To improve the localization precision of unmanned aerial vehicle (UAV), a novel framework is established by jointly utilizing multiple measurements of received signal strength (RSS) from multiple base stations (BSs) and multiple points on trajectory. First, a joint maximum likelihood (ML) of exploiting both trajectory information and multi-BSs is proposed. To reduce its high complexity, two low-complexity localization methods are designed. The first method is from BS to trajectory (BST), called LCSL-BST. First, fixing the nth BS, by exploiting multiple measurements along trajectory, the position of UAV is computed by ML rule. Finally, all computed positions of UAV for different BSs are combined to form the resulting position. The second method reverses the order, called LCSL-TBS. We also derive the Cramer-Rao lower boundary (CRLB) of the joint ML method. From simulation results, we can see that the proposed joint ML and separate LCSL-BST methods have made a significant improvement over conventional ML method without use of trajectory knowledge in terms of location performance. The former achieves the joint CRLB and the latter is of low-complexity.