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== Definitions ==

'''CompareOBJ RMS:''' The root mean square of the distance from each bigmap pixel/line location to the nearest facet of the truth OBJ.<<BR>>
'''PTG:''' The formal camera pointing uncertainty.
'''SCOBJ:''' The S/C position vector from the center of the asteroid.
'''VSO:''' The formal SCOBJ uncertainty.

== S/C position and pointing uncertainties ==

The Detailed Survey PolyCam F3G data set had large S/C position and pointing uncertainties, unsuitable for Detailed Survey Baseball Diamond trajectories:
 * VSO = 1km;
 * PTG = 1mrad.
An additional suite of tests was therefore run with a duplicate Detailed Survey PolyCam dataset with S/C position and pointing uncertainties set to one-sigma:
 * VSO = 6.4m;
 * PTG = 0.217mrad.

Results for both data sets are presented herein.

== Comments ==

The results show no significant difference in the final S/C position (SCOBJ) and model accuracy (as measured with CompareOBJ RMS) with respect to the magnitude of S/C position and pointing perturbation within the ranges tested, indicating that the SPC-driven modeling is immune to S/C position and pointing perturbation up to three standard deviations.

It should be noted that S/C position perturbation was divided equally between the SCOBJ components, resulting in a distance from the truth position which was a multiple of the standard deviation of 6.4m. Therefore:
 * maximum lateral perturbation was a multiple of 3.7m (6.4m/sqrt(3));
 * maximum normal perturbation (wrt body center) was 3.7m (6.4m/sqrt(3)).
It is assumed that the worst case scenario is a 3 x sigma (19.2m) lateral perturbation. The maximum possible lateral perturbation tested was 3 x 3.7m = 11.1m.

In all cases, the final SPC-derived S/C position is within 8m of the true S/C position, but in only two cases is within 2m of the true S/C position. The actual distance from the true S/C position is not dependent on the initial perturbed position - for example in the 0.25 x sigma case, the SPC-derived S/C position (distance from truth: 1.6m to 6.9m) in most cases moves further away from the true S/C position than its initial position (distance from truth: 1.6m).

The final SPC-derived S/C positions appear to be clustered around an incorrect solution 2m-8m distant from the true S/C position.

== CompareOBJ RMS ==

The CompareOBJ RMS (for the final 5cm resolution 20m x 20m evaluation bigmap) does not appear to be affected by the magnitude of S/C position and pointing perturbation within the ranges tested.

{{attachment:CompareOBJ_RMS_resized.png}}

'''CompareOBJ Optimal Translations:'''
||'''Sub-Test'''||'''Perturbation Magnitude'''||||||'''Translation (cm)'''||
||F3G7||0.25 x sigma||85.0698||62.3596||-14.3765||
||F3G6||0.50 x sigma||84.5538||61.6624||-15.3434||
||F3G5||0.75 x sigma||95.8438||59.9313||-21.6901||
||F3G3||1.00 x sigma||106.4870||58.2162||-27.3527||
||F3G4||1.50 x sigma||79.1224||63.2865||-19.6432||
||F3G2||2.00 x sigma||110.1339||58.9454||-23.2403||
||F3G1||3.00 x sigma||93.5937||61.6997||-26.8422||

== Image Footprints ==

The first graph shows footprints for all Detailed Survey PolyCam pictures which were included in the model. The second graph shows the four pictures down-selected due to their coverage of the 20m x 20m evaluation region, and their almost complete containment within the iterated 100m x 100m region.

{{attachment:vertices_all_resized.png}}

{{attachment:vertices_eval_resized.png}}

== Distance SCOBJ(truth) to SCOBJ(solution) ==

The distance of the final SPC-derived S/C position from the true S/C position is plotted for the full Detailed Survey PolyCam image set for each magnitude of perturbation. The evaluation images are plotted in red.

3D graphs of final SPC-derived SCOBJ and true SCOBJ are then plotted for each picture. The first four are the down-selected evaluation pictures, the rest of the image set is included for comparison.

The pattern of final SPC-derived SCOBJ is broadly consistent across magnitudes of perturbation. The position correction is mostly a normal correction with lateral movement, bringing the modeled S/C position within an approx. 8m-radius sphere around the true position (or, in the case of perturbations<8m, pushing SCOBJ outwards up to 8m).

