In the field of medical applications, precise localization of medical instruments and bone structures is crucial to ensure computer-assisted surgical interventions. In orthopedic surgery, existing devices typically rely on stereoscopic vision. Their purpose is to aid the surgeon in screw fixation of prostheses or bone removal. This article addresses the challenge of localizing a rigid object consisting of randomly arranged planar markers using a single camera. This approach is especially vital in medical situations where accurate object alignment relative to a camera is necessary at distances ranging from 80 cm to 120 cm. In addition, the size limitation of a few tens of centimeters ensures that the resulting locator does not obstruct the work area. This rigid locator consists of a solid at the surface of which a set of plane markers (ArUco) are glued. These plane markers are randomly distributed over the surface in order to systematically have a minimum of two visible markers whatever the orientation of the locator. The calibration of the locator involves finding the relative positions between the individual planar elements and is based on a bundle adjustment approach. One of the main and known difficulties associated with planar markers is the problem of pose ambiguity. To solve this problem, our method lies in the formulation of an efficient initial solution for the optimization step. After the calibration step, the reached positioning uncertainties of the locator are better than two-tenth of a cubic millimeter and one-tenth of a degree, regardless of the orientation of the locator in space. To assess the proposed method, the locator is rigidly attached to a stylus of about twenty centimeters length. Thanks to this approach, the tip of this stylus seen by a 16.1 megapixel camera at a distance of about 1 m is localized in real time in a cube lower than 1 mm side. A surface registration application is proposed by using the stylus on an artificial scapula.