{
  "title": "Synthetic known-correspondence attitude and relative magnitude",
  "status": "Seeded numerical illustration; no star recognition or hardware test",
  "seed": 20260927,
  "rows": {
    "directions": 6,
    "trials": 300,
    "summary": 3,
    "magnitudes": 303
  },
  "rotation_inertial_to_camera": [
    [
      0.9887692138764507,
      -0.12622970501588374,
      -0.08000939483428614
    ],
    [
      0.12140559376013015,
      0.9906300093553531,
      -0.06255290855238521
    ],
    [
      0.08715574274765817,
      0.05213680212878224,
      0.994829447880333
    ]
  ],
  "parameters": {
    "focal_length_px": 800,
    "image_size_px": [
      1280,
      960
    ],
    "principal_point_px": [
      640,
      480
    ],
    "pixel_y_convention": "upward",
    "centroid_noise_sd_px": [
      0,
      0.1,
      1
    ],
    "trials_each": 100,
    "extinction_mag": [
      0,
      1,
      2
    ]
  },
  "fit": "Equal-weight Wahba orthogonal Procrustes: H=sum(b*s^T), U,S,Vt=svd(H), R=U diag(1,1,det(UVt)) Vt",
  "checks": {
    "all_pass": true,
    "unit_vector_pair_dot_invariance": true,
    "zero_noise_rotation_recovery": true,
    "identity_rotation": true,
    "joint_permutation_invariance": true,
    "wrong_correspondence_detectably_wrong": true,
    "one_vector_and_collinear_no_attitude": true,
    "magnitude_inverse_and_extinction": true
  },
  "limits": [
    "Six synthetic directions have known correct labels. No catalogue search, source detection, recognition success rate or geographic position is estimated.",
    "Gaussian pixel centroid errors are independent; focal length, distortion and principal point are exact. Conditional error distributions are not camera certification.",
    "One direction or collinear repeated directions cannot determine full attitude; near-parallel geometry can also be ill-conditioned.",
    "Magnitude uses positive flux in the same photometric band/system; zero or negative flux has no ordinary logarithmic magnitude.",
    "Extinction is assigned per band. No distance, intrinsic luminosity, universal photometric zero point or signal-to-noise magnitude uncertainty is inferred."
  ]
}