Risk Metrics
Conjunction events are evaluated using multiple metrics to quantify collision risk under uncertainty. Measurement covariance grows with propagation, making layered risk assessments essential for robust Go / No Go decisions.
Time of Closest Approach (TCA)
- Definition: The instant when two RSOs reach minimum separation.
- Precision: Reported to millisecond accuracy, and essential for timely maneuver planning.
Miss Distance (MD)
- Relative separation at TCA, expressed as a vector in the RIC frame.
- Based on nominal trajectory estimates.
Measurement Covariance
- Position and velocity uncertainties from orbit determination are expressed as a 6x6 covariance matrix.
- Used to evaluate trajectory uncertainty and generate probability-based assessments.
Mahalanobis Distance
Calculates how far the nominal miss distance lies from the center of the uncertainty distribution:
d_M = sqrt(Δrᵀ · Σ⁻¹ · Δr)
Where:
- Δr is the miss distance vector
- Σ is the combined 3x3 covariance matrix
Higher values indicate that small deviations could significantly increase collision risk.
Tau Bounds
The Tau bounds metric represents the time interval around TCA during which the positional uncertainty volumes of two RSOs overlap the combined hard-body radius. This interval is derived by projecting relative motion and covariance into the encounter plane and applying a statistical confidence threshold to identify when collision risk is non-negligible.
Probability of Collision
Probability of collision (Pc) estimates the likelihood that two objects will collide by integrating the combined uncertainty over the collision volume defined by their hard-body volumes. Different methods are used depending on the event geometry and the available data.
Pc Methods
| Method | Description |
|---|---|
| Foster-1992 (2D) | Standard encounter plane assessment. Assumes Gaussian uncertainties, rectilinear motion, and no offset violations. |
| Hall (3D Nc) | Used when 2D assumptions break down. Required for precise Pc in high-curvature or low-relative velocity cases. |
| SDMC | Simplified-dynamics Monte Carlo using equinoctial sampling at TCA and two-body Keplerian dynamics |
| Frisbee (Max Pc) | Conservative estimate used when only one object's covariance is available, or the Pc is in the dilution region. |
The Frisbee method estimates an upper bound by assuming a worst-case relative geometry when full covariance data is not available.
Pc Enhancement
Satcat computes the following Event risk mtrics when a close approach event is detected:
- Compute TCA and nominal MD
- Validate and remediate NPD covariance
- Compute Mahalanobis distance
- Identify best HBR and update CDM if needed
- Determine Pc method:
- Use Foster-1992 when 2D geometry assumptions are satisfied
- Escalate to 3D Nc [Hall] when the 2D assumptions are violated
- Apply SDMC when the 3D Nc method fails to converge or reports an extended violation
- Use Frisbee Max Pc estimate if only partial covariance is available
- Flag dilution and report the Max Pc where applicable
- Recalculate metrics as new data are ingested
Pc Dilution
In certain high-uncertainty conjunctions, nominal probability of collision (Pc) values may underrepresent the actual risk. These dilution region events arise when one or both object covariances are large enough to suppress computed Pc, despite close geometry. Satcat detects these events and reports an additional metric, Maximum Pc, computed by scaling covariance to estimate the worst-case likelihood. Satcat services detect dilution scenarios and surface conservative Max Pc as a fallback.
Hard Body Radius (HBR)
Collision probability estimates across Satcat depend heavily on the HBR values used for the primary and secondary RSOs. Satcat pulls from these authoritative data sources to identify the best HBR values for each object:
- Satcat Operators: Manually specified values from RSO O/Os
- NASA CARA: Values provided by NASA's Conjunction Assessment Risk Analysis group
- Satcat DB: Values from Satcat's internal database
- From CDM: Uses the HBR specified in the associated Conjunction Data Message
- Fallback Space-Track
OBJECT_TYPElogic (ex: 5 m for Payloads)
The selected HBR directly impacts computed collision probabilities and should be reviewed carefully, especially when validating risk thresholds for operational decision-making. HBR source information is provided in Event page details and selectable in Maneuver Designer projects.