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The speed estimation has been widely used for tracking mobile device locations, providing essential information in location/mobility-aware communications, enhancing received signal quality/robustness, and reducing energy consumption and latency. Deep learning can be used to improve the performance constrained by signal/system model. This work focuses on the issues on machine learning (ML) based speed estimation using primary synchronous signal (PSS), which is embedded in the 5G standards, over general time-variant multipath channels. Aiming to reduce the complexity involved in the ML algorithms for the speed estimation in mobile networks, we propose a pipelined ML algorithm to decompose the original ML model into several smaller ones. The advantages of the proposed convolutional neural network (CNN) based approach have been verified by simulations.