Using IoT devices to locate targets is widely applied in many scenarios. However, replacing the batteries of these devices is time and labor consuming. In this article, we propose a wireless power-driven positioning system (WPS) that employs MIMO-based wireless power transfer access points to supply energy to batteryless anchors. In this case, the IoT localization devices will have unlimited power. We formulate the equivalent Fisher information matrix (EFIM) as a fundamental tool to analyze the system performance. Then, we propose resource allocation schemes for optimal location estimation and energy efficiency problems by relaxing the objectives as semidefinite programming problems. In addition, we also analyze the impacts of channel uncertainty, anchor uncertainty, and NLOS for the performances of location estimation and energy consumption. The robust algorithms are developed according to uncertainty models. Both the analysis and simulations demonstrate that the estimation accuracy relies heavily on the transmitted power and the uncertainty models will consume more power to meet the location requirements.