  In this paper, the generalized regression neural network is used to predict
the GNSS position time series. Using the IGS 24-hour final solution data for
Bad Hamburg permanent GNSS station in Germany, it is shown that the larger the
training of the network, the higher the accuracy is, regardless of the time
span of the time series. In order to analyze the performance of the neural
network in various conditions, 14 permanent stations are used in different
countries, namely, Spain, France, Romania, Poland, Russian Federation, United
Kingdom, Czech Republic, Sweden, Ukraine, Italy, Finland, Slovak Republic,
Cyprus, and Greece. The performance analysis is divided into two parts,
continuous data-without gaps-and discontinuous ones-having intervals of gaps
with no data available. Three measure of error are presented, namely, symmetric
mean absolute percentage error, standard deviation, and mean of absolute
errors. It is shown that for discontinuous data the position can be predicted
with an accuracy of up to 6 centimeters, while the continuous data positions
present a higher prediction accuracy, as high as 3 centimeters. In order to
compare the results of this machine learning algorithm with the traditional
statistical approaches, the Theta method is used, which is well-established for
high-accuracy time series prediction. The comparison shows that the generalized
regression neural network machine learning algorithm presents better accuracy
than the Theta method, possibly up to 250 times. In addition, it is
approximately 4.6 times faster.
