Fabio Rocca

1. 3D motion recovery with multi-angle and/or left right interferometry FabioRocca Dipartimento di Elettronica e Informazione Politecnico di Milano Rocca, Fringe 03 poster, ESRIN, Frascati, December 3, 2003

2. SAR Differential Interferometry yields the components vi of the pixel motion vector x along the i-th (i=1…N) Line Of Sight vector ai vi= ai*x To measure the three components of x : x=[x1, x2, x3] we need N3 motion components along LOS motion vectors not belonging to the same plane: v=[v1, v2, .., vN] = Ax so that the estimate is well conditioned. The 3 eigenvalues of the matrix A*A[3xNxNx3] of the LOS vectors directions give the conditioning analysis . Rocca, Fringe 03 poster, ESRIN, Frascati, December 3, 2003

3. Rocca, Fringe 03 poster, ESRIN, Frascati, December 3, 2003

4. We can consider two cases: A) N=4 acquisitions, ascending and descending, with two different incidence angles, e.g. 230 and any other angle between 170 and 450 As an example (the red line), we can consider the case of 2 neighbouring ERS frames at 450 latitude. In this case, the best retrieved component corresponds approximately to Up Down motion. Its SNR increases by 6 dB, due to the 4 measurements. SNR loss of the second best, EW component, -16dB SNR loss of the worst, NS component, -25dB Rocca, Fringe 03 poster, ESRIN, Frascati, December 3, 2003

5. SNR changes 2 neighbouring ERS frames Incidence Angle Rocca, Fringe 03 poster, ESRIN, Frascati, December 3, 2003

6. The second case considered is: B) 8 acquisitions, ascending and descending with two different incidence angles, i.e. 230 and any other angle between 170 and 450 (fig.1), but sharing the acquisitions between left and right, with different percentages: 0 (only right acq., lowest dotted blue line), 1%, 2%, 4%, 8%, 50% (green line). The best estimated component is UpDown and has the same SNR improvement (6 dB) as before. The second best component is also the EW one. The estimates of these 2 components do notdepend on the percentages of left acquisitions. Rocca, Fringe 03 poster, ESRIN, Frascati, December 3, 2003

7. The variances of the components of the noise vector n are inverse to the number of acquisitions dedicated to left or right views. To avoid bias, ε is supposed to be very small. The error matrix Q =E[|x-Bv|2] has to be scaled back; the error components are along its eigenvectors. Rocca, Fringe 03 poster, ESRIN, Frascati, December 3, 2003

8. The NS component is the only component affected by the partition weights; if the second acquisition is at 450, the SNR losses go from 18 dB (no left) to 10 dB (50% left). Using 450 acquisitions, the advantages of left views are limited to 8dB for the worst component. The red line at 230 shows what happens if all acquisitions are with the same incidence angle; the NS component is not available, unless there are some left acquisitions. If the second acquisition at 450 is not available, even 1% left acquisitions improve the SNR. Rocca, Fringe 03 poster, ESRIN, Frascati, December 3, 2003

9. UD EW SNR changes NS: No left acquisitions NS: 50% left acquisitions NS: 1% left acquisitions NS: only 230 acquisitions Incidence Angle Rocca, Fringe 03 poster, ESRIN, Frascati, December 3, 2003

10. If the phase dispersion of the LOS measure of each pixel is σφ, for each quadruple of measures: To have similar precision for the EW (NS) component we need 10 (250) pixels, with 230 and 450 acquisitions; if we have 230 - 260 acquisitions,we need about 250 (2000). Rocca, Fringe 03 poster, ESRIN, Frascati, December 3, 2003

11. An incoherent analysis based on the differences between two images has some interest. The estimate of the shift δ of a function x(t), spectrally white up to pulsation π/T, T being the azimut sampling interval, using a time series MT pixels long, with coherence γ, is: For γ=0.7, if we wish to have a dispersion of about 1.5mm, i.e. δ=3x10-4xT, we need M400000. Rocca, Fringe 03 poster, ESRIN, Frascati, December 3, 2003

12. Discussion In order to have a good quality NS component, we need thousands of points characterized by high coherence. In semi rural areas, where we expect say 50 PS/km2, we need at least 50 km2 with the same motion to be able to make a very good estimate of NS component (2mm). However, this area would correspond to a grid with 7km side, still much finer than that usually achieved using GPS receivers. Thus, DIFSAR could improve on GPS even for its worst conditioned NS component. The non coherent approach is more pixel hungry by two orders of magnitude. Moreover, it cannot be carried out, unless we have contiguous high coherence pixels, i.e. only in desert areas. However, if carried out on the moduli (further 3dB loss in precision or duplication of the pixels needed) it is independent of atmospheric noise. Rocca, Fringe 03 poster, ESRIN, Frascati, December 3, 2003

13. Conclusions DIFSAR can retrieve the 3 motion components, albeit with different quality. The UD and EW component quality does not change if the acquisitions are left, right, or mixed. The NS component quality improves even with a few left acquisitions; nonetheless, multiple incidence angles acquisitions yield reasonable quality NS components. Non coherent techniques, based on the moduli, are useful for low quality measurements of the NS component. They can be used only if the NS motion stays the same over vast, coherent areas. Rocca, Fringe 03 poster, ESRIN, Frascati, December 3, 2003