Rational interpolation from phase data by subspace methods

In this paper, two simple subspace-based identification algorithms to identify stable linear-time-invariant systems from corrupted phase samples of frequency response function are developed. The first algorithm uses data sampled at nonuniformly spaced frequencies and is strongly consistent if corruptions are zero-mean additive random variables with a known covariance function. However, this algorithm is biased when corruptions are multiplicative, yet it exactly retrieves finite-dimensional systems from noise-free phase data using a finite amount of data. The second algorithm uses phase data sampled at equidistantly spaced frequencies and also has the same interpolation and strong consistency properties if corruptions are zero-mean additive random variables. The latter property holds also for the multiplicative noise model provided that some noise statistics are known a priori. Promising results are obtained when the algorithms are applied to simulated data.