Measurement Uncertainty

CTS projects each detection's footpoint from image pixels into the shared floor-plan frame with a camera homography. The detector's pixel error is roughly circular in the image, but the homography can stretch that error unevenly on the floor. Oblique or far views therefore produce an elongated floor-plane error ellipse.

The per-observation model is:

R_obs = J * Sigma_px * J^T + R_cal + epsilon * I

Where:

• R_obs is the full single-camera measurement covariance in floor-plan m².
• J is the analytic homography Jacobian at the bbox bottom-centre footpoint, in m/px.
• Sigma_px is detector footpoint covariance in px².
• R_cal = (k_cal * floor_residual_m)² * I is the systematic calibration term in m².
• epsilon * I is a small numeric floor that keeps R_obs invertible.

Footpoint reliability controls the scale of Sigma_px. A bounding box clipped against the bottom or sides of the image means the bottom-centre point is probably the image boundary, not the person's floor contact point. If pose is available and both ankles have low visibility, the feet are likely occluded. CTS keeps those observations but marks footpoint_reliable=False, which steeply inflates the pixel covariance before applying J.

The random term has the expected units:

(m/px) * px² * (m/px) = m²

The calibration term is kept separate because it is systematic. Cross-camera fusion can shrink the random term with more independent camera observations, but it must not fuse away a fixed camera calibration bias. See Multi-Camera Fusion for how the random/systematic split is applied during fusion.

Trajectory persistence keeps the uncertainty audit trail with each person_trajectories row: position_sigma_m stores the PH position covariance summary, primary_camera_id records the stabilized best-view camera, contributing_camera_count records how many camera observations fed the point for that frame, and footpoint_reliable records the representative observation's footpoint reliability.

Image pixels                         Floor-plan metres

    bbox
  +------+
  |      |
  |      |
  +--x---+  footpoint_px                camera
      \                                  o
       \                                  \
        \ homography                       \ viewing ray
         \                                  \
          v                                  \        major axis
     circular Sigma_px                        \      .--------.
          (px^2)                               \    /          \
                                                \   \          /
                                                 \   '--------'
                                                  x footpoint_m

                                             elongated R_obs ellipse (m^2)

Code references

Concern	Code
Jacobian, Sigma_px, R model	tracking-orchestrator/app/tracking/world/observation_model.py
Covariance through the homography	tracking-orchestrator/app/tracking/floor_projector.py (project_with_covariance)

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