The openness of the lower-layer protocol stacks in cognitive radios increases the flexibility of dynamic spectrum access and promotes spectrally-efficient communications. To ensure the effectiveness of spectrum sharing, it is desirable to locate primary users, secondary users, and unauthorized users in a non-interactive fashion based on limited measurement data at receivers. In this work, we present two range-free localization algorithms based on dynamic mapping of received signal strength (RSS) to perform non-interactive localization that does not require the cooperation from the cognitive device to be located. A fine-grained signal strength map across the surveillance area is constructed dynamically through interpolation. By making use of this signal map, the proposed schemes can achieve higher accuracy of location estimation than existing non-interactive and RSS based methods in most channel variation conditions. Both our simulation results as well as testbed evaluations have demonstrated the feasibility of the proposed algorithms.