Traditionally, there has been a method to extract the charge radius of a hadron based on the fits of its form factor with some model assumptions. In contrast, a completely different method has been proposed, which does not depend on the models. In this report, we explore several improvements to this model-independent method for analyzing the pion charge radius. Furthermore, we compare the results of the pion charge radius obtained from $N_{f}=2+1$ lattice QCD data at $m_{\pi}=0.51$ GeV using the three different methods: the traditional model-dependent method, the original model-independent method, and our improved model-independent method. In this comparison, we take into account systematic errors estimated in each analysis.