Simultaneous Orbit and Atmospheric Density Estimation for a Satellite Constellation

Abstract

A method is defined for simultaneous atmospheric density calibration and satellite orbit determination for a satellite constellation, and a linearized observability analysis is performed to evaluate the feasibility of the approach. Such an estimation scheme will provide data-based estimates of upper atmosphere density that improve on existing models, e.g. the Jacchia models, along with enhanced accuracy of the associated satellites' orbits. A new spline-based atmospheric density parameterization is developed that meshes well with the structure of the orbit determination problem and can be initialized so as to match the outputs of a traditional model. While conceptually similar to previous atmospheric calibration efforts, the proposed constellation approach restricts its global density estimates to the relevant satellite altitude range and thus reduces the complexity of the estimation problem. Measurements include dual-one-way-ranging between pairs of adjacent satellites in the same orbital plane, and carrier phase and pseudorange measurements between ground stations and satellites. Equations for a linearized observability analysis are derived and shown to be equivalent to the covariance calculations of an extended square-root information filter. In addition to the system observability evaluation, the impact of incorporating some a priori density information is explored. The results show that atmospheric density can be observed, but a reasonable amount of a priori information is necessary to obtain useful estimates. Degree of observability depends on the constellation configuration and dynamic model parameter values.

Localized In-Situ Density Measurement in Low Earth Orbit via Drag Torque Estimation

“…A self-referential constellation could provide better density tracking information. It has been shown by Hinks and Piaki [11] that a constellation of 50-100 satellites in multiple orbital planes could well estimate the atmospheric density using ranging crosslinks with centimeter-scale accuracy to produce a set of cross-constellation ranges, which can then be observed to note high-drag areas. The model requires some prior knowledge about the density in order to manage estimate error, but has been shown to be able to reduce uncertainty in known measurements as well as to increase the fidelity of the constellation's own orbit propagation.…”

Calibration of atmospheric density model using two-line element data

“…(13). If k > p, the observations (TLE data) are more believable, otherwise the empirical model is more believable.…”

“…M (t i )|| (13) whereñ M (t i ) andñ M (t k ) are the mean mean-motion read from these two sets of TLE data. From Eq.…”

“…The λ and φ in Eq. (3) are defined in a Sun-fixed coordinate frame [13], whose three axes of coordinates are defined as follows:…”