High-accuracy state and parameter estimation using Chebyshev spectral discretization method

In this paper, we propose an algorithm for state and parameter estimation of nonlinear dynamical systems. In a usual manner, estimation is obtained by solving iteratively a sequence of linear least squares problems with equality constraints. Formulation of the least squares problem is based on Chebyshev spectral discretization. Chebyshev grid resolution is determined automatically to maximize computation accuracy. The key quality of the algorithm lies in the use of the barycentric interpolation formula when solving the least squares problem with various grid resolutions. High-accuracy of the proposed estimation method is contributed to this interpolation formula that is found to be numerically stable and computationally effective. Two numerical examples are presented to demonstrate accuracy of the proposed algorithm.