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Location awareness is a prominent characteristic of cognitive radio technologies. Realizing such awareness in cognitive radios require an underlying advanced positioning system that have cognition capabilities. In this paper, an innovative cognitive positioning system (CPS) that have cognition capabilities by means of adjusting positioning accuracy adaptively in both indoor and outdoor environments is proposed. Bandwidth determination and hybrid overlay and underlay enhanced dynamic spectrum management (H-EDSM) are two main components that form the proposed CPS technique. Bandwidth determination equations are derived through Cramer-Rao lower bound (CRLB) for additive white Gaussian noise (AWGN). H-EDSM that provides optimum available bandwidth to the CPS is proposed. A switching mechanism that manages the transition between overlay and underlay spectrum usage modes for the H-EDSM algorithm is presented. Theoretical analysis of the mechanism is carried out using two-slope model. Simulation results, challenges and complexity options for the implementation of the CPS are outlined. Our study reveals the existence of a trade-off between accuracy and complexity in the adaptive positioning systems for cognitive radios.