  The solar radio flux at F10.7 cm and F30 cm is required by most models
characterizing the state of the Earth's upper atmosphere, such as the
thermosphere and ionosphere to specify satellite orbits, re-entry services,
collision avoidance maneuvers and modeling of space debris evolution. We
develop a method called RESONANCE ("Radio Emissions from the Sun: ONline
ANalytical Computer-aided Estimator") for the prediction of the 13-month
smoothed monthly mean F10.7 and F30 indices 1-24 months ahead. The prediction
algorithm includes three steps. First, we apply a 13-month optimized running
mean technique to effectively reduce the noise in the radio flux data. Second,
we provide initial predictions of the F10.7 and F30 indices using the
McNish-Lincoln method. Finally, we improve these initial predictions by
developing an adaptive Kalman filter with the error statistics identification.
The root-mean-square-error of predictions with lead times from 1 to 24 months
is 5-27 sfu for the F10.7 and 3-16 sfu for F30 index, which statistically
outperforms current algorithms in use. The proposed approach based on Kalman
filter is universal and can be applied to improve the initial predictions of a
process under study provided by any other forecasting method. Furthermore, we
present a systematic evaluation of re-entry forecast as an application to test
the performance of F10.7 predictions on past ESA re-entry campaigns for
payloads, rocket bodies, and space debris that re-entered from June 2006 to
June 2019. The test results demonstrate that the predictions obtained by
RESONANCE in general also lead to improvements in the forecasts of re-entry
epochs.
