Exploiting cellular long-term evolution (LTE) downlink signals for navigation purposes is considered. First, the transmitted LTE signal model is presented and relevant positioning and timing information that can be extracted from these signals are identified. Second, a software-defined receiver (SDR) that is capable of acquiring, tracking, and producing pseudoranges from LTE signals is designed. Third, a threshold-based approach for detecting the first peak of the channel impulse response is proposed in which the threshold adapts to the environmental noise level. This method is demonstrated to be robust against noise and interference in the environment. Fourth, an approach for estimating pseudoranges of multiple base stations by tracking only one base station is proposed. Fifth, a navigation framework based on an extended Kalman filter is proposed to produce the navigation solution using the pseudorange measurements obtained by the proposed SDR. Finally, the proposed SDR is evaluated experimentally on an unmanned aerial vehicle (UAV) and a ground vehicle. The root mean squared-error (RMSE) between the GPS navigation solution and LTE signals from three base stations produced by the proposed SDR for the UAV is shown to be 8.15 m with a standard deviation of 2.83 m. The RMSE between the GPS navigation solution and LTE signals from six base stations in a severe multipath environment for the ground vehicle is shown to be 5.80 m with a standard deviation of 3.02 m.