Parameter identification using the Hilbert transform
  Many physical systems can be adequately modelled using a second order approximation. The problem of plant identification reduces to the problem of estimating the position of a single pair of complex conjugate poles. One approach to the problem is to apply the method of least squares to the time domain data. This type of computation is best carried out in "batch" mode and applies to an entire data set. Another approach would be to design an adaptive filter and to use autoregressive, AR, techniques. This would be well suited to continuous real-time data and could track slow changes on the underlying plant. I this paper we present a very fast but approximate technique for the estimation of the position of a single pair of complex conjugate poles, using the Hilbert transform to reconstruct the analytic signal. 
Andrew Allison and Derek Abbott