On frequency-domain maximum likelihood identification of state-space time-varying systems

This paper addresses the problem of identifying state-space models for time-varying systems using maximum likelihood estimation in the frequency domain. We use the sliding discrete Fourier transform (S-DFT) to incorporate new data available on-line. Two possible approaches are explored. First, a Taylor series expansion is used to approximate the likelihood function in order to obtain a recursive maximisation algorithm. In the second approach, the Expectation-Maximisation algorithm used to maximise the likelihood function is modified to incorporate S-DFT data in each iteration. Examples are presented confirming the feasibility and performance of the two proposed algorithms.