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This paper presents a novel reconfigurable intel-ligent surface (RIS)-based localization approach for mobile user equipment (UE) in a millimeter-wave uplink cellular environment. The proposed approach develops a measurement engine that employs a state-of-the-art carrier-aided code-phase-based navigation receiver and incorporates a passive correlation-based angle-locked loop (ALL) for TOA and AOA estimation. An extended Kalman filter (EKF)-based RIS-aided navigation framework is deployed, providing accurate 3D position and velocity estimates for the mobile UEs utilizing the RIS-based navigation observables, which are then leveraged to optimize the RIS phase profile to maximize the signal-to-noise ratio (SNR) for the various UEs. Finally, the paper demonstrates the accuracy of the navigation solution through extensive Monte Carlo simu-lations that encompass different scenarios involving pedestrians, ground vehicles, and unmanned aerial vehicles (UAVs), These simulations emphasize the utility of our proposed approach in delivering sub-meter and meter-level posltioning accuracies.