A framework for differential Doppler navigation with Starlink low Earth orbit (LEO) space vehicle (SV) signals of opportunity is presented, and the framework’s performance is assessed. The differential framework assumes a rover (vehicle) navigating without global navigation satellite system (GNSS) signals, through the simultaneous tracking and navigation (STAN) approach. In STAN, the vehicle aids its inertial navigation system (INS) with Doppler measurements extracted from LEO SVs via an extended Kalman filter (EKF), simultaneously estimating the vehicle’s and LEO SVs’ states. In addition, the differential framework assumes a stationary base with a known position, making Doppler measurements to the same Starlink LEO SVs and communicating these measurements with the rover. The objective of the proposed differential framework is to mitigate the effects of poorly known LEO SVs’ ephemerides, unknown LEO SVs’ dynamic clock error states, and atmospheric delays. Simulation results are presented to assess the performance of the proposed differential framework compared to a non-differential STAN. The simulations assume an aerial vehicle equipped with a tactical-grade inertial measurement unit (IMU) and an altimeter, navigating for 28 km in 300 seconds, the last 23 km of which without GNSS, while receiving signals from 14 Starlink LEO SVs. It is shown that the non-differential STAN achieves a position root-mean squared error (RMSE) of 15.63 m, while the differential STAN with one, two, and three bases reduces the position RMSE to 5.26 m, 3.88 m, and 1.94 m, respectively. Experimental results are presented in which a stationary base and a stationary rover, located at a distance of 1 km apart, extract Doppler observables from 3 Starlink LEO SVs. The differential framework was able to estimate the rover’s three-dimensional (3-D) and 2-D position with an error of 33.4 m and 5.6 m, respectively.