Simultaneous estimation of density and Fourier drag-coefficient

Estimates of atmospheric densities from satellite data not only allow the calibration of semi-empirical atmospheric density models used in orbit determination but provide invaluable insights into the evolution of Earth's atmosphere. Therefore, any biases in the derived densities have far reaching consequences from both engineering and scientific perspectives. One of the primary biases is introduced in the inversion of atmospheric densities from satellite data as a result of simplifying assumptions pertaining to the drag coefficient. Due to the highly correlated nature of density and drag-coefficient, it is difficult to estimate them simultaneously during the orbit determination process. A method developed by Wright (2003) allows both the quantities to be observable in the filtering methodology. The philosophy behind this approach is to model the ballistic coefficient and density as exponentially correlated Gauss-Markov processes with very different half-lives in a sequential filter and has been used by McLaughlin et al. (2011) to arrive at densities derived using CHAMP POD. The ballistic coefficient is assumed to have a much slower variation than the density which allows separation of the two. This assumption ignores the higher-frequency variations in the ballistic coefficient, especially during space weather events and/or changes in attitude. It also ignores the correlation of bias components for the estimated drag coefficient and density values. We propose the use of Fourier drag-coefficient models in the methodology outlined by Wright. The Fourier model developed previously by the authors (2020) captures these high frequency variations with slower variations attributed to the estimated Fourier coefficients. Spatial and temporal Fourier expansions were proposed to capture time-variations of the drag-coefficient attributable to periodic changes in the ambient parameter and/or attitude, with the Fourier coefficients assumed to be constant. Therefore, the Fourier coefficients satisfy the assumption of slower variation than density more closely than the effective ballistic coefficient. We will implement simultaneous estimation of densities and Fourier coefficients using a sequential filter-smoother with GRACE and CHAMP POD serving as measurements.