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.

Additional Tests

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.

Model shift

In the process of generating the 35cm Preliminary Shape Model a shift in the body center with respect to the inertial center occurred. The magnitude of the shift was approximately 2m. Since the final S/C position across F3G subtests lay in a region 2m to 8m from the true S/C position, the effect of the body center shift came into question. To investigate, an alternative 35cm Preliminary Shape Model with no body-center shift was generated. One subtest was re-run using the alternative start model.

Key Findings

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

Three CompareOBJ RMS values are presented for each subtest and each S/C position and camera pointing uncertainty:

• The largest CompareOBJ RMS (approx. 65cm across subtests) is obtained by running CompareOBJ on the untranslated and unrotated evaluation model.
• The second smallest CompareOBJ RMS (approx. 15cm across subtests) is obtained by running CompareOBJ with its optimal translation and rotation option.
• The smallest CompareOBJ RMS (approx. 9cm across subtests) is obtained by manually translating the evaluation model and searching for a local CompareOBJ RMS minimum.

The CompareOBJ optimal translation routine is not optimized for the evaluation model scale (5cm pix/line resolution). Manual translations of the bigmap were therefore conducted in an attempt to find a minimum CompareOBJ RMS. The manually translated evaluation models gave the smallest CompareOBJ RMSs.

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 RMSs differ slightly with S/C position and camera pointing uncertainties:

• approx. 5cm difference for CompareOBJ RMS without translation/rotation;
• approx. 2cm difference for CompareOBJ RMS with optimal translation and rotation;
• approx. 0.4cm difference for CompareOBJ RMS with manual translation.

CompareOBJ Optimal Translations:

CompareOBJ Manual Translations:

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.

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:

Final solution SCOBJs:

Remaining Detailed Survey PolyCam Pictures