{{attachment:scobj_distance_resized.png}}

=== Evaluation Pictures ===

'''Example nominal SCOBJs:'''

{{attachment:P601293751G3_nominal_resized.png}}

''' Final solution SCOBJs:'''

{{attachment:P601293751G3_final_resized.png}}

{{attachment:P601372862G2_final_resized.png}}

{{attachment:P601372868G2_final_resized.png}}

{{attachment:P601372874G2_final_resized.png}}

=== Remaining Detailed Survey PolyCam Pictures ===

{{attachment:P601293196G2_final_resized.png}}

{{attachment:P601293757G3_final_resized.png}}

{{attachment:P601372298G3_final_resized.png}}

{{attachment:P601372304G3_final_resized.png}}

{{attachment:P601372310G3_final_resized.png}}

{{attachment:P601372316G3_final_resized.png}}

{{attachment:P601372856G2_final_resized.png}}

TestF3G - Results

Definitions

CompareOBJ RMS: The root mean square of the distance from each bigmap pixel/line location to the nearest facet of the truth OBJ.
PTG: The formal camera pointing uncertainty. SCOBJ: The S/C position vector from the center of the asteroid. VSO: The formal SCOBJ uncertainty.

S/C position and pointing uncertainties

The Detailed Survey PolyCam F3G data set had large S/C position and pointing uncertainties, unsuitable for Detailed Survey Baseball Diamond trajectories:

  • VSO = 1km;
  • PTG = 1mrad.

An additional suite of tests was therefore run with a duplicate Detailed Survey PolyCam dataset with S/C position and pointing uncertainties set to one-sigma:

  • VSO = 6.4m;
  • PTG = 0.217mrad.

Results for both data sets are presented herein.

Comments

The results show no significant difference in the final S/C position (SCOBJ) and model accuracy (as measured with CompareOBJ RMS) with respect to the magnitude of S/C position and pointing perturbation within the ranges tested, indicating that the SPC-driven modeling is immune to S/C position and pointing perturbation up to three standard deviations.

It should be noted that S/C position perturbation was divided equally between the SCOBJ components, resulting in a distance from the truth position which was a multiple of the standard deviation of 6.4m. Therefore:

  • maximum lateral perturbation was a multiple of 3.7m (6.4m/sqrt(3));
  • maximum normal perturbation (wrt body center) was 3.7m (6.4m/sqrt(3)).

It is assumed that the worst case scenario is a 3 x sigma (19.2m) lateral perturbation. The maximum possible lateral perturbation tested was 3 x 3.7m = 11.1m.

In all cases, the final SPC-derived S/C position is within 8m of the true S/C position, but in only two cases is within 2m of the true S/C position. The actual distance from the true S/C position is not dependent on the initial perturbed position - for example in the 0.25 x sigma case, the SPC-derived S/C position (distance from truth: 1.6m to 6.9m) in most cases moves further away from the true S/C position than its initial position (distance from truth: 1.6m).

The final SPC-derived S/C positions appear to be clustered around an incorrect solution 2m-8m distant from the true S/C position.

CompareOBJ RMS

The CompareOBJ RMS (for the final 5cm resolution 20m x 20m evaluation bigmap) does not appear to be affected by the magnitude of S/C position and pointing perturbation within the ranges tested.

CompareOBJ Optimal Translations:

Sub-Test

Perturbation Magnitude

Translation (cm)

F3G7

0.25 x sigma

85.0698

62.3596

-14.3765

F3G6

0.50 x sigma

84.5538

61.6624

-15.3434

F3G5

0.75 x sigma

95.8438

59.9313

-21.6901

F3G3

1.00 x sigma

106.4870

58.2162

-27.3527

F3G4

1.50 x sigma

79.1224

63.2865

-19.6432

F3G2

2.00 x sigma

110.1339

58.9454

-23.2403

F3G1

3.00 x sigma

93.5937

61.6997

-26.8422

Image Footprints

The first graph shows footprints for all Detailed Survey PolyCam pictures which were included in the model. The second graph shows the four pictures down-selected due to their coverage of the 20m x 20m evaluation region, and their almost complete containment within the iterated 100m x 100m region.

vertices_all_resized.png

vertices_eval_resized.png

Distance SCOBJ(truth) to SCOBJ(solution)

The distance of the final SPC-derived S/C position from the true S/C position is plotted for the full Detailed Survey PolyCam image set for each magnitude of perturbation. The evaluation images are plotted in red.

3D graphs of final SPC-derived SCOBJ and true SCOBJ are then plotted for each picture. The first four are the down-selected evaluation pictures, the rest of the image set is included for comparison.

The pattern of final SPC-derived SCOBJ is broadly consistent across magnitudes of perturbation. The position correction is mostly a normal correction with lateral movement, bringing the modeled S/C position within an approx. 8m-radius sphere around the true position (or, in the case of perturbations<8m, pushing SCOBJ outwards up to 8m).

Evaluation Pictures

Example nominal SCOBJs:

P601293751G3_nominal_resized.png

Final solution SCOBJs:

Remaining Detailed Survey PolyCam Pictures

TestF3G - Results (last edited 2016-05-05 09:47:57 by DianeLambert)