Josephson junction is an important superconducting device, values of the critical parameters within the Josephson junction model are mapped with different orders of magnitude. As a result, the unknown parameters with smaller order of magnitude can not be detected with high precision by using the original scheme of adaptive synchronization. Based on the Lyapunov stability theory, appropriate controller and parameter observers with gain coefficients are approached analytically, a scheme of scale conversion is proposed to estimate the unknown parameters with different orders of magnitude. By defining the statistical error function, the areas of synchronization and non-synchronization are demarcated. It is found that the area of synchronization becomes larger when two smaller unknown parameters are amplified simultaneously. In this way, precision of the identified results is increased greatly, and the results confirm that the scheme is successful to identify the unknown parameters with small order of magnitude.