Conjunction Assessment

This tutorial walks through the full space situational awareness (SSA) workflow: setting up spacecraft with covariance, analyzing conjunctions, screening catalogs, evaluating avoidance maneuvers, and exporting CCSDS-compliant Conjunction Data Messages.

Setting up spacecraft with covariance

Collision probability needs a position and velocity covariance on the protected (primary) and secondary objects. Covariance is attached to the initial StateVector as a 6x6 matrix.

Covariance is not propagated to TCA

The covariance used at the time of closest approach (TCA) is resolved in this order, for each participant:

1. the covariance carried by the participant's state at TCA, when there is one (age zero). The ILocalizable and PropagationSolution entry points sample states without covariance, so in practice this applies to hand-built states only;
2. otherwise the covariance of the participant's initial StateVector, held fixed in the RTN frame: rotated into RTN with the initial state, then back into the inertial frame with the state at TCA. It is not propagated. Its age, the time between its epoch and TCA, is reported in EncounterState.ProtectedCovarianceAge / SecondaryCovarianceAge, and EncounterQualityFlags.StaleCovarianceUsed is raised when it exceeds ConjunctionAnalysisOptions.StaleCovarianceThreshold (60 s by default);
3. otherwise no covariance: MissingProtectedCovariance or MissingSecondaryCovariance, and CovarianceUnavailable when both are missing.

Holding the covariance in RTN keeps its shape relative to the orbit (large along-track, small radial), but its size does not grow with time as a propagated covariance would. Keep the initial epoch close to the TCA, or supply covariances from a recent orbit determination.

// Build a 6x6 covariance matrix (diagonal for simplicity)
var protectedCov = new Matrix(6, 6);
protectedCov.Set(0, 0, 25.0);   // sigma_x^2  (m^2)
protectedCov.Set(1, 1, 25.0);   // sigma_y^2
protectedCov.Set(2, 2, 25.0);   // sigma_z^2
protectedCov.Set(3, 3, 0.01);   // sigma_vx^2 (m^2/s^2)
protectedCov.Set(4, 4, 0.01);   // sigma_vy^2
protectedCov.Set(5, 5, 0.01);   // sigma_vz^2

var protectedState = new StateVector(
    new Vector3(6800000.0, 0.0, 0.0),
    new Vector3(0.0, 7656.2204182967143, 0.0),
    earth, epoch, Frame.ICRF, protectedCov);

var protectedSpacecraft = new Spacecraft(
    -1001, "Protected", 120.0, 150.0,
    new Clock("Protected_CLK", 256), protectedState,
    hardBodyRadius: 8.0);

The hardBodyRadius parameter sets the physical keep-out sphere around the object and is used in miss-distance calculations and collision probability.

Set up the secondary object the same way:

var secondaryCov = new Matrix(6, 6);
secondaryCov.Set(0, 0, 50.0);
secondaryCov.Set(1, 1, 50.0);
secondaryCov.Set(2, 2, 50.0);
secondaryCov.Set(3, 3, 0.02);
secondaryCov.Set(4, 4, 0.02);
secondaryCov.Set(5, 5, 0.02);

var secondaryState = new StateVector(
    new Vector3(6800500.0, 100.0, 50.0),
    new Vector3(-50.0, 7656.0, 10.0),
    earth, epoch, Frame.ICRF, secondaryCov);

var secondarySpacecraft = new Spacecraft(
    -2001, "Secondary", 80.0, 100.0,
    new Clock("Secondary_CLK", 256), secondaryState,
    hardBodyRadius: 3.0);

Basic conjunction analysis

The simplest analysis evaluates a single protected-vs-secondary pair over a time window. ConjunctionAssessment.Analyze samples both objects' ephemerides and returns the closest-approach encounter. For a spacecraft that has not been propagated, its ephemeris is the initial orbit extrapolated on a Keplerian orbit (SGP4 for a TLE); propagate it first, or use the PropagationSolution overloads, for a high-fidelity trajectory.

var encounter = ConjunctionAssessment.Analyze(
    new ProtectedSpacecraftProfile(protectedSpacecraft),
    secondarySpacecraft,
    new Window(epoch, epoch.AddMinutes(10.0)));

