Article Figures & Data
Figures
- FIGURE 1
Flowchart of the loosely coupled (blue line) and tightly coupled (red line) GNSS-INS integrations implemented using the EKF
- FIGURE 2
Illustration of the graph structure of the implemented loosely coupled and tightly coupled Global Navigation Satellite System–inertial navigation system integrations using factor graph optimization
- FIGURE 3
The left image shows the experimental vehicle and sensor setup, and the right image illustrates the tested urban canyon in Hong Kong
- FIGURE 4
Trajectories of the LC GNSS/INS integrations using EKF and FGO in the east, north, and up (ENU) frame. The black curve denotes the reference trajectory. The red and blue curves in the left-hand side figure represent the trajectories from LC integrations using EKF and FGO, respectively. The right figure shows the 2D error
- FIGURE 5
Trajectories of TC GNSS/INS integrations using EKF and FGO in the east, north, and up (ENU) frame. The black curve denotes the reference trajectory. The red and blue curves in the left-hand side figure represent the trajectories from TC integrations using EKF and FGO, respectively. The right figure shows the 2D error
- FIGURE 6
2D residuals of the loosely coupled GNSS/INS integrations using EKF and FGO
- FIGURE 7
2D residuals of the tightly coupled GNSS/INS integrations using EKF and FGO
- FIGURE 8
2D positioning errors under different window sizes used in TC GNSS/INS integrations using FGO. The x-axis denotes the epochs, and the y-axis represents the value of 2D positioning errors. The red and green rectangles denote the sliding windows of sizes 30 and 256 s, respectively
- FIGURE 9
Sky-view and satellite visibilities of the four selected epochs in Figure 8. The blue and red circles denote the line-of-sight (LOS) and non-line-of-sight (NLOS) satellites, respectively
- FIGURE 10
Histogram of GPS (left) and BeiDou (right) pseudorange errors and the corresponding fitted Gaussian mixture model (GMM) inside a sliding window of epoch D with a size of 30 s (as indicated by the red rectangle in Figure 8). The x-axis denotes the value of pseudorange errors acquired by the ray-tracing technique. The y-axis denotes the counts of errors within the histogram. The blue curve represents the GMM fitted by the histogram using three Gaussian components
- FIGURE 11
Histogram and Gaussian mixture models (GMMs) of pseudorange residuals near epoch D with a sliding window of 30 s. These are similar to Figure 10, with the major difference being that the histogram and GMMs are based on the residuals
- FIGURE 12
Histogram and Gaussian mixture models (GMMs) of pseudorange residuals similar to Figure 11, with the major difference being that the histogram and GMMs are based on the residuals near epoch D with a sliding window of 256 s
- FIGURE 13
Comparison of the computational time used in tightly coupled (TC) integration using factor graph optimization (FGO) and the TC incremental smoothing and mapping algorithm (iSAM) (Kaess et al., 2008)
Tables
Parameter F T A Value 10 45 30 Parameter SUERE (m) 
Value 10 8.17e-3 1.31e-4 All data Loosely coupled EKF Tightly coupled EKF Loosely coupled FGO Tightly coupled FGO Mean error 9.14 m 8.03 m 7.01 m 3.64 m Std 7.60 m 7.15 m 6.41 m 2.84 m Used Time 0.053 s 0.071 s 15.41 s 75.30 s
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