This paper presents an online algorithm for mobile user speed estimation in 3GPP Long Term Evolution (LTE)/LTE-Advanced (LTE-A) networks. The proposed method leverages on uplink (UL) sounding reference signal (SRS) power measurements performed at the base station, also known as eNodeB (eNB), and remains effective even under large sampling period. Extensive performance evaluation of the proposed algorithm is carried out using field traces from realistic environment. The on-line solution is proven highly efficient in terms of computational requirement, estimation delay, and accuracy. In particular, we show that the proposed algorithm can allow for the first speed estimation to be obtained after 10 seconds and with an average speed underestimation error of 14 kmph. After the first speed acquisition, subsequent speed estimations can be obtained much faster (e.g., each second) with limited implementation cost and still provide high accuracy.