The Effect of Colored Noise on Doppler Measurements for Planetary Geodesy: Application to the VERITAS Gravity Science Experiment

Measurements of the Doppler shift of a carrier signal have always been the basis of radio science experiments, particularly for planetary gravity field recovery. Doppler observables are affected by correlated (colored) noise; however, standard orbit estimation filters assume that the noise is white and Gaussian. This assumption simplifies the code and reduces the runtime, as the weight matrix is diagonal. In this work, we present a method for incorporating colored noise into least-squares estimation filters by constructing a full noise covariance matrix that reflects the spectral characteristics of all contributing error sources, guaranteeing the proper estimation of parameters and their associated uncertainties. We apply this methodology to the gravity science experiment of NASA’s upcoming Venus Emissivity, Radio Science, InSAR, Topography, And Spectroscopy (VERITAS) mission. Our analysis finds that the white noise assumption is valid for VERITAS—thus supporting the robustness of earlier simulation results. The approach, however, is general and particularly valuable for future missions in which colored noise, such as plasma-induced red noise, dominates the Doppler error budget.