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

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

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The same four ground control and nine tie points are used in the triangulation in the three scenarios that include<br />

triangulation.<br />

The off-nadir look angles for the images are about 37 degrees and 25 degrees. The stereo convergence angle for<br />

the two images is about 31 degrees. The GSDs are 0.55m to 0.62 m (measured normal to the line of sight). The<br />

replace/extract absolute CE statistics are around 5.1 m, within the specification of 6.5 m and the range of 4.0-5.5 m<br />

stated as a typical horizontal accuracy for WorldView images (at nadir, apart from terrain effects). The other<br />

scenarios, which include triangulation with control, have CE within the 2 m stated for WorldView images with<br />

control. Note that the ground control point accuracy has been estimated at one-meter (one-standard-deviation along<br />

all three axes), which is easily obtainable with GPS surveying. Prior to triangulation the errors between the ground<br />

control points are assumed to be uncorrelated.<br />

For all of the scenarios, the <strong>RSM</strong> performance is excellent in all respects, for both absolute and relative<br />

geopositioning. For absolute geopositioning, the statistics are over the four extracted points (9 tie points for the<br />

replace/triangulate scenario). For relative geopositioning, the statistics are over the six possible pairs of extracted<br />

points (36 tie point pairs for the replace/triangulate scenario). The largest differences in error estimates (absolute or<br />

relative CE or LE) for any of the tests is under 0.01 m. The largest solution differences (absolute or relative<br />

horizontal or vertical position) are about 0.04 m for the replace/triangulate scenario, where these differences are an<br />

insignificant 2 % or less of the corresponding error estimate.<br />

Table 9. Absolute geopositioning results for 2 WorldView images<br />

Scenario Statistic Original <strong>RSM</strong> Original <strong>RSM</strong> Horiz. Pos. Vert. Pos.<br />

CE (m) CE (m) LE (m) LE (m) diff. (m) diff. (m)<br />

Replace/Extract RMS 5.076 5.077 8.287 8.287 0.014 0.030<br />

Max 5.136 5.136 8.307 8.313 0.014 0.030<br />

Triangulate/ RMS 1.845 1.845 2.668 2.668 0.002 0.001<br />

Replace/Extract Max 1.860 1.860 2.677 2.678 0.002 0.002<br />

Replace/<br />

RMS 1.846 1.846 2.687 2.686 0.011 0.016<br />

Triangulate Max 1.889 1.888 2.733 2.731 0.024 0.038<br />

Replace/<br />

RMS 1.845 1.845 2.668 2.668 0.004 0.005<br />

Triangulate/Extract Max 1.860 1.860 2.677 2.677 0.005 0.007<br />

Table 10. Relative geopositioning results for 2 WorldView images<br />

Scenario Statistic Original<br />

CErel (m)<br />

<strong>RSM</strong><br />

CErel (m)<br />

Original<br />

LErel (m)<br />

<strong>RSM</strong><br />

LErel (m)<br />

ASPRS 2008 Annual Conference<br />

Portland, Oregon ♦ April 28 - May 2, 2008<br />

Horiz. Rel.<br />

Pos. diff. (m)<br />

Vert. Rel.<br />

Pos. diff.<br />

(m)<br />

Replace/Extract RMS 1.981 1.981 3.227 3.227 0.001 0.000<br />

Max 1.991 1.991 3.240 3.240 0.001 0.001<br />

Triangulate/ RMS 1.979 1.979 3.227 3.227 0.001 0.000<br />

Replace/Extract Max 1.991 1.991 3.240 3.239 0.001 0.001<br />

Replace/<br />

RMS 1.982 1.982 3.252 3.252 0.013 0.019<br />

Triangulate Max 2.025 2.025 3.299 3.299 0.027 0.043<br />

Replace/<br />

RMS 1.979 1.979 3.227 3.227 0.003 0.004<br />

Triangulate/Extract Max 1.991 1.991 3.240 3.239 0.004 0.005<br />

Excellent <strong>RSM</strong> performance for triangulation and geopositioning has been seen in all of the WorldView<br />

scenarios in this section. These studies have been done with one stereo pair. Photogrammetric triangulations often<br />

involve many images, but all of the complexity of the problem is already present with two images, multiple tie<br />

points, and multiple ground control points, and these are very large images.<br />

CONCLUSION<br />

The tests conducted for this study show excellent agreement in triangulation and geopositioning between <strong>RSM</strong><br />

and the rigorous commercial satellite sensor models they replace. Not only is the <strong>RSM</strong> projective model a very

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