The use of autonomous vehicles for target localization in modern applications has emphasized their superior efficiency, improved safety, and cost advantages over human-operated methods. For localization tasks, autonomous vehicles can be used to increase efficiency and ensure that the target is localized as quickly and precisely as possible. However, devising a motion planning scheme to achieve these objectives in a computationally efficient manner suitable for real-time implementation is not straightforward. In this paper, we introduce a motion planning solution for enhanced target localization, leveraging Bernstein polynomial basis functions to approximate the probability distribution of the target's trajectory. This allows us to derive estimation performance criteria which are used by the motion planner to enhance the estimator efficacy. To conclude, we present simulation results that validate the effectiveness of the suggested algorithm.