In this paper, a high coverage algorithm termed enhanced camera assisted received signal strength ratio (eCA-RSSR) positioning algorithm is proposed for visible light positioning (VLP) systems. The basic idea of eCA-RSSR is to utilize visual information captured by the camera to estimate the incidence angles of visible lights first. Based on the incidence angles, eCA-RSSR utilizes the received signal strength ratio (RSSR) calculated by the photodiode (PD) to estimate the ratios of the distances between the LEDs and the receiver. Based on an Euclidean plane geometry theorem, eCA-RSSR transforms the ratios of the distances into the absolute values. In this way, eCA-RSSR only requires 3 LEDs for both orientation-free 2D and 3D positioning, implying that eCA-RSSR can achieve high coverage. Based on the absolute values of the distances, the linear least square method is employed to estimate the position of the receiver. Therefore, for the receiver having a small distance between the PD and the camera, the accuracy of eCA-RSSR does not depend on the starting values of the non-linear least square method and the complexity of eCA-RSSR is low. Furthermore, since the distance between the PD and camera can significantly affect the performance of eCA-RSSR, we further propose a compensation algorithm for eCA-RSSR based on the single-view geometry. Simulation results show that eCA-RSSR can achieve centimeter-level accuracy over 80% indoor area for both the receivers having a small and a large distance between the PD and the camera.