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

Abstract

In this paper, we obtain the Complex Natural Resonances of an object from the backscattered response in the frequency domain with a novel rational function approximation method based on both Vector Fitting and Cauchy methods. We determine the system order and an initial set of poles, which are used as a basis for a rational function approximation. The results from the simulations and experiments show an improvement in the reconstructed signals and the accuracy of the CNRs calculated, with an increased tolerance to the critical Signal-to-Noise Ratio. This is being used in the problem of GPR landmine humanitarian detection in Colombia.

Hardware Suitability of Complex Natural Resonances Extraction Algorithms in Backscattered Radar Signals

“…This approach is based on vector-fitting and Cauchy's methods for calculating CNRs of a backscattered signal [10,12,21]. The VMC starts with the frequency domain signal treated as the response of the system Y(s) and its transfer function approximation as a ratio of u k and v k coefficients, as in Equation ( 16).…”

“…The singularities in the time or frequency domain can be calculated using methods such as matrix pencil method (MPM), Prony's method, Cauchy's method, or vector-fitting Cauchy method (VCM) [6][7][8][9][10][11][12]. However, besides VCM, there is no reconstruction of the signal validated through numerical results that validate the poles for object identification scenarios or any analysis for real-time implementation.…”

RCS Prediction Using Prony Method in High-Frequency Band for Military Aircraft Models

“…It is especially widely utilized in the fields of power system electromechanical oscillation, biomedical monitoring, radioactive decay, radar, sonar, geophysical sensing and speech processing. The Prony Method estimation equation is written as a complex attenuated sine function with y(t) as output under the l total number of damped exponential components as Equation (19).…”

“…Methods to precisely estimate the RCS at a high frequency based on the RCS observed at a low frequency have been researched as a supplement to existing indirect RCS measuring methods using simulation, including CST, in order to improve the time-consuming disadvantage of high-frequency bands. There is a case of predicting the RCS at high-frequency utilizing the Rational Function prediction method [16][17][18][19][20] based on MoM, one of the low-frequency scattering analysis approaches, as an example of the RCS prediction method at high frequency. However, because the prediction result is produced by only the Rational Function and its result is not compared with those of other prediction methods, it is difficult to confirm that the Rational Function is the best way to forecast RCS in the high-frequency bands in this case.…”