Multiple global navigation satellite systems (multi-GNSS) Doppler solutions are analyzed for low-Earth-orbit (LEO) satellites. Precise satellite displacement and change-in-clock offset can be calculated using four satellites if an approximate position solution is available. The position can be calculated using seven or more satellites if time is provided. The precise displacement or average velocity at the millimeter-per-second level is based on accumulated carrier-phase measurements. A novel linearized Doppler position and velocity solution smoothed at the millimeter level is presented. The Doppler position solution is combined with a high-accuracy displacement solution in a complementary filter that provides two new benefits: after initialization with a full seven-satellite position solution, the complementary filter can continue with only four satellites; and the short (1 to 5 s) Doppler tracks can be checked for faults before the complementary filter, using displacement techniques requiring five satellites versus the usual eight. The Doppler solutions are evaluated using data from a LEO satellite and contrasted against a multi-GNSS pseudorange solution. Applications of the Doppler solution include satellite maneuver control, formation flight, thruster monitoring, docking, and scientific applications that require satellite motion compensation, such as synthetic aperture radar.