Maximum likelihood ratio detection of abrupt state change for MIMO linear systems based on frequency domain data

Summary This paper is devoted to the detection of abrupt changes for multiple-input, multiple-output (MIMO) linear systems based on frequency domain data. The real discrete-time Fourier transform is used to map the measured inputs and outputs from the time domain to the frequency domain. Under the hypothesis that the state change occurrence time is k, the system is split up into two systems at the time instant k. One of them describes the frequency dynamics before the hypothetical state change occurs, whereas the other describes the frequency dynamics after the hypothetical occurrence. Thus, the latent state change is modeled as an initial state disturbance to be estimated on the basis of frequency domain samples. Furthermore, the occurrence time is estimated by maximizing a likelihood ratio function. Finally, a numerical example is presented to show the performance.