REPLACEMENT SENSOR MODEL (RSM) PERFORMANCE ... - asprs

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Table 4. Alternative adjustable parameter selection and error covariance mapping statistics for WorldView RSM adjustable parameter set Maximum normalized Maximum frobenius norm condition number Baseline (6 linear combinations of imagespace adjustments as a function of imagealigned ground coordinates) 0.000826 1.14e+7 6-parameter ground-space offset and rotation 0.002570 1.52e+9 6-parameter image-space adjustment linear in image coordinates 0.003024 3.46e+8 2-parameter image-space offsets 0.010016 1.01 The adjustable parameter selection and covariance mapping results show that the RSM Generator has arrived at a superior adjustable parameter set for these test images, and it has done so automatically given the original sensor models and the RSM Generator configuration. RSM GEOPOSITIONING PERFORMANCE STUDIES WITH QUICKBIRD The geopositioning performance studies conducted with QuickBird test images were of the type outlined in Figure 2, termed the "replace/extract" scenario. Original support data Extract Generate RSM Extract ASPRS 2008 Annual Conference Portland, Oregon ♦ April 28 - May 2, 2008 Compare: absolute and relative point positions, absolute and relative error estimates Figure 2. "Replace/Extract" RSM geopositioning performance test procedure. The rigorous "original" sensor model is provided to the testbed by the Socet Set libraries. Prior to testing, the images have been imported with Socet Set, so the "original support data" consists of Socet Set support files. The "extract" operation is done with BAE Systems Multiple-Image Geopositioning (MIG) service. It consists of a simultaneous least squares solution for the point positions given their measurements in all images. In the case of extraction from a single image, Digital Terrain Elevation Database (DTED) is used to establish the point heights. The sources of error in MIG error propagation are image measurement errors (estimated at 2 pixels 1-sigma), sensor model adjustable parameter errors, and DTED errors. The RSM support data generation is done with the RSM Generator, and the sensor model used in the RSM extraction is provided by the RSM support data and the RSM Exploiter. The RSM extraction is done with the same MIG service used for the original sensor model extraction. The same image measurements and uncertainty are used as for the original sensor model extraction. The sensor model adjustable parameters for the RSM extraction are the ones selected by the RSM Generator and communicated via the RSM support data. The first test set for RSM geopositioning tests with QuickBird consists of a pair of overlapping images acquired on different passes. The first image has an off-nadir angle of 8 degrees and the second has an off-nadir angle of 29 degrees. The stereo convergence angle is 24 degrees. The ground sample distances (GSDs) are 0.6 m to 0.7 m (measured normal to the nominal line of sight). The horizontal CE for the QuickBird images is 23 m at nadir, and somewhat larger off-nadir. (The confidence level for all absolute and relative CE and LE metrics in this paper is 90 % and is computed from the appropriate a posteriori ground point error covariance matrix.) Two corresponding points were measured in each of these two images, and geopositioning was performed for each image with DTED,
and for the stereo pair. The original sensor model results and the RSM results are tabulated in Table 5 (absolute geopositioning) and Table 6 (relative geopositioning). The first two columns of Table 5 identify the images and point used for the row. The third and fourth columns are the horizontal CE for geopositioning with the original sensor model and with RSM. In every case these are in extremely good agreement. Note that for single-image geopositioning the CE is larger for the second point than the first, because the off-nadir angle is greater, and therefore the DTED vertical error affects it to a greater degree. The fifth and sixth columns of Table 5 are the vertical LE using the original sensor model and RSM. For single-image geopositioning, the LE is strictly determined by the DTED accuracy, so it is not surprising that the original sensor model and RSM are in good agreement, but the agreement is excellent for stereo geopositioning as well. (The LE is larger for stereo geopositioning than for mono, because the convergence angle is not very favorable, and the DTED was not used to assist the stereo geopositioning for these tests.) The seventh column of Table 5 is the difference in the horizontal position for RSM geopositioning as compared to the original sensor model geopositioning. The largest difference in the table is 0.074 m, which is an insignificant fraction of the horizontal uncertainty of 26.239 m for the same point. The last column of Table 5 is the difference in the vertical position for the RSM geopositioning as compared to the original sensor model geopositioning. Only the last two rows are significant (because DTED is the only source of vertical information for the single-image cases), and these are in extremely good agreement. Table 5. Absolute geopositioning results for 2 QuickBird images Image(s) Point Original RSM Original RSM Horiz. Pos. Vert. Pos. CE (m) CE (m) LE (m) LE (m) diff. (m) diff. (m) 1 1 24.550 24.556 18.001 18.001 0.001 0.000 1 2 25.055 25.062 18.000 18.000 0.000 0.000 2 1 31.361 31.309 18.001 18.001 0.004 0.000 2 2 31.942 31.884 18.002 18.002 0.006 0.000 1 and 2 1 26.239 26.233 63.901 63.779 0.074 -0.028 1 and 2 2 26.562 26.558 65.256 65.136 0.067 -0.084 It is not enough to assess the RSM performance with absolute geopositioning results. Sensor models are also used to compute point-to-point distances, angles, and so forth, which requires high-fidelity relative geopositioning. The relative geopositioning results in Table 6 below show that RSM has excellent performance for these purposes just as it has for absolute geopositioning. The first two columns identify the images and points used for the row. The third and fourth columns are the relative CE for the point pair, computed with the original sensor model and RSM. Note that CErel is larger for the second image, because the off-nadir angle is greater and the random DTED error has a greater horizontal effect. The fifth and sixth columns of Table 6 are the relative LE for original sensor model and RSM geopositioning, respectively. The results are identical for single-image geopositioning, due to the use of the same DEM, and the result is in excellent agreement for stereo geopositioning. The seventh column of Table 6 is the relative horizontal position difference, that is, the difference in the horizontal distance from the two geopositioning solutions. The small differences are negligible in comparison with the horizontal error estimates. The last column of Table 6 is the relative vertical position difference, that is, the difference in the height of the second point relative to the first as computed using RSM as compared with the original sensor model. Only the last entry is significant due to use of the same DEM for single-image geopositioning, and the difference of 0.056 m is tiny in comparison with the relative LE of 10.096 m. Table 6. Relative geopositioning results for 2 QuickBird images Image(s) Points Original RSM Original RSM Rel. Horiz. Rel. Vert. CErel (m) CErel (m) LErel (m) LErel (m) Pos. diff. (m) Pos. diff. (m) 1 1-2 5.504 5.505 25.457 25.457 0.001 0.000 2 1-2 15.447 15.448 25.458 25.458 0.002 0.000 Stereo 1-2 4.112 4.113 10.096 10.097 0.008 0.056 ASPRS 2008 Annual Conference Portland, Oregon ♦ April 28 - May 2, 2008
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