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INTRODUCTION
Mars exploration has received much attention over the last few years (Jin and Zhang, 2014). The Positioning and Navigation (PN) issues for explorers or rovers have been a research focus since the 1960s (Jin et al., 2013; Wei et al., 2013; Liu et al., 2017). Among these PN designs, the Mars Exploration Rovers (MER), Spirit and Opportunity, use several integrated PN methods that are considered state-of-the-art. The absolute positions of several initial points of the MER rovers are determined by Radio Tracking (RT) technology (Arvidson et al., 2004). The determination requires continuous tracking and would take several days, and the result is verified by the photographic feature recognition method. The differences between the two methods are within 350 m (Squyres et al., 2004). Once the first several absolute locations are determined, the rest of the trajectory is deduced by relative navigation methods which include Celestial Navigation (CN), Wheel Code Odometry (WCO), and Vision Odometry (VO) (Li et al., 2004; Arvidson et al., 2005; Squyres et al., 2006; Maimone et al., 2007). WCO is adopted for location estimation; the distance is counted by how many times the wheels have turned (wheel odometry). Then, the absolute heading (with respect to the true north of Mars) is measured by CN which uses a celestial sensor to track the line-of-sight of the Sun. VO is implemented to control the systematic errors (Li et al., 2004; Cheng et al., 2006). These methods can complete the relative positioning process, the accuracy of which is within 1 m (Maimone et al., 2007). The absolute locations of the whole trajectory are solved by integrating the RT initial points and the relative traverse.
Matthies (1989) developed Visual Odometry to estimate the motion of mobile robots by using stereo images. The key idea of the method is to detect the position and attitude changes of the rover between consecutive image pairs. The trajectory of the photographing centres can be fixed by calculating the rotation and transition relationship of the pairs. For a Mars rover, the bias between ground truth (trajectory in images) and VO are within 1 m in three axes (local system) (Li et al., 2005; Cheng et al., 2006; Maimone...