## 7 Experimental Description and Result Analysis
In order to demonstrate and assess how different sensory-integration schemes perform in challenging environments, we gradually reduce the number of visible GPS/GLONASS satellites with lower elevation angles over time and compare the performance between the tightly coupled GNSS/IMU integration and our proposed camera/IMU/GNSS scheme. A Google Earth visualization of 1 Hz navigation trajectories of different integration schemes is qualitatively given in Figure 7 with common start/end times. The drive test started at the lower left and ended at the upper middle with the upside indicating the north direction. The black trajectory serves as the truth reference which was obtained by leveraging three RTK GPS receivers. The tightly coupled GNSS/IMU solution is illustrated in red and the vision/IMU/GNSS integration is shown as cyan line. Two purple arrows directly denote the place where the number of available satellites changes. A more quantitative comparison of the horizontal accuracy is shown in Figure 8 to reveal how the different integrated architectures react in terms of reduced observability of GNSS measurements in challenging environments. Based on Figures 7 and 8, the tight coupling of GNSS and IMU measurements yields an accurate solution when an adequate number of satellites are available (above four). Meanwhile, the gradually accumulated error of proposed camera/IMU/GNSS approach reaches a maximum of 5 m before the number of visible satellites drops to three. The small systematic error mainly stems from erosions of unexpected pixel positioning error, camera calibration error, numerical instability, and remnants of the outliers after RANSAC processing and so forth. After the number of satellites drops to three, the tightly coupled GNSS/IMU integration still enables a continuous navigation solution with insufficient observability, however the estimation tends to sharply drift away from the truth reference over time and its horizontal error exceeds 20 m at the end of the test. Contrarily, compared to previous navigation results, the camera/IMU/GNSS integration yields a slightly better accuracy with only three utilizable satellites. The reasons for this phenomenon are twofold. First, based on Equation (17) which contains two unknown quantities, three observation equations still maintain a redundant constraint provided that the measurements are derived from LOS directions. More importantly, the systematic error of the image processing module gives rise to the reversal of the positioning error during the vehicle's U-turn operation. As seen in Figure 7, the cyan line slightly tends to the left side of truth reference prior to the U-turn and therefore the same directionality of the systematic error makes the horizontal accuracy be partially compensated after the U-turn. Figure 8: Comparison of horizontal error between the tightly coupled GNSS/IMU and camera/IMU/GNSS integrations in terms of reduced observability of GNSS measurements. Figure 9: Horizontal positioning error statistics of the camera/IMU/GNSS integration. According to the above-mentioned facts, the camera/IMU/GNSS integration brings us a potential advantage compared with the traditional tightly coupled GNSS/IMU technique in challenging environments with sparse GNSS observations. A more detailed horizontal positioning error analysis of the camera/IMU/GNSS integration is presented in Figure 9 with the same hypothesis. The left side shows the horizontal positioning error in two different zoom levels. The right side shows the histograms, cumulative distribution curves and other related statistics. All the subfigures and corresponding statistics are based on 1 Hz solution. Refer to [1,43] which define these statistics/plots in detail. Researchers sometimes refer to quaternions, rather than Euler angles, for orientation representation, particularly for high dynamic applications [14,15].