The Matrix Pencil method applied to smart monitoring and radar

Abstract

The paper deals with the Matrix Pencil method, an efficient numerical method to identify deterministic signals based on either simulation or measurement. The method is usually referred to as a high-resolution technique as it is capable of identifying non-stationary signals, even in the presence of numerical or measurement noise, respectively. The basis functions are complex exponentials with a damping factor. Those functions are rather appropriate to identify electromagnetic waves or distributed currents with an optimal number of elements. The method is applied either in time domain, in frequency domain or in space domain allowing one to identify the original signal by means of a limited number of singular values, poles and residues.

Vector Fitting–Cauchy Method for the Extraction of Complex Natural Resonances in Ground Penetrating Radar Operations

“…The system described in Equation ( 3), which for a given frequency sample i is described in Equation ( 4), is the basis for the polynomial expansion matrix [C] in Equation (5).…”

“…This motivates again a TLS solution to find the transfer function parameters a and b from the matrix system in Equation (5). The SVD of this matrix [C] results in Equation (12).…”

“…In this context, the Singularity Expansion Method (SEM), initially proposed by Baum in 1971 [1], states that the electromagnetic Complex Natural Resonances (CNRs) of an object can be calculated from the backscattered late time response in the time domain [2,3]. This has been used in the evaluation of geological formations, buried objects, and other radar operations, for example [4,5]. In Equation (1), which is the starting SEM time-domain equation, the signal y(t) is decomposed in complex residues R i and poles s i = α i + jω i , each with a damping factor and a complex frequency.…”