Conjunction Assessment

Pro

Conjunction assessment, screening, avoidance trade studies, and CDM export are all Pro features requiring the IO.Astrodynamics.Pro package.

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

Conjunction assessment requires position and velocity covariance on both the protected (primary) and secondary objects. Covariance is attached to the initial StateVector as a 6x6 matrix.

// 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 propagates both objects and returns the closest-approach encounter.

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 any additional screening configuration (e.g., custom covariance scaling).

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
MinCollisionProbability	Lower bound on collision probability
MaxResults	Maximum number of encounters to return

Results are ranked by collision probability (highest first).

Reusing propagated trajectories

If you have already propagated the protected spacecraft (e.g., from a previous analysis), pass the pre-computed trajectory to avoid redundant propagation:

// Propagate once
var protectedProfile = new ProtectedSpacecraftProfile(protectedSpacecraft);

// Reuse for multiple secondaries
var enc1 = ConjunctionAssessment.Analyze(protectedProfile, secondary1, window);
var enc2 = ConjunctionAssessment.Analyze(protectedProfile, secondary2, window);

The profile caches the propagated trajectory after the first call.

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)
{
    Console.WriteLine($"Lead={opt.LeadTime.TotalHours:F0}h, " +
                      $"DV={opt.DeltaV:F3} m/s => " +
                      $"Miss={opt.ResultingMissDistance:F0} m, " +
                      $"Pc={opt.ResultingProbability: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}");

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: computed using the single-covariance maximum probability method

Best practices and quality flags

Covariance quality

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

• Covariance realism: Diagonal-only covariance underestimates probability. Use full 6x6 matrices from orbit determination when available.
• Covariance age: Covariance propagated far from the last observation epoch becomes unreliable. Prefer recent OD solutions.
• 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.