegger et al. (2015) presented a keyframe-based lation test to verify the positioning capacity of S-VINS,
Visual-Inertial Navigation System (VINS) and used the vehicle-borne experiment was also carried out in the
Google’s Ceres solver to perform the nonlinear optimi- campus of Wuhan University to assess the positioning
zation (Agarwal et al. 2012). Besides, the sliding window performances of the S-VINS aided PPP solution and the
strategy was adopted in their study to reduce the com- multi-GNSS PPP/S-VINS solution. Te contribution of
putation complexity of optimization. Qin et al. (2018) the proposed method to precise positioning is presented
proposed a complete and versatile monocular VINS, and analyzed. In the following parts of this paper, we frst
which can realize the indoor positioning of drones with describe the methods used in this study and then explain
accuracy at a decimeter-level. Additionally, the transla- the algorithm implementation for the triple integrated
tion error of the stereo VINS (S-VINS) is about 1% of the system. Subsequently, the experimental situation is intro-
driving distance in an outdoor vehicular experiment (Qin duced, and the results are analyzed. Finally, the conclu-
et al. 2019). Although VINS can achieve a robust and sions are summarized.