Interpolation-based matrix pencil method for parameter estimation of dispersive media in civil engineering

In this paper, we propose a modified matrix pencil method for the problem of time delay estimation in dispersive media obeying a particular frequency power law, namely, the constant-Q model. Being based on a Vandermonde decomposition of the prediction matrix, the matrix pencil method produces biased estimates when applied directly to data of the constant-Q model. The proposed approach allows to compensate for the bias inherent to the classical method by restoring the Vandermonde structure via a spline-interpolation technique. The restoration involves an iterative procedure where each iteration selects a set of interpolated samples depending on the value of the quality factor of the previous iteration. The algorithm is tested on simulated data representing radar acquisitions over a stratified dispersive medium, and its performance is assessed against the Cramér–Rao lower bound.