Console.WriteLine($"TCA:            {encounter.EncounterState.Epoch}");
Console.WriteLine($"Miss distance:  {encounter.EncounterState.MissDistanceMeters:F1} m");
Console.WriteLine($"Probability:    {encounter.CollisionRisk.ProbabilityOfCollision:E3}");
Console.WriteLine($"Relative speed: {encounter.EncounterState.RelativeState.RelativeVelocityInertial.Magnitude():F1} m/s");

The ProtectedSpacecraftProfile wraps the protected spacecraft with the maneuver constraints used by avoidance studies (ManeuverConstraints).

Analyzing all encounters

When objects have multiple close approaches in the window, use AnalyzeAll to return every encounter rather than just the closest:

var allEncounters = ConjunctionAssessment.AnalyzeAll(
    new ProtectedSpacecraftProfile(protectedSpacecraft),
    secondarySpacecraft,
    new Window(epoch, epoch.AddHours(24.0)));

foreach (var enc in allEncounters)
{
    Console.WriteLine($"TCA: {enc.EncounterState.Epoch}, Miss: {enc.EncounterState.MissDistanceMeters:F1} m, " +
                      $"Pc: {enc.CollisionRisk.ProbabilityOfCollision:E3}");
}

Ranked screening

For operational SSA, you typically screen one protected asset against many secondary objects. Screen evaluates all pairs, filters by distance or probability thresholds, and returns a ranked list.

var encounters = ConjunctionAssessment.Screen(
    new ProtectedSpacecraftProfile(protectedSpacecraft),
    new ILocalizable[] { secondary1, secondary2, secondary3 },
    window,
    new ScreeningOptions
    {
        MaxMissDistanceMeters = 10000.0,
        MaxResults = 20
    });

foreach (var enc in encounters)
{
    Console.WriteLine($"{enc.SecondaryObject.Name}: " +
                      $"Miss={enc.EncounterState.MissDistanceMeters:F1} m, " +
                      $"Pc={enc.CollisionRisk.ProbabilityOfCollision:E3}");
}

ScreeningOptions supports filtering by:

Property	Description
MaxMissDistanceMeters	Upper bound on miss distance
MaxResults	Maximum number of encounters to return

Results are ranked by collision probability (highest first), then by miss distance.

Reusing propagated trajectories

If you have already propagated both trajectories, pass the PropagationSolution objects to reuse their dense output instead of sampling the participants' ephemerides:

var protectedTrajectory = protectedSpacecraft.Propagate(window, perturbingBodies, false, false, step);
var secondaryTrajectory = secondarySpacecraft.Propagate(window, perturbingBodies, false, false, step);

var encounter = ConjunctionAssessment.Analyze(
    new ProtectedSpacecraftProfile(protectedSpacecraft), protectedTrajectory,
    secondarySpacecraft, secondaryTrajectory,
    window);

The profile itself caches nothing: each call samples the trajectories it is given.

Avoidance trade study

Once a conjunction is identified, EvaluateAvoidance generates a matrix of avoidance options by varying lead time and delta-v magnitude. Each option shows the resulting miss distance and collision probability after the maneuver.

var options = ConjunctionAssessment.EvaluateAvoidance(
    encounter,
    new AvoidanceSearchOptions
    {
        LeadTimes = new[]
        {
            TimeSpan.FromHours(1),
            TimeSpan.FromHours(3),
            TimeSpan.FromHours(6)
        },
        DeltaVMagnitudesMetersPerSecond = new[] { 0.05, 0.10, 0.25 }
    });

foreach (var opt in options)
{
    var after = opt.PostManeuverEncounter;
    Console.WriteLine($"Burn at {opt.BurnEpoch}, " +
                      $"DV={opt.DeltaVInertial.Magnitude():F3} m/s => " +
                      $"Miss={after.EncounterState.MissDistanceMeters:F0} m, " +
                      $"Pc={after.CollisionRisk.ProbabilityOfCollision:E3}");
}

The trade study helps operators select the minimum delta-v that achieves an acceptable miss distance within operational lead-time constraints.

