Parameter estimation of dispersive media using the matrix pencil method with interpolated mode vectors

A modified matrix pencil method (MPM) inspired by interpolated arrays is proposed for the problem of parameter estimation in dispersive media obeying a frequency power law. A direct consequence of the arising dispersive signal model is that the Hankel prediction matrix can no longer be expressed using the Vandermonde decomposition, which hinders the direct application of all matrix-shifting techniques including the MPM. This is remedied by restoring the Vandermonde structure of the mode vectors via two different interpolation procedures. The first procedure is two dimensional, whereas the second one is one dimensional and iterative. The two versions of the interpolated algorithm are tested on simulated data representing radar acquisitions over a stratified dispersive medium, and their performance is assessed against the CraméŕRao lower bound. The obtained results indicate that the iterative interpolation procedure affords the optimal performance of its two-dimensional counterpart at a reduced computational burden.