The GPOF-based Ground Return Deembedding in SteppedFrequency Ground Penetrating Radar

Egor Zaikov*

Institute of Applied PhysicsAkademicheskaya, 16, Minsk-220072, BELARUS

email: zaikov@iaph.bas-net.byAbstract: The work is devoted to aproblem ofdetecting shallow underground objects likeanti-personnel mines using ultra-wideband ground penetrating radar (GPR). In case ofstep-frequency radar, an inverse discrete Fourier transform (IDFT) is a standard dataprocessing technique to convert the raw radar data into the range profile. The latter canbe usedfor detecting buried targets and estimating their depth. Here, an advanced dataprocessing algorithm based on a general-pencil-of-functions (GPOF) method is proposedto improve the radar performance.

1. IntroductionBeing a subject to clutter which originates mostly from absolute dominance of ground return,ground penetrating radar signals require efficient clutter removal procedures. Manytechniques, differing by both the necessary amount of GPR data and by the mathematicalapproach, are described in literature. On the other hand, super-resolution techniques likeMUSIC and GPOF are often applied as advanced signal processing tools instead of IDFT inorder to enhance the spatial resolution of GPR system. However, one must realize thatresolution is mostly determined by the wavelength at the highest frequency that can penetratethe soil to the target of interest. The super-resolution methods cannot overcome this limitationto any desired extent. The more components of the signal are derived in the attempt toincrease resolution, the less stable is the result. The difficulties of the efficient straightforwardimplementation of super-resolution techniques to GPR data are that the parameters necessaryfor the reliable performance of those methods should be determined beforehand. However,they may be used in certain way for the clutter subtraction. So, in this paper, the methodemploying the high resolution of GPOF algorithm for the particular case of ground returnremoval is proposed.

2. Application of GPOF method to ground return deembeddingThe theoretical approach of the GPOF algorithm is described in [1]. Unlike the Fouriertransform, the GPOF method gives a discrete spectrum. Its core idea is to obtain the reflectioncoefficients r, and the poles zi of the signal components in the presence of noise n(k) withthe use of a special algorithm, the main procedure of which is the eigenvalue decomposition:

M

y(k) = Yr,zk + n(k) (1)

The poles contain spatial information about reflections found in the original signal. Thenumber of signal components M and the model order in the GPOF algorithm should bechosen beforehand. Unfortunately, the parameters of GPOF method well fitting givenexperimental data are not stable enough.

In various techniques targeted at ground return removal, different aspects of the GPR signalsare taken into account to solve the problem. In particular, statistical methods rely onresemblance between the A-scans when there is no shallowly buried mine and on thedifference, that appears when the mine is present [2]. Another approach implies that bothamplitude and phase of the ground response in frequency domain may be represented aspolynomials of some order [3] after the ground return is highlighted on the stage ofpreprocessing. This may be done by means of filtering. The early time gating or non-adaptivefiltering is the simplest way to eliminate the ground response but obviously not the best one.Nevertheless, introducing this preprocessing stage may improve performance of othermethods due to the fact that a lot of redundant information is not taken into consideration.Thus, the method is focused on its main task, namely the ground return evaluation in possiblepresence of shallowly buried object. At the preprocessing stage, a rough estimate of groundreturn is derived. This estimate uses only preliminary spatial information about the groundreturn. The key point is that the whole ground return should be included, possibly at cost of asubsurface object being obscured. Besides, the degree of polynomial to be estimated dependson the surface roughness and on the moisture content in soil.In this paper, the GPOF method is used to estimate the problem of ground return quantatively.The main advantage of using GPOF is that this method can resolve closely situated reflectionsin case when IDFT fails. Obviously, this aspect could be very useful for the separation ofground return and shallowly buried mine, as the enhanced resolution of the GPOF algorithmmeans that these two signal components may be shown as different poles in case they overlap.Thus, the preprocessing stage at which a priori spatial information about the ground return isutilized, may be replaced by the GPOF method which is likely to discern the ground signaland the subsurface object in case the latter is present.To put it in a more particular way, the GPOF algorithm was used for the ground returncancellation in the following manner. First, the number M of components to be estimated wasset to 2. Thus, the a priori information about strong ground return component and possiblesubsurface object is passed to the GPOF procedure. Second, the distance to the closest to theantenna opening spatial component is taken as the only output of the GPOF method used forfurther processing. Then, the pole z, which is deemed corresponded to the ground return, isused to solve the problem y(k) = rzk of finding the amplitude r of the ground return withrespect to the input data y . Thus, the problem of computing the complex amplitude of theground return to be subtracted is solved in a least-squares sense with respect to the obtainedpole in order to minimize the presence of surface-originated clutter in the input data.Two complex poles yielded by the GPOF method in such processing technique correspondusually to the ground return and subsurface object. In the case of shallowly buried objectreflections can be effectively resolved and thus the estimate of the ground response withoutshallow object would be subtracted. Therefore, only one pole obtained by means of GPOF isused, and this one corresponds to the strong enough signal component. Using suchimplementation of GPOF, instabilities inherent to this method may often be suppressed.

