Although adaptive estimation of constant parameter has been studied for decades, most of existing methods cannot achieve satisfactory performance for timevarying parameters in particular for nonlinearly parameterized systems. In this paper, a novel adaptive parameter estimation framework based on parameter estimation errors, is proposed to estimate time-varying parameters for generally nonlinearly parameterized systems. The main idea is to restructure the system as a linearly parameterized form through Taylor expansion. Following the introduction of auxiliary filtered variables, the estimation errors of the unknown parameter are derived and used to design an adaptive law to achieve uniform ultimate boundedness under the persistent excitation condition. Furthermore, it is verified that the suggested methods are robust against bounded disturbances. Numerical simulation results validate the effectiveness of adaptive time-varying parameter estimation methods.