APPLICATION OF THE PREDICTION DECONVOLUTION TECHNIQUE TO SIGNAL PROCESSING IN GROUND PENETRATING RADAR SYSTEMS

Ground penetrating radar (GPR) systems emit electromagnetic energy into ground and receive reflection signals to process and display images of objects underground. The technology can be applied to variety of fields such as military, constructions, geophysics, ... In the paper, we will propose the prediction deconvolution technique for signal processing in GPR systems. The technique is developed based on the method of Least Square filter and Wiener filter. Our processed results have shown that by applying the proposed technique, received signals will be eliminated interference and give better images with high resolution. In addition, to get good results we see that it is necessary to predict the accuracy of pulse response of environments.


Ground
Signal processing techniques until now have been used techniques of image processing such as noise removal, smooth processing by two dimensional multiplication convolution, or median filter, ... [12]. However, for GPR signals, we need to not only process images but also recover transmitted narrow pulses. In the paper, we propose a method of prediction deconvolution, which can do two simultaneous The remaining of the paper is organized as follows. In the next section, the model of GPR systems is described. The proposed technique of predict convolution is presented in section 3.
In section 4, we show the process of the technique and discuss its results. Finally, we conclude the paper in section 5.

Invert filter
A concept of invert filter is shown in Fig.2.

If w(t) is GPR wavelet signals received and δ(t)
is desired output signals, then f(t) must satisfy the below condition: By conducting z-transform of (1), we have The expression shows the determination of the filter's coefficients by inverting the ztransform of GPR wavelet. However, the filter usually gives enormous error, especially when GPR wavelet signals are different from desired signals.

Least square filter
This is the method to find the filter's coefficients so that the difference between received signals and the desired signals is minimal. A concept of Least Square filter is shown in Fig. 3. The filter's coefficients f 1 , f 2 ,…,f n are initial with arbitrary values, then convolute with GPR received signals w(t) as: Then, the coefficients are determined by applying the least square error algorithm for the error between signals y(t) and desired signals d(t) as: ,..., , ,..., , After receiving the coefficients, the filter deconvolutes again with GPR received signals to get output signals.

Fig. 3. Least Square Filter
According to [12], the method is significantly dependent on the initial phase of desired signal d(t). If the phase is small, then the error is small; and if the phase is large, then the error is large. In addition, the method is quite complex when the order of filter is high.
The autocorrelation of received signals (r 0 ,r 1 ,… r n-1 ) is given by The cross-correlation of received signals (g 0 , g 1 ,…, g n-1 ) is calculated as follows: The coefficients of Weiner filter (a 0 , a 1 ,…,a n-1 ) can be determined by solving the below equations: After receiving the coefficients, the filter deconvolutes again with GPR received signals to get output signals.

Prediction deconvolution filter
For the technique, the coefficients of the filter are determined so that output signals will be prediction signals considering as input signals in future. A concept of the proposed filter is shown in Fig. 5. Assuming that input signals are By augmenting the right side to the left side we obtain  1  0  1  2  3  4   0  2  1  0  1  2  3  1  3  2  1  0  1  2  2  4  3  2  1  0  1  3  5  4  3  2  1  0  4 1 0 0 0 0 0 r r r r r r a r r r r r r a r r r r r r a r r r r r r a r r r r r r a After changing and rearranging the equations, we have new equations as follows:

SIMULATION RESULTS
In the section, we apply the prediction deconvolution filter to a real GPR data