Reducing loss of significance in the computation of Earth-based two-way Doppler observables for small body missions

Two-way Doppler measurement is a typical Earth-based radiometric technique for interplanetary spacecraft navigation and gravity science investigation.The most widely used model for the computation of two-way Doppler observables is Moyer’s differenced-range Doppler(DRD) formula,which is based on a Schwarzschild approximation of the Solar-System space-time.However,the computation of range difference in DRD formula is sensitive to round-off errors due to approximate numbers defined by the norm IEEE754 in all PCs.This paper presented two updated models and their corresponding detailed instructions for the computation of the two-way Doppler observables so as to impair the effects of this type of numerical error.These two models were validated by two case studies related to the Rosetta mission—asteroid Lutetia flyby and comet 67 P/Churyumov-Gerasimenko orbiting case.In these two cases,the numerical noise from the updated models can be reduced by two orders-of-magnitude in the computed two-way Doppler observables.The results showed an accuracy from better than 6 × 10^(-3) mm s^(-1) at 1 s counting time interval to better than 3 × 10^(-5) mm s^(-1) at 60 s counting time interval.