Navigation using carrier Doppler shift from a LEO constellation: TRANSIT on steroids

A new global navigation system concept is studied that relies entirely on carrier Doppler shift measurements from the downlink signals of a large LEO constellation. This system seeks to provide a back-up or alternative to existing pseudorange-based MEO GNSS by exploiting the large LEO constellations that are currently being planned or fielded, constellations such as Starlink, OneWeb, and Kuiper. The navigation concept is based on a high-fidelity model of the received carrier Doppler shift. This model is used to develop a point-solution nonlinear least-squares batch filter that simultaneously estimates 8 unknowns: the 3 components of the position vector, the receiver clock offset, the 3 components of the velocity vector, and the receiver clock offset rate. The filter must use 8 or more measured carrier Doppler shifts in its least-squares fit in order to make its 8 unknowns observable. A generalized GDOP analysis has been developed for this system. It indicates that absolute position accuracies on the order of 1-5 meters and absolute velocity accuracies on the order of 0.01 to 0.05 m/sec may be achievable if the range-rate precision of the carrier Doppler shift measurements is 0.01 m/sec. These accuracies are comparable to current pseudorange-based GNSS. Clock offset accuracy is on the order of 0.0001 to 0.0010 sec 1-?, which is orders of magnitude poorer than current pseudorange-based GNSS. This degraded clock accuracy occurs because clock error standard deviation is inversely proportional to the maximum range acceleration between the satellites and the receiver. Batch filter point-solution results for truth-model simulation data confirm the conclusions of the GDOP analysis. One set of truth-model simulations considers the effects of satellite ephemeris and clock frequency errors. They indicate that good performance can be achieved with 1-? ephemeris errors of 2 m in position and 0.002 m/sec in velocity and with 1-? transmitter clock frequency errors of 3.3×10?11 seconds/second. This level of transmitter clock stability could be achieved with a high quality quartz oscillator, thereby obviating any need for the satellites to carry atomic clocks or to use GPS disciplining of their oscillators.