Hierarchical Parameter Estimation for the Frequency Response Based on the Dynamical Window Data

This paper studies the problem of parameter estimation for frequency response signals. For a linear system, the frequency response is a sine signal with the same frequency as the input sine signal. When a multi-frequency sine signal is applied to a system, the system response also is a multi-frequency sine signal. The signal modeling for multi-frequency sine signals is very difficult due to the highly nonlinear relations between the characteristic parameters and the model output. In order to obtain the parameter estimates of the multi-frequency sine signal, the signal modeling methods based on statistical identification are proposed by means of the dynamical window discrete measured data. By constructing a criterion function with respect to the model parameters to be estimated, a hierarchical multi-innovation stochastic gradient estimation method is derived through parameter decomposition. Moreover, the forgetting factor and the convergence factor are introduced to improve the performance of the algorithm. The simulation results show the effectiveness of the proposed methods.