The Compact Lightweight Surgery Robot from the University of Hawaii includes two teleoperated instruments and one endoscope manipulator which act in accord to perform assisted interventional medicine. The relative positions and orientations of the robotic instruments and endoscope must be known to the teleoperation system so that the directions of the instrument motions can be controlled to correspond closely to the directions of the motions of the master manipulators, as seen by the the endoscope and displayed to the surgeon. If the manipulator bases are mounted in known locations and all manipulator joint variables are known, then the necessary coordinate transformations between the master and slave manipulators can be easily computed. The versatility and ease of use of the system can be increased, however, by allowing the endoscope or instrument manipulator bases to be moved to arbitrary positions and orientations without reinitializing each manipulator or remeasuring their relative positions. The aim of this work is to find the pose of the instrument end effectors using the video image from the endoscope camera. The P3P pose estimation algorithm is used with a Levenberg-Marquardt optimization to ensure convergence. The correct transformations between the master and slave coordinate frames can then be calculated and updated when the bases of the endoscope or instrument manipulators are moved to new, unknown, positions at any time before or during surgical procedures.