TestF3G - Navigation Error Sensitivity Test Results

Definitions

Additional Tests

S/C Position and Camera 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 Center-of-Body Shift

In the process of generating the 35cm Preliminary Shape Model, a shift in the body center with respect to the inertial center was applied. 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

CompareOBJ RMSs (with and without translation/rotation) show no trend with the magnitude of S/C position and camera pointing perturbation within the perturbation ranges tested. The correlation score also does not vary with the magnitude of S/C position and camera pointing perturbation and is approx. 0.76 giving a very good indication of correlation. The accuracy of the evaluation model is therefore invariant to the S/C position or camera pointing perturbation up to three standard deviations.

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

With the large S/C position and camera pointing uncertainties, the final SPC-derived S/C position is within 8m of the true S/C position, and in two cases is within 2m of the true S/C position. With the reduced (1 sigma) S/C position and camera pointing uncertainties, all the final SPC-derived S/C positions are within 2m of the true S/C position. The distance between the final S/C position and the true S/C position is not dependent on the initial perturbed S/C position - indeed, in the 0.25 x sigma case, the SPC-derived S/C position in most cases moves further away from the true S/C position (final distance from truth: 1.6m to 6.9m) than its initial position (initial distance from truth: 1.6m).

The final SPC-derived S/C positions appear to be clustered around an incorrect solution 2m distant from the true S/C position (in the VSO=1sigma tests). This distance appears to correspond with a shift in the center-of-body which was applied during the generation of the 35cm Preliminary Survey Start Model. However, this finding persisted when a subtest was re-run with a 35cm Preliminary Survey Start Model which had not had a shift applied to the center-of-body. Measures of both model accuracy and S/C position did not vary with center-of-body shift.

Important Notes

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 a multiple of 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.

Results and Discussion

CompareOBJ RMS

Three CompareOBJ RMS values for the final 5cm resolution 20m x 20m evaluation bigmap 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.

CompareOBJ RMSs do not show a trend with 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, with smaller RMS values corresponding with lower 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:

Cross Correlation Scores

The evaluation maps were compared with a truth map via a cross-correlation routine which derives a correlation score. As a guide the following scores show perfect and excellent correlations:

• A map cross-correlated with itself will give a correlation score of approx. 1.0;
• Different sized maps sampled from the same truth (for example a 1,100 x 1,100 5cm sample map and a 1,000 x 1,000 5cm sample map) give a correlation score of approx. 0.8.

The correlation scores show no trend with S/C position and camera pointing perturbation in the perturbation-range tested. The correlation scores also do not differ with S/C position and camera pointing uncertainties. The correlation score across subtests is approx. 0.76 giving a very good indication of correlation.

Correlation Scores:

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 evaluation Detailed Survey PolyCam image set for each magnitude of perturbation. The distance of the final SCOBJ from the true S/C position is invariant with the perturbation to the initial SCOBJ within the perturbation-range tested. The variance in distances across pictures does vary with S/C position uncertainty however, with:

• distances ranging from approx. 1m to 8m with VSO=1km;
• distances ranging from approx. 1m to 2m with VSO=6.4m (1 sigma).

SCOBJ

3D graphs of final SPC-derived SCOBJ and true SCOBJ are plotted for each evaluation picture.

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. 2m to 8m of the true S/C position. Note that the SCOBJs form a cluster which is offset from the truth indicating that the model is converging to a solution different to the truth.

Evaluation Pictures

Example nominal SCOBJs:

Final solution SCOBJs:

SCOBJ without center-of-body shift

3D graphs of final SPC-derived SCOBJ and true SCOBJ are re-plotted for each evaluation picture, now including the single result from the additional subtest conducted from a 35cm Preliminary Survey Start Model with no center-of-body shift. The graphs show that the final SCOBJ is not affected by center-of-body shift up to 2m. This result also dispels the notion that the distance of the final SCOBJs from truth is connected to the center-of-body shift.