IJCAS

This paper considers the parameter estimation problem of nonlinear models, which are related to the impulse or step response functions of linear time-invariant (LTI) dynamical systems, based on the response data. In terms of the nonlinear characteristic of the models, the nonlinear dynamical optimization scheme is adopted for obtaining the system parameter estimates. By constructing a gradient criterion function, a gradient recursion algorithm is derived. In order to overcome the difficulty of determining the step-size in the gradient recursion algorithm, a trying method and a numerical approach are proposed to achieve the step-size. On this basis, a stochastic gradient estimation method is presented by using a recursive step-size. Furthermore, a multi-innovation stochastic gradient method is deduced for enhancing the estimation accuracy by using the dynamical window data. Finally, a dynamical length stochastic gradient estimation technique is offered to obtain more accurate parameter estimates by using dynamical length measured data from the step response. The examples are provided to examine the algorithm performance and the simulation results indicate that the presented approaches are effective.

Keywords: Gradient search, multi-innovation theory, nonlinear model, parameter estimation, recursive identification.