A computational algorithm based on pseudospectral discretization of differential equations is developed to solve parameter estimation problems in nonlinear dynamical systems. The method approximates parameters and state trajectories by using Chebyshev interpolation polynomials. Nonlinear estimation problem discretized on the Chebyshev grid is solved iteratively. In each iteration a linear least squares sub-problem is solved a number of times on successfully finer grids till achieving the highest possible accuracy. The algorithm is applied to the problem of modelling inter-area oscillations using synchronized measurements obtained at terminals of transmission corridor of a large interconnected power system. Results of a simulation study are presented to demonstrate numerical accuracy of the proposed algorithm.