Point localization in multi-camera setups has been widely studied in computer vision. Recently, in finite-resolution camera settings, a consistent and optimal point localization algorithm called SHARP has been proposed, under the assumption of noiseless camera poses and error-free matching. In this work, we relax this assumption on noiseless camera poses and propose a new point localization algorithm. We formulate this point localization task as a gradient-ascent optimization function, for maximizing the objective function under computational geometric constraints. Experimental results verify the efficacy of our approach as compared to the current state-of-the-art localization algorithms.