Short-arc measurement and fitting based on the bidirectional prediction of observed data

To measure a short arc is a notoriously difficult problem. In this study, the bidirectional prediction method based on the Radial Basis Function Neural Network (RBFNN) to the observed data distributed along a short arc is proposed to increase the corresponding arc length, and thus improve its fitting accuracy. Firstly, the rationality of regarding observed data as a time series is discussed in accordance with the definition of a time series. Secondly, the RBFNN is constructed to predict the observed data where the interpolation method is used for enlarging the size of training examples in order to improve the learning accuracy of the RBFNN's parameters. Finally, in the numerical simulation section, we focus on simulating how the size of the training sample and noise level influence the learning error and prediction error of the built RBFNN. Typically, the observed data coming from a 5 degrees short arc are used to evaluate the performance of the Hyper method known as the 'unbiased fitting method of circle' with a different noise level before and after prediction. A number of simulation experiments reveal that the fitting stability and accuracy of the Hyper method after prediction are far superior to the ones before prediction.