Doppler Positioning

Doppler Positioning is a navigation technique that determines a receiver's position by measuring the frequency shift (Doppler effect) of radio signals transmitted by satellites or other moving platforms with known trajectories.

When a transmitter moves relative to a receiver, the received frequency shifts proportionally to the relative velocity along the line of sight: Δf = f₀ · (v_r / c), where f₀ is the transmitted frequency, v_r is the radial velocity, and c is the speed of light. By measuring Doppler shifts from multiple transmitters with known orbits, a receiver can compute its position through geometric intersection of iso-Doppler surfaces (constant-Doppler cones around each transmitter's velocity vector).

The concept has a rich heritage: the U.S. Navy's Transit satellite navigation system (1964-1996) was the world's first satellite navigation system and operated entirely on Doppler positioning. A single Transit satellite pass (lasting ~18 minutes) provided positioning accuracy of approximately 200 meters.

Kepler Nav extends classical Doppler positioning with two innovations. First, the system measures not just first-order Doppler (frequency shift) but second-order Doppler rate (rate of change of frequency), which provides additional geometric constraints equivalent to range-acceleration measurements. Second, by processing Doppler from 15-40 simultaneous LEO satellites (Starlink, OneWeb, Iridium) rather than a single satellite pass, the system achieves real-time positioning updates at 1-10 Hz with geometric dilution of precision (GDOP) values comparable to GPS.