CDM export and validation

Export any encounter as a CCSDS Conjunction Data Message (CDM) for sharing with conjunction assessment providers or archival.

Exporting a CDM

var cdm = encounter.ToCdm(new CdmExportOptions
{
    Originator = "MyOpsCenter",
    MessageId = "CDM-001"
});

// Write to XML file
cdm.WriteToFile("encounter.cdm.xml");

Validating a CDM

Validate any CDM file against the CCSDS schema:

var validation = Cdm.ValidateSchema("encounter.cdm.xml");

if (validation.IsValid)
    Console.WriteLine("CDM is schema-valid.");
else
    foreach (var error in validation.Errors)
        Console.WriteLine($"Validation error: {error.Message}");

CDM fields

The exported CDM includes:

• Header: message ID, creation date, originator
• Relative metadata: TCA, miss distance, reference frame
• Object 1 / Object 2: state vectors, covariance (RTN frame), physical properties (mass, area, drag/SRP coefficients)
• Collision probability: the Pc of the encounter, with COLLISION_PROBABILITY_METHOD set to FOSTER-2D. Export requires a covariance for both participants, so the single-covariance maximum Pc is never exported; CdmExportOptions.CollisionProbabilityMethod overrides the method name
• Covariance age: when a participant's covariance comes from its initial state, a comment gives its age at TCA. An encounter flagged StaleCovarianceUsed is refused unless CdmExportOptions.AllowStaleCovariance is set

Best practices and quality flags

Covariance quality

The accuracy of collision probability depends heavily on covariance quality. Watch for these indicators:

• Covariance realism: A diagonal covariance ignores the correlations between axes. Depending on the geometry, that can raise or lower the probability, so neither direction is a safe bound. Use full 6x6 matrices from orbit determination when available.
• Covariance age: The library does not propagate covariance: it holds the initial covariance fixed in RTN up to TCA, so its size does not grow with time. Check EncounterState.ProtectedCovarianceAge and SecondaryCovarianceAge, and prefer covariances from a recent orbit determination.
• Hard-body radius: Setting this too large inflates probability artificially. Use realistic physical dimensions.

Screening thresholds

• Start with a generous miss-distance threshold (e.g., 10 km) and tighten based on operational experience.
• For LEO, relative speeds are typically 7--15 km/s; for GEO, under 1 km/s. Adjust screening windows accordingly.

Avoidance decisions

• Prefer maneuvers with the longest feasible lead time --- they require less delta-v for the same miss-distance improvement.
• Always re-screen after a planned avoidance maneuver to verify the new trajectory does not introduce secondary conjunctions.

Recommended workflow

A typical operational SSA workflow proceeds as follows:

1. Ingest updated orbital data (state vectors + covariance) for your protected asset and the catalog of tracked objects.

2. Screen the protected asset against the catalog:

   var encounters = ConjunctionAssessment.Screen(
       profile, catalog, window, screeningOptions);
   

3. Triage the ranked results. Focus on encounters exceeding your probability threshold (e.g., Pc > 1e-5).

4. Analyze high-priority encounters in detail:

   var details = ConjunctionAssessment.Analyze(
       profile, highPrioritySecondary, refinedWindow);
   

5. Evaluate avoidance if the risk is unacceptable:

   var trades = ConjunctionAssessment.EvaluateAvoidance(
       details, avoidanceOptions);
   

6. Export CDM for coordination with partner agencies:

   var cdm = details.ToCdm(exportOptions);
   cdm.WriteToFile("cdm_report.xml");
   

7. Execute the chosen avoidance maneuver and return to step 2 to verify the post-maneuver trajectory is clear.

Summary

• Use Analyze for single-pair assessment and Screen for catalog-wide screening.
• AnalyzeAll returns every encounter in the window, not just the closest.
• EvaluateAvoidance produces a lead-time/delta-v trade matrix.
• Export encounters as CCSDS CDMs with ToCdm and validate with Cdm.ValidateSchema.
• Covariance quality is the single most important factor in collision probability accuracy.