An iterative physically bounded Gauss-Newton (PGN) method has been formulated to estimate unknown kinetic parameters from experimental measurements. A physically bounded approach is adopted to reduce the size of the search space and ensure search within physically meaningful ranges of kinetic rates. First-order sensitivity information of state variables, with respect to unknown rate parameters, is computed simultaneously with the integration of the governing ordinary differential equations (ODEs). Optimal kinetic parameters are obtained by iteratively solving the Gauss-Newton update equations within the physical parameter range. Four different reaction systems, including both simple and complex networks, have been utilized for validating the performance of the proposed method. Comparisons with other state-of-the-art algorithms showed its efficiency, robustness, and accuracy. The methodology was also applied to analyze ethane oxidation based on the widely cited GRI-Mech 3.0 mechanism to demonstrate the algorithm's performance in large-scale practical applications. The model predictions have been greatly improved by determining the optimal pre-exponential factors for five unimolecular reactions from experimental data obtained at elevated pressures.