Time-Delay Estimation Using Ground-Penetrating Radar With a Support Vector Regression-Based Linear Prediction Method

Abstract

Ground penetrating radar (GPR) is widely used in media parameters estimation and targets localization. This paper focuses on time-delay estimation (TDE) using GPR signal, which contains important information about the probed media structure. But TDE tends to be a challenging task in GPR applications, in the scenarios of overlapping, coherent signals and limited snapshots. Forward-backward linear prediction (FBLP) is a high time resolution method, which is able to directly deal with coherent signals. Support vector regression (SVR) is robust with small samples. Therefore, we propose to combine the theory of FBLP and SVR together to enhance the robustness of TDE in the case of coherent, overlapping signals as well as limited snapshots. The proposed method is tested both with numerical and experimental data. Both of the results demonstrate the effectiveness of the proposed method.

A Linear Prediction and Support Vector Regression-Based Debonding Detection Method Using Step-Frequency Ground Penetrating Radar

“…The -insensitive loss function is used here [17]. The optimization problem can be written as follows [15]:…”

“…where x n is the nth column of R H and y n = y( f n ); ξ r n and ξ r n stand, respectively, for positive and negative errors in the real part of the output y n , while ξ i n andξ i n stand for the corresponding imaginary part; Re(•) and Im(•) denote the real and imaginary parts, respectively; the value C controls the tradeoff between the structural and empirical errors. To solve (7), we employ the Lagrangian multipliers and the Karush-Kuhn-Tucker theorem with Wirtinger's calculus on the complex variable ω [15]. Thus, the weighting vector ω can be written as follows:…”

“…The signal model from [6] and [15] is adopted in this letter. It represents the backscattered radar echoes (time-shifted and attenuated replicas of the transmitted signal) from lossless stratified media.…”

“…Unfortunately, this assumption may not hold true in the case of SF-GPR. Recently, Pan et al [15] proposed a new forward-backward linear prediction (FBLP) method to estimate the time delays of backscattered GPR echoes with a limited number of frequency samples and A-scans. To achieve this, they proposed to combine the FBLP and support vector regression (SVR) theories.…”

“…Based on the structural risk minimization principle, the SVR serves as a good machine learning algorithm for sparse modeling [16]. Due to the potential advantages, it is of great interest to extend the detection method of [14] by using the techniques in [15]. Thus, the proposed detection method requires only a small number of frequency samples and A-scans.…”