Frequency Domain Identification of a Linear System Using Maximum Likelihood Estimation

Abstract A frequency-domain algorithm for the maximum likelihood estimation of a dynamic system is developed. The model of a multivariable linear system is represented by a discrete-type steady-state Kalman filter. The measured data are assumed in the form of Fourier series expansion. The loglikelihood function of the complex innovations is formulated and the expressions for the first and second-order gradient of this function given. Then the maximum likelihood algorithm is simplified to the output error method considering the measured data either as the transformed input and output variables or as frequency response curves. The advantages and limitations of the frequency domain approach are briefly discussed. The paper is completed by examples using the flight data measured in still and turbulent air or the computer-generated data.