3. MeasurementsAll experimental data were collected with the network analyzer E5071B. Two Vivaldiantennas in bistatic configuration operating from 1 GHz to 4 GHz were used. The object,PMN2 mine was embedded into the sandy medium in different positions and at depthsshallow enough to cause overlapping of target and surface returns (about 1.5 cm). On theother hand, the scans of empty soil with a rather rough surface were collected in order tocompare results of using GPOF in this case with those of using it in the case of mine-containing data and thus to highlight the practical aspect of the method's performance.

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C) C)Figure 1. Mine-containing profile Figure 2. Empty soil profile

In Figures 1 and 2, the range profiles of mine-containing and empty data synthesized with theIDFT are presented. The solid line represents raw data without ground return removalprocedure. The range profile after the GPOF-based ground return removal is shown in thedash-dotted line. The abrupt dashed peaks mark distances corresponding to the poles of theGPOF algorithm.

It may be observed in Figure 2, that the air-ground interface was represented with one pole,and that corresponded distance is near the center of the peak, which represents the groundreturn when no subtraction is used. It is also evident that in such situation the ground return issuccessfully subtracted with the procedure described above. The reason is that the other poledoes not yield distance within the region of ground return.On the other hand, it may be derived from Figure 1, that when the shallowly buried mine ispresent, there are two poles produced by the GPOF procedure within the area of groundreturn, and none of them coincides with the maximum value of the peak on the raw dataprofile. This is exactly what should to be expected from the super-resolution technique, whenits super-resolution capacity is sufficient to discern two close signal components. Themaximum value on the raw data range profile in such situation is not the ground, as it isdistorted with the presence of another reflector and the GPOF algorithm allocates twodifferent signals according to its mathematical model. Since the first pole is used for furthersubtraction, the early-time part of the peak is associated with the unwanted ground return andeliminated by means of further processing, while the other part persists since it is deemed theburied object.

4. ConclusionsThe important feature of the GPOF-based ground return deembedding is that all A-scans arehandled separately and thus the performance of the technique is independent on the amount ofavailable data. The experimental results prove that technique performs satisfactorily, althoughit is evident, that the method has limitations related both to the depth of buried mine and tothe roughness of soil surface since the complicated surface may attract the second pole andproduce the false alarm. In the experiments the soil was slightly rough, the minimal depthwhere the information about the mine may be derived with the method described is about 1.5cm.

Reference:[1] Yingbo Hua, Tapan K. Sarkar, Generalized Pencil-of-Function Method for Extracting Poles of

an EM System from Its Transient Response. IEEE Transactions on Antennas andPropagations, vol. 37, no. 2, February 1989, pp 229-234.

[2] B. Karlsen, J. Larsen, K. Jakobsen, H. Sorensen, and S. Abrahamson: Antenna Characteristicsand Air-Ground Interface Deembedding Methods for Stepped-Frequency Ground Penetratingradar measurements. In Proc. of SPIE, AeroSense 2000, vol. 4038-157, April 2000.

[3] V. A. Mikhnev and P. Vainikainen, Single-Reference Near-Field Calibration Procedure forStep-Frequency Ground Penetrating Radar. IEEE Transactions on Geoscience and RemoteSensing, vol. 41, no.1, January 2003, pp 75-80.