## 7 Experimental Description and Result Analysis
The quaternion expression avoids the gimbal lock phenomenon when the pitch angle approaches \(\pm\)90 deg, and operates more efficiently compared with multiplications of direction cosine matrices. Whereas, since a ground vehicle is incapable of operating orthogonal to the ground plane, Euler angles do not suffer from the singularity problem and can provide an intuitive manner for the user to perceive the vehicle direction. We, therefore, choose roll, pitch and yaw angles for representing the vehicle's orientation based on Tait-Bryan convention. Figure 10 shows the yaw angle error statistics of the camera/IMU/GNSS integration. Yaw jitters occur as a result of the abrupt change in the centrifugal force when the vehicle underwent the U-turn operation. Although the angle residual is maintained within 1 deg in a majority of the time during the test segment, the relatively low level of systematic error still can be observed from the zoomed-in subfigure due to the imperfection of the computer vision module. This further proves the reversal of the positioning error during the vehicle's cornering as shown in Figure 8. It can be inferred that the accumulated position and orientation errors will gradually erode the navigation solution if the dataset is long enough without any other sources of corrections. In addition, the IMU sensor bias estimation is shown in Figure 11. Those large biases from both the accelerometer and gyroscope sensors inevitably cause erroneous IMU mechanization solutions in a matter of seconds without sensor calibration. The non-smoothly varying biases, particularly for the  
Figure 10: Yaw angle error statistics of the camera/IMU/GNSS integration. accelerometer components, gave rise to the unpredictability of the sensor errors. Simply averaging the sensor biases within even a few seconds may yield an inaccurate navigation solution, particularly when the vehicle dynamics significantly change with velocity and cornering stiffness. As seen in Figure 11, during the vehicle's cornering, the accelerometer bias on x-axis dramatically dropped by approximately 200 milli-g. However, the actual sensor biases may be, to a certain extent, different from the estimation shown in Figure 11 in terms of the fidelities of the utilized filtering models [16]. In an effort to balance the tradeoff between practical performance and computational cost, we deliberately reduce the image frame rate and examine the position solution of our integrated scheme by comparing with the truth reference. Figure 12 demonstrates a comparison of the horizontal positioning errors with different image frame rates based on the same GNSS observability as discussed previously. As the interval of images is gradually enlarged, EKF filtering leans more on the inertial navigation alone which gives rise to larger location and orientation errors, and moreover, those fewer detected  
Figure 11: Accelerometer and gyroscope estimation based on the camera/IMU/GNSS integration. Figure 12: Horizontal positioning error comparison by using different image frame rate. feature correspondences tend to degrade the reliability of camera motion estimation. The sawtooth-shaped curves therefore arise with worse accuracy. During the U-turn operation when the images partially overlap each other, SIFT/RANSAC algorithms acquire much fewer feature correspondences with lower frame rate, which results in abrupt change in positioning accuracy as seen in Figure 12, particularly for the low frame rates of 0.25 and 0.50 Hz. The worst situation may occur when no overlap can be found in two consecutive images. Consequently, the strategy to determine an image frame rate is primarily dependent on the vehicle dynamics, IMU quality and fidelity of utilized filtering models.