RMS error Surface(a)
6.4 Conclusions on the performance of the multi channel processing method.
In this chapter, we have observed how the multi-channel processing method reduces the speckle noise effect and the topographic effect on the measurement. These effects give rise to a high bias in the retracking method. In addition, we have also examined and compared two techniques for the multi-channel processing method, separable estimation and best linear estimation. In this section, we shall conclude the results obtained from the multi-channel processing method.
For the surface topographic effect, multi-channel processing has improved the measurement accuracy by 530% for the surface correlation length 8km. When the surface correlation length further reduces to 4km, the improvement ratio decreases to 350%. When the surface correlation becomes smaller, the retracking method tends to measure the mean surface which will give a bias that equals the surface height standard deviation. In addition, for the multi-channel processing method, when the surface correlation length reduces without increasing the amount of data used in the
estimation, the bias increases. In consequence, the improvement ratio decreases.
The multi-channel processing method is immune to the speckle noise because it is a natural noise filtering process. For a surface with less topographic effect, like the surface with 25km correlation length, the speckle noise effect on the retracking method and the multi-channel processing method can be examined easily. The increase of speckle noise in the echoes from the speckle-free level to the level equivalent to the parameter N=5 has caused 4% rise in the bias in the multi-channel processing method, whereas the bias has increased by 530% in the retracking method.
In practice, the true surface is not known a priori and, in turn, the accuracy of the measured surface obtained from the retracking method can not be determined. In the multi-channel processing method, the a posteriori error, which is analytically derived from this method, can be calculated. This error gives the least RMS error in the surface height estimate. The a posteriori error has been compared with the RMS error of the retrieved surfaces obtained from this method. Their differences are, on average, about Im, which is less than one range bin equivalent. This has shown that the a posteriori error is a good indicator of the accuracy of the measurement.
The results of two techniques for multi-channel processing are shown and compared in this chapter. Separable estimation takes into account the surface topography in the along-track and across-track directions. However, the best linear estimation would require a huge amount of computer resources if it were to consider the surface topography in both track directions. Hence, the best linear estimation implemented here only takes into account the surface topography in one direction. The results show that the separable estimation gives better measurement accuracy than the best linear estimation. For example, for the surfaces with 8km and 4km correlation lengths, the best linear estimate gives a 60% and 40% higher bias than the separable estimate respectively. It is believed that the additional bias given by the best linear estimate is due to the unresolvable topography in the direction from which the data are absent in the estimation. From this point, it can be verified that the data from both tracks directions are important for measuring the surface topography accurately.
The disadvantage of the separable estimation is that many correlations that result from correlations between across-track and along-track topography are ignored.
In addition, the final estimated error of the surface will be the sum of the error from two estimation processes instead of a single process like the best linear estimation. For these reasons, it is believed that the best linear estimation would do better than the separable estimation if the along-track and across-track data were included in the former estimation.
The best linear estimation was shown to be better than the retracking method in terms of the accuracy of the measurement. For the surfaces of 8km and 4km correlation length, the accuracy has been improved by 330% and 220% by the best linear estimation respectively over the retracking method.
As a conclusion, the feasibility of the multi-channel processing method has been confirmed and has shown significant improvement over retracking.
6.5 Chapter summary.
The re tracked surfaces suffer from two effects. Speckle noise gives rise to a noisy component of the re tracked surface and the effect of surface topography results in a major bias. The multi-channel processing method has completely removed the speckle noise effect and gives a smooth measured surface. The topographic effect also has been improved by the multi-channel processing method from which surfaces of smaller correlation length can be measured more accurately.
In practice, the true surface is not known a priori, and hence the accuracy of the measured surface can not be determined. However, in the multi-channel processing method, the results have shown that the a posteriori error is a good indicator of the accuracy of the measurement.
To reduce the computational requirements, only single along-track data are used in the best linear estimation. The accuracy of the best linear estimate is worse than the separable estimate because the across-track topography has been ignored in the best linear estimation. However, the best linear estimation has shown considerable improvement over the retracking method.
The feasibility of the multi-channel processing method has been confirmed in this chapter. In addition, significant improvement has been shown from this method