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This paper presents the design, simulation, and experimental results of a new scheme for the robust parameter estimation of uncertain nonlinear dynamic systems. The technique is established on the estimation of robust time derivatives using a variable-structure differentiator observer. A second-order sliding motion is established along designed sliding manifolds to estimate the time derivatives of flat outputs and inputs, leading to better tracking performance of estimates during transients. The parameter convergence and accuracy analysis is rigorously explored systematically for the proposed class of estimators. The proposed method is validated using two case studies; first, the parameters of an uncertain nonlinear system with known, but uncertain nominal parametric values are estimated to demonstrate the convergence, accuracy, and robustness of the scheme; in the second application, the experimental parameter estimation of an onboard-diagnosis-II-compliant automotive vehicle engine is presented. The estimated parameters of the automotive engine are used to tune the theoretical mean value engine model having inaccuracies due to modeling errors and approximation assumptions. The resulting dynamics of the tuned engine model matches exactly with experimental engine data, verifying the accuracy of the estimates.