Identification of Linear Systems from their Pulse Responses

This paper discusses a system identification algorithm employing the Hankel matrix of system Markov parameters. This algorithm is an extended version of the Eigensystem Realization Using Data Correlation (ERA/DC) and Q-Markov Covariance Equivalent Realization (Q-Markov Cover) algorithms. Under the assumptions that the Markov parameters are obtained from system pulse response measurements and that the measurement noises have rational spectrums, the effects of the measurement noises on the identification will be discussed and analytic formulas explicitly discribing these effects will be derived. We will show that under certain conditions system eigenvalues can always (with probability one) be correctly identified and the identified model can be partitioned into two submodels, a submodel containing correct System parameters and a submodel resulting from the measurement noises.