Theoretical Bounds on Random Errors in Satellite Doppler Navigation

Analytic expressions of the random errors in a satellite Doppler navigation system are developed. The errors in the along-track and across-track coordinates are expressed as functions of the geometry (range and angle), pass-length, and signal-to-noise ratio (SNR). Such an analytic result becomes possible due to an explicit solution to a simplified rectilinear model of the satellite pass over a flat Earth. It is shown that the explicit solution performance in the presence of noise is identical to that of the iterative solution, used in the real navigation problem.