Multi-step-length gradient iterative algorithm for equation-error type models

This letter develops a multi-step-length gradient iterative algorithm for equation-error type (EET) models. The algorithm analysis is based upon the gradient search principle. By applying the Gram-Schmidt procedure, the EET model can be turned into an orthogonal model, in which each parameter in the parameter vector is independent of the other parameters. Then a multi-step-length gradient iterative algorithm is proposed for the orthogonal model, and can estimate the parameters in one iteration. Finally, based on the estimated parameters, the parameter estimates of the EET model can be computed. Different from the traditional gradient iterative algorithm which has slower convergence rates and is sensitive to the initial values of the unknown variables, the method in this letter has quicker convergence rates and is robust to the initial values of the unknown variables. The simulation studies demonstrate the feasibility and effectiveness of the proposed algorithm.