Principles of Modern Radar - Volume 2 1891121537

8.6 Error Sources 375The second method relies on using the unwrapped IPD to estimate delay differencesbetween the two InSAR channels. However, these differences must be estimated to a precisionequivalent to 1% to 0.1% of a pixel in range, requiring very precise interpolation anddelay estimation algorithms. In addition, the technique is sensitive to a variety of systematicerrors as well as to phase noise. Accuracy is improved by increasing the interpolationratio (to support finer cross-correlation peak location estimates) and the degree of spatialaveraging of the interferogram (to reduce noise). The accuracy of this method is describedin [34].8.5.8 Orthorectification and GeocodingThe next step in InSAR processing is orthorectification, which uses the newly gainedelevation information to correct the displacement of image pixels due to foreshorteningor layover. For each pixel in the measured (and distorted) SAR image a(x,y), the correspondingestimated elevation ĥ(x,y) is used to estimate the foreshortening −htanψpresent in that pixel, and a corrected image a ′ (x,y) is formed by moving the image pixel:a ′ (x,y + h(x,y) tan ψ) = a(x,y) (8.40)In general, this involves fractional shifts of the range coordinate, requiring interpolationof the image in the range dimension. If the radar is operated in a squint mode, there is alsoforeshortening in the cross-range (x) dimension, and a similar shift in the x coordinate isrequired [20].It is possible to detect regions where the foreshortening is severe enough to generateactual layover of pixels. As the ground range coordinate y is increased in the uncorrectedimage, the corrected ground range y ′ ≡ y + ĥ(x,y) tan ψ is computed. Any region inwhich the gradient dy ′ /dy is negative is exhibiting layover [53].The orthorectified image, along with the corresponding elevation map, locates eachpixel in a three-dimensional coordinate system relative to the SAR platform trajectory. Toform the final DEM, the data may then be translated to a standard geographical coordinatesystem or projection, a process known as geocoding [33]. The first step is typically toexpress the coordinates in the universal Cartesian reference system, which has its originat the earth’s center, the z axis oriented to the north, and the x–y plane in the equatorialplane. The x axis crosses the Greenwich meridian. The next step expresses the elevationsrelative to an Earth ellipsoid, usually the WGS 84 standard ellipsoid. At this stage, the(x,y,z) coordinates are expressed as a new geographic coordinate set (θ long , θ lat , z), whereθ long is longitude, and θ lat is latitude. The last step projects the geographic coordinates ontoa standard cartographic map, such as the universal transverse Mercator (UTM) projection,which represents points in a north–east–elevation (N, E, z) system. Finally, the data areregridded (interpolated) to uniform spacing in the north and east coordinates.8.6 ERROR SOURCESSince the relative elevation is estimated as a multiple of the interferometric phase difference,errors in the IPD measurements will translate directly into errors in the elevationestimate. These errors arise from several sources, including thermal noise; various processingartifacts such as quantization noise, point spread response sidelobes, and focusing