4.2. Alpine Meadow Amplitude PDF
The alpine meadow is covered with low vegetation, and the soil is moist. The ground is relatively flat. An alpine meadow test environment is shown in
Figure 6.
The 200 periodic signals are used to analyse signal amplitude PDF. The per period contains 512 points. Range between maximum amplitude and minimum amplitude is divided into 512 parts. The point number in per part is calculated, and know the measured signal PDF curve. According to the theoretical distribution formulas, theoretical distribution curves can be obtained.
The measured data amplitude PDF contains 512 points. Theoretical distribution curves also contains 512 points. The corresponding points are subtracted, and then difference sums is used as the fitting error. Use fitting error to determine the fit degree between the measured signal PDF curve and theoretical distribution curves.
is the measured data amplitude PDF curve.
is theoretical distributions curve. The fitting error is expressed as:
The goodness of fit is introduced to describe the shape fit degree between the theoretical distribution curve and the ground echo amplitude PDF curve. The statistical parameter of goodness is expressed as the determination coefficient . The maximum value is 1, indicating that the shape fit result between the curves is perfect.
Next, the measured echo amplitude PDF curve is compared with theoretical distributions curve. At grazing angle 20°, the ground echo amplitude PDF and theoretical distributions curve are shown in
Figure 7. The fitting error and goodness of fit
are shown in
Table 1.
The first picture is the comparison between the measured data amplitude distribution and the normal distribution. The second picture shows the comparison between the measured data amplitude distribution and other theoretical distributions. Different theoretical distribution curves are distinguished by different curve shapes. Through observation, it is found that the curves degree of fit between the measured data amplitude distribution and the normal distribution is high. Other theoretical amplitude distribution curves and measured data distribution curves reflect the differences in peak, peak position, and curve fluctuations.
Fitting error describes the difference from the digital perspective. Fitting error from measured signal amplitude PDF curve and normal distribution curve is 0.13. It is the smallest among all fitting errors. Fitting error from measured signal amplitude PDF curve and G0 distribution curve is 0.18. describes the difference from the curve shape perspective. Normal distribution curve is 0.97, and it can explain that normal distribution curve shape is closest to measured signal amplitude PDF curve. The suboptimal value is G0 0.95. Through the above analysis, at grazing angle 20°, measured signal amplitude PDF curve can be described as normal distribution.
At grazing angle 45°, the ground echo amplitude PDF and theoretical distributions curve are shown in
Figure 8. The fitting error and goodness of fit
are shown in
Table 2.
The first picture is the comparison between the measured data amplitude distribution and the normal distribution. The second picture shows the comparison between the measured data amplitude distribution and other theoretical distributions. Through observation, it is found that the degree of fit between the measured data amplitude distribution and the normal distribution is high at grazing angle 45°. The four distribution functions of Lognormal, Gamma, G0, K-root four distribution functions gradually approach the measured data amplitude distribution, and the divergence gradually decreases.
Fitting error from measured signal amplitude PDF curve and normal distribution curve is 0.10. It is the smallest among all fitting errors. Fitting error from measured signal amplitude PDF curve and G0 distribution curve is 0.13. Normal distribution and measured signal amplitude PDF curve is 0.98, and it explain that normal distribution curve shape is closest to measured signal amplitude PDF curve. The suboptimal value is G0 0.97. Through the above analysis, at grazing angle 45°, measured signal amplitude PDF curve can be described also as normal distribution.
At grazing angle 65°, the ground echo amplitude PDF and theoretical distributions curve are shown in
Figure 9. The fitting error and goodness of fit
are shown in
Table 3.
The first picture is the comparison between the measured data amplitude distribution and the normal distribution. It is obvious that the peak value position of the measured data amplitude distribution curve moves forward with the increase of the grazing angle. The normal distribution is no longer the optimal description curve. Through observation, it is found that the degree of fit between the measured data amplitude distribution and the G0 distribution curve distribution is high.
Fitting error from measured signal amplitude PDF curve and normal distribution curve is 0.15. Fitting error from measured signal amplitude PDF curve and G0 distribution curve is 0.14, same as Weibull distribution. It is the smallest among all fitting errors. Normal distribution curve is 0.94. Weibull distribution and G0 distribution curve value is G0 0.96. Through the above analysis, at grazing angle 65°. In terms of and fitting error, Weibull distribution and G0 distribution has ability to describe the measured signal amplitude PDF curve.
At grazing angle 85°, the ground echo amplitude PDF and theoretical distributions curve are shown in
Figure 10. The fitting error and goodness of fit
are shown in
Table 4.
It is observed that the peak value position of the measured data distributions curve further moves forward, and the difference with the normal distribution curve is further enlarged. Other theoretical distribution curves are gradually approaching the measured data distribution curve. Weibull distribution and G0 distribution from peak value, peak position, and curve fluctuation can describe the measurement data distribution well.
Fitting error from measured signal amplitude PDF curve and normal distribution curve is 0.14. Fitting error from measured signal amplitude PDF curve and G0 distribution curve is 0.12. Weibull Fitting error is 0.12. From the digital perspective, G0 distribution curve and Weibull distribution curve are optimal description curve. Normal distribution curve is 0.94. G0 distribution curve is 0.97. Weibull distribution curve is 0.96 and is the basically same as G0 distribution . Weibull distribution and G0 distribution curve are close to measured signal amplitude PDF curve, at grazing angle 85°.