In this study, a miniature artificial compound eye (15 mm in diameter) called the curved artificial compound eye (CurvACE) was endowed for the first time with hyperacuity, using similar micro-movements to those occurring in the fly's compound eye. A periodic micro-scanning movement of only a few degrees enables the vibrating compound eye to locate contrasting objects with a 40-fold greater resolution than that imposed by the interommatidial angle. In this study, we developed a new algorithm merging the output of 35 local processing units consisting of adjacent pairs of artificial ommatidia. The local measurements performed by each pair are processed in parallel with very few computational resources, which makes it possible to reach a high refresh rate of 500 Hz. An aerial robotic platform with two degrees of freedom equipped with the active CurvACE placed over naturally textured panels was able to assess its linear position accurately with respect to the environment thanks to its efficient gaze stabilization system. The algorithm was found to perform robustly at different light conditions as well as distance variations relative to the ground and featured small closed-loop positioning errors of the robot in the range of 45 mm. In addition, three tasks of interest were performed without having to change the algorithm: short-range odometry, visual stabilization, and tracking contrasting objects (hands) moving over a textured background.