In this correspondence, we investigate unmanned aerial vehicle (UAV)-base stations (BSs) assisted and received signal strength (RSS) based mobile station (MS) localization. A practical air-to-ground path loss model is utilized, where the path loss exponent (PLE) varies with the elevation angle and altitude of UAV, and the accurate PLE estimate is often difficult to obtain. With unknown and unequal PLEs for different UAVs, the UAVs assisted localization problem becomes nonlinear and non-convex, which cannot be solved by the existing methods. We propose a piecewise convex approximation aided localization (PCAL) approach to convert the localization problem into linear and convex, without requiring the knowledge of PLE. The proposed PCAL approach with unknown and unequal PLEs achieves much higher accuracy than the existing methods which require perfectly known and equal PLE, due to its higher robustness against shadowing. In addition, a grid search aided ambiguity elimination (GSAE) method, which is more effective than the state-of-the-art methods, is proposed to determine the final MS localization estimate based on multiple tentative estimates derived from PCAL. The effectiveness of PCAL is also verified by the Cramer-Rao lower bound (CRLB) derived.