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Pc Dilution

In a high-uncertainty conjunction, the nominal probability of collision (Pc) can understate the actual risk. Satcat identifies these conjunctions and reports Maximum Pc alongside the nominal value.

The Dilution Region​

Pc Dilution describes a region in conjunction assessment where nominal Pc values decrease as covariance size increases despite geometric proximity suggesting high probability of collision risk.

  • A Dilution region arises when the orbital covariance grows large relative to the nominal miss vector magnitude. In this zone, increasing covariance initially increases Pc up to a peak, then reduces it as the probability density spreads beyond the conjunction sphere.
  • The Maximum Pc construct applies scaled-down covariance (preserving aspect ratio and nominal miss distance) to compute the largest possible Pc under assumed additional tracking data. Max Pc is reached by iteratively shrinking covariance until Pc peaks.

Recognizing Dilution​

  • Nominal Pc stays low even when the miss distance is small or the geometry looks convergent.
  • Mahalanobis distance is low, meaning the state means are close, while the combined uncertainty volumes are large. That mismatch is the signal.

How Satcat Marks It​

Satcat flags conjunctions whose Pc falls in the dilution region as Diluted, and reports Max Pc alongside nominal Pc.

Operational Context​

Max Pc is an upper bound: the largest Pc the conjunction could produce under any scaling of the covariance, holding the nominal miss vector fixed. Two conclusions follow.

  • If Max Pc exceeds the remediation risk threshold (e.g. 1e-4), the conjunction is genuinely serious and worth remediating. The maneuver required may need to be larger than usual, because the uncertainties are large.
  • If Max Pc is below the remediation risk threshold, the conjunction does not require remediation unless updated tracking data prompts reevaluation.

Large covariances can also be reduced directly, by uploading a refined ephemeris or by requesting Sensor Tasking. Tasking is particularly useful for poorly tracked secondaries.

Further Reading​

The paper below assesses two proposed approaches to the dilution region. Satcat implements the Max Pc approach.