Accurate estimation of relative atmospheric density error on the example of uncertain geomagnetic activity information

Errors in neutral atmospheric density are the dominant contributor to unrealistic orbital state-vector covariances in low Earth orbits (LEO). Density uncertainty is caused by model-uncertainty at spatial scales below and within the model resolution, as well as input-uncertainty of the environmental parameters supplied to the semi-empirical atmospheric model.The paper at hand provides multiple contributions. First, analytic equations are derived to estimate the relative density error due to an input parameter uncertainty in any of the environmental parameters supplied to the model. Second, it is shown on the example of uncertain geomagnetic activity information, how to compute the required inputs to facilitate the accurate estimation of the relative density error.A clamped cubic splining approach for the conversion from geomagnetic amplitude (ap) to the kp index is postulated to perform this uncertainty propagation, as other algorithms were found unsuitable for this task. Results of numerical simulations with three popular semi-empirical models are provided to validate the set of derived equations. It is found that geomagnetic input uncertainty is especially important to consider in case of low global geomagnetic activity. The findings seamlessly integrate with prior work by the authors to perform density-uncertainty considering orbit estimation.