State-space Identification in Frequency Domain from Missing Measurements

Data samples for system identification can get lost in some applications due to sensor failure or data transmission errors. We want to overcome this problem by the means of identification from incomplete data rather than repeating the measurement and the experiment, because this can be either impossible or expensive. Recently extended local polynomial method (LPM) provides us a useful tool to estimate the frequency response matrix (FRM) of a linear system from missing samples. Combined with LPM and maximum likelihood estimation (MLE) in the frequency domain, a computationally efficient approach is presented in this paper, which enables us to identify the state space model from missing samples at noisy outputs. It is applicable to arbitrary (random) inputs, and no particular pattern for the missing output data is assumed. The numerical comparisons show that the proposed approach provides an economical solution to tackle missing measurements, which ensures highly accurate parameter estimation and small computation cost simultaneously.