A new Sense and Avoid (SAA) method for safe navigation of small-sized UAVs within an airspace is proposed in this paper. The proposed method relies upon cooperation between the UAV and the surrounding transponder-equipped aviation obstacles. To do so, the aviation obstacles share their altitude and their identification code with the UAV by using a miniaturized Mode S operation Secondary surveillance radar (SSR) after interrogation. The proposed SAA algorithm removes the need for a primary radar and a clock synchronization since it relies on the estimate of the aviation obstacle's elevation angle for ranging. This results in more accurate ranging compared to the round-trip time-based ranging. We also propose a new radial velocity estimator for the Mode S operation of the SSR which is employed in the proposed SAA system. The root-mean-square error (RMSE) of the proposed estimators are analytically derived. Moreover, by considering the pulse-position modulation (PPM) of the transponder reply as a waveform of pulse radar with staggered multiple pulse repetition frequencies, the maximum unambiguous radial velocity is obtained. Given these estimated parameters, our proposed SAA method classifies the aviation obstacles into high-, medium-, and low-risk intruders. The output of the classifier enables the UAV to plan its path or maneuver for safe navigation accordingly. The effectiveness of the proposed estimators and the SAA method is confirmed through simulation experiments.