Accurate and rapid position information is essential for the green Unmanned Aerial Vehicle (UAV) networks. However, in critical environments such as indoors, disaster areas, and urban canyons, the traditional Global Navigation Satellite Systems (GNSS) positioning method struggles to adapt to the dynamic topology of UAV networks and can’t meet the high-accuracy and fast-convergence positioning demands of UAV networks. Moreover, energy consumption is also a key constraint on the development of UAV networks. To address these challenges, we propose a Weighted Extended Kalman Filtering Positioning Algorithm based on Time Difference of Arrival/Received Signal Strength with the Gossip Mechanism (G-WKTR). The G-WKTR algorithm simultaneously performs neighbor discovery and positioning, effectively improving network energy efficiency and contributing to the establishment of green networks. By introducing gossip mechanism, the algorithm can leverage neighbor information to complete fast positioning convergence. And the weighted fusion of different measurement information sources can improve the positioning accuracy. Numerical results demonstrate that the G-WKTR algorithm reduces energy consumption by 66.1% - 82.0% compared with the traditional algorithm, and the positioning accuracy and convergence speed are also significantly improved.