An iterative procedure for the state estimation of a nonlinear discrete process

The iterative procedure for the state estimation of a nonlinear discrete process is presented. The proposed method is proved to give the optimal estimate of the least-mean-square error criterion after infinite iteration for a class of optimal estimates. The calculation formula for the quadratic nonlinear process is presented to illustrate the procedure. In the formula, the coefficient of the iteration is calculated by assuming the estimation error is Gaussian. This assumption is found not to affect the convergence as long as the error caused by the assumption is less than 100 percent. The application to the identification is given, and it leads to satisfactory results.