The solar radio index F_10.7 is a critical indicator of solar activity intensity. Accurate forecasting of F_10.7 is essential for advancing many fields. A promising direction for addressing such complex forecast problems is known as neurodynamics, which incorporates dynamic perspectives into neural networks. In this study, we introduce a forecast model based on neurodynamics to achieve high-precision, long-term forecasting of the F_10.7 index. First, we construct an F_10.7 dataset making up for the missing period of F_10.7 measurements by converting sunspot numbers, and we propose a new fitting method, improving the accuracy of converting sunspot number to F_10.7 index. For the forecast modeling, we employ a neurodynamics model to capture the variation characteristics of historical datasets selected by clustering. This approach enhances the objectivity of long-term F_10.7 forecasting, enabling accurate forecast spanning even an entire solar cycle. In the cycle used to validate the forecasting method, the model effectively captured the long-term trend of F_10.7 index, and the forecasted values closely matched the observed values. To simplify forecasting, we develop a method for calculating F_10.7 for an entire solar cycle using only the Modified Julian Day, thereby expanding the usability of the forecasts.

The reliability theory has been an important element of the classical geodetic adjustment theory and methods in the linear Gauss-Markov model. Although errors-in-variables (EIV) models have been intensively investigated, little has been done about reliability theory for EIV models. This paper first investigates the effect of a random coefficient matrix A on the conventional geodetic reliability measures as if the coefficient matrix were deterministic. The effects of such geodetic internal and external reliability measures due to the randomness of the coefficient matrix are worked out, which are shown to depend not only on the noise level of the random elements of A but also on the values of parameters. An alternative, linear approximate reliability theory is accordingly developed for use in EIV models. Both the EIV-affected reliability measures and the corresponding linear approximate measures fully account for the random errors of both the coefficient matrix and the observations, though formulated in a slightly different way. Numerical experiments have been carried to demonstrate the effects of errors-in-variables on reliability measures and compared with the conventional Baarda's reliability measures. The simulations have confirmed our theoretical results that the EIV-reliability measures depend on both the noise level of A and the parameter values. The larger the noise level of A, the larger the EIV-affected internal and external reliability measures; the larger the parameters, the larger the EIV-affected internal and external reliability measures.