Investigation of Simulated Ground Penetrating Radar
Data for Buried Objects Using Quadratic
Time-Frequency Transformations
Mesut Dogan
Dept. of Electrical and Electronics Engineering, Middle East Technical University
06800 Ankara, Turkey
Dept. of Electrical and Electronics Engineering, Ardahan University, 75000 Ardahan, Turkey
mesut.dogan@metu.edu.tr
Gonul Turhan-Sayan
Dept. of Electrical and Electronics Engineering, Middle East Technical University
06800 Ankara, Turkey gtsayan@metu.edu.tr
Abstract—Sub-surface sensing is a challenging area of research that highly benefits from the use of ultra-wideband ground penetrating radar (GPR) technology. Detection and classification of buried objects with reduced false alarm rates is still open to improvements. Use of joint temporal and spectral target features obtained from electromagnetic GPR signals using time-frequency representation (TFR) methods is highly promising because TFRs provide detailed information about the energy distribution of GPR signals over the two-dimensional domain of time and frequency. 1In this
study, single-channel down-looking GPR data are simulated for spherical targets composed of different material contents. Following the removal of dominating ground reflections, energy distribution signatures of the A-scan GPR signals of different targets are investigated using the Wigner-Ville Distribution and Page Distribution type quadratic TFRs.
Keywords—ground penetrating radar; A-scan signals; time-frequency representations; target feature extraction
I. INTRODUCTION
Detection and classification of landmines is a problem of critical importance. As compared to other sensor technologies, GPR is known to be the most effective sensor for automatic target recognition (ATR) of buried targets [1]. Implementation of sensor fusion [2] as well multi-aspect data and feature fusion [3] are powerful approaches to reduce false alarm rates in automatic target recognition problems in general, including the GPR applications.
Distribution of wideband scattered signal energy over the two-dimensional joint time-frequency domain provides valuable information about the complex natural resonance (CNR) frequencies of a target [4] as they form a set of aspect and polarization independent features characterizing that target in a
1 This work was supported by the Middle East Technical
University (ODTÜ) Research Project No: BAP-03-01-2016-005.
unique way. Therefore, use of quadratic time-frequency representations [5] such as Wigner-Ville distribution (WD) and Page distribution (PD) are useful tools in subsurface target recognition.
II. GPRSIGNAL ANALYSIS BY WD AND PDMETHODS
While the Fourier transformation is useful to analyze a given stationary signal x(t) either in time domain or in frequency domain, TFRs are capable of analyzing non-stationary transient signals (such as GPR data) as they investigate the frequency content of a nonstationary signal over a selected time interval. The Wigner-Ville distribution (WD) is a real-valued, quadratic TFR preserving time shifts and frequency shifts of the signal. The auto-WD of a given time domain signal x(t) is computed [5] as
)e d 2 t ( x ) 2 t ( x ) f , t ( Wx j2 f (1)where the superscript (*) denotes complex conjugation. As the auto-WD satisfies so called “marginal properties” [5], is interpreted as an energy density function in the joint time-frequency domain. The Page Distribution (PD) is another quadratic, time-frequency shift invariant TFR and it is defined [5] as
t d t f 2 j e ) t t ( x dt d ) f , t ( x PD (2)
III. SIMULATIONS AND RESULTS
GPRMax is an FDTD based simulator software [6]. It is used to generate GPR signals in this study for identical-size spherical targets with a radius of 5.5 cm. Spherical target volumes are assumed to be filled
235
by different materials; perfect electric conductor (PEC), water and plastic. The test sphere is buried within homogeneous dry sand with its center is 10.5 cm below the ground surface. FDTD simulations are performed from 0.2 GHz to 7 GHz using the dry sand parameters of relative permittivity and permeability as
. 2 , 3 r
r
Data are synthesized in every 1 cm along the down-track direction. As an example, B-scan and A-B-scan GPR data for a water-filled spherical target are shown in Fig. 1 and Fig. 2, respectively, after removing air-ground reflections.
Fig. 1. B-scan GPR signal (composed of 90 down-track samples) simulated for the water-filled spherical target buried in 5 cm depth.
Fig. 2. A-scan GPR signal corresponding to the 50th down-track
sample of the B-scan data shown in Fig. 1.
WD and PD outputs for the GPR signal (given in Fig. 2) are computed and displayed in Fig.3 and Fig.4, respectively. The PD output has a stronger late-time energy patterns with reduced interference terms. PD outputs of the A-scan signals belonging to the PEC and plastic spheres (at the 50th track) are also
computed as shown in Fig. 5 and Fig. 6, respectively.
Fig. 3. WD output for the GPR signal simulated for the water-filled spherical target.
Fig. 4. Page Distribution of the A-scan GPR signal simulated for the water-filled spherical target.
Fig. 5. Page Distribution of the A-scan GPR signal simulated for the spherical PEC target.
Fig. 6. Page Distribution of the A-scan GPR signal simulated for the spherical plastic target.
CONCLUSION
Energy distribution patterns presented in Fig.4 thru Fig.6 reveal that the material content (e.g. water, conductor or plastic) of the spherical targets makes a big difference in the extracted TFR-based energy features. The PD type TFR-based feature extraction is, in particular, looks promising in the GPR target recognition problem.
References
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