Data Summary

Covariance Matrix

	RA_error	DEC_error	Roll_error
RA_error	1.071931529731781e-05	2.9585521218141e-08	0.0004044725690919465
DEC_error	2.9585521218141e-08	6.190014088584843e-06	-0.0001625924476595249
Roll_error	0.0004044725690919465	-0.0001625924476595249	75.43528880682577

We computed the covariance matrix by first calculating per‐image errors
(RA_error = RA_adv - RA_gen, DEC_error = DEC_adv - DEC_gen, Roll_error = Roll_adv - Roll_gen)
for every genuine–adversarial pair in master csv - attitude_errors_combined.csv. We then loaded these into a pandas DataFrame and ran errors.cov(), which uses the unbiased estimator Cov(X,Y) = Σᵢ (Xᵢ − X̄)(Yᵢ − Ȳ) / (N − 1) to produce the 3×3 covariance matrix (diagonal = variances, off-diagonals = covariances).

(Shapiro–Wilk is performed on up to 5k samples; p-values far below 0.05 indicate deviation from a perfect Gaussian.)

Metric	Count	Mean	Std Dev	Skewness	Kurtosis	Shapiro-W p
RA_error	300,000	~0.0000°	0.0033°	~0.15	~4.8	p ≪ 0.05
DEC_error	300,000	~0.0000°	0.0025°	~0.12	~4.6	p ≪ 0.05
Roll_error	10,000	~0.0137°	8.6820°	~0.05	~3.2	p ≪ 0.05

Star Tracker Adversarial Analysis Outputs

This folder contains the results of our adversarial-image generation and subsequent attitude-solution analysis. Below is a breakdown of each file, what it represents, and pointers on where to find the per-image deviations and summary statistics.

We ran the STT pipeline (Star Tracker Software) over: 300,000 adversarial images (all 10 000 originals × 6 attack types × 5 levels) and 10 000 genuine images (the matching subset used to generate those adversarials)

For our baseline (genuine) dataset we extracted Level-0 FITS frames from the SECCHI/HI-1A instrument on NASA’s STEREO-A spacecraft. In total we processed images collected during eight mission years — 2009, 2010, 2011, 2012, 2013, 2018, 2019, and 2020.

1. Raw STT Outputs

• genuine_attitude.csv

  • Columns:
    • filename — original genuine .fts file name
    • type — always "genuine"
    • RA_center, DEC_center, sig, Nr — match-candidate metrics from SExtractor
    • RA, DEC, Roll — attitude solution angles in degrees
  • Usage:
    • Baseline attitude solutions for genuine images.

• adversarial_attitude.csv

  • Columns: same as above, but type="adversarial" and filename includes attack and level suffix.
  • Usage:
    • Attitude solutions after each tampering attack.

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2. Per-Image Error Table

• attitude_errors_combined.csv
  • Columns:
    • filename_adv, type_adv, RA_center_adv, …, Roll_adv
    • base_name — original genuine filename
    • attack, level — tampering type & severity
    • filename_gen, type_gen, RA_center_gen, …, Roll_gen
    • RA_error, DEC_error, Roll_error — per-image deviations (adversarial minus genuine)
  • Usage:
    • Your primary per-image “deviation” table — each row shows exactly how much RA, DEC, and Roll shifted for a given adversarial file.

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3. Per-Attack/Level Breakdowns

• attitude_errors_<attack>_<level>.csv
  Example: attitude_errors_salt_pepper_moderate.csv
  • Subset of attitude_errors_combined.csv for one attack type & level.
  • Usage:
    • Quickly inspect or plot the error distribution for a single tampering scenario.

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4. Summary Statistics

• summary_stats.csv

  • Columns:
    • attack, level
    • RA_error_mean, DEC_error_mean, Roll_error_mean
    • RA_error_std, DEC_error_std, Roll_error_std
    • sig_gen_mean, sig_adv_mean, Nr_gen_mean, Nr_adv_mean
    • sig_gen_std, sig_adv_std, Nr_gen_std, Nr_adv_std
  • Usage:
    • Overall bias & precision of each tampering scenario.
    • Look at <axis>_error_std for the typical deviation per image.

• covariance_matrix.csv

  • 3×3 covariance of (RA_error, DEC_error, Roll_error).
  • Usage:
    • Understand how errors in different axes co-vary (off-diagonals) and their variances (diagonals).

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5. Visualizations

• distribution_plots/
  • Histograms & KDEs for each error metric, boxplots by attack type & level.

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“Per-image deviations” live in the three <axis>_error columns of attitude_errors_combined.csv.
Overall scenario‐level deviations (mean & std) are in summary_stats.csv.

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6. Dynamics / PID Simulation

pid_simulation.py loads the pointing-error tables and applies three PID controllers to emulate how STEREO‑A might respond. The script now includes a very simple dynamics model of the spacecraft. It uses the published spacecraft mass (~620 kg), approximate 1.1 m cube geometry, and heliocentric orbital period (~347 days) to propagate the attitude state. The output CSV (pid_corrections.csv by default) contains both the PID torques and the integrated attitude and orbit angle. If matplotlib is installed, the script also saves a plot called pid_corrections.png.

Example usage:

python3 pid_simulation.py --input attitude_errors_combined.csv --output pid_corrections.csv

This can help visualize how STEREO-A's orientation might be corrected over time when faced with the perturbations captured in this dataset.