This paper presents a numerical framework for parameter estimation of a single-phase diode-bridge rectifier with capacitive filtering. The proposed approach integrates a state-space model of the rectifier, numerically solved using the second-order Backward Differentiation Formula (BDF2), with a derivative-free Nelder–Mead optimization algorithm. Parameter estimation is performed using only terminal voltage and current measurements, eliminating the need for explicit conduction-interval detection or direct measurement of internal circuit states. The framework is experimentally validated under three operating conditions: steady-state operation, dynamic load variation, and startup transient. Five estimation scenarios are analyzed to assess the influence of the excitation condition and the inclusion of the initial capacitor voltage $U_{C0}$ as an additional unknown parameter on estimation accuracy. The results demonstrate that excitation conditions strongly influence parameter estimation accuracy. Steady-state excitation yields the largest estimation errors, particularly for the series resistance and DC-link capacitance, whereas dynamic load variation improves the estimation accuracy of several parameters. The startup transient provides the highest overall estimation accuracy, with all four estimated parameters exhibiting relative errors below 5.5%. The proposed framework provides a practical approach for parameter estimation of single-phase rectifiers using terminal measurements only and highlights the importance of the excitation condition for reliable parameter estimation. The method can support the identification and modeling of nonlinear electronic loads in power-system and power-quality studies.