Assessing the Threat of a Collision Using the Advanced CAT Tool

STK Premium (Space) or STK Enterprise
You can obtain the necessary licenses for this tutorial by contacting AGI Support at support@agi.com or 1-800-924-7244.

The results of the tutorial may vary depending on the user settings and data enabled (online operations, terrain server, dynamic Earth data, etc.). It is acceptable to have different results.

Capabilities covered

This lesson covers the following STK Capabilities:

  • STK Pro
  • STK SatPro

Problem statement

Two satellites are in close proximity of each other. You need to determine two things:

  • the distance between the objects at the time of closest approach, based on a fixed threat volume and object location
  • the probability of collision

You also want to determine if the conjunction's relative motion appears linear or nonlinear. Covariance data is available.

Solution

Use STK's Conjunction Analysis capability to carry out a close-approach analysis for the satellites. You'll also perform a close approach analysis between the primary object (your satellite) and the secondary object (the satellite presenting a risk of collision), with reference to a threshold. The threshold is a minimum acceptable distance between the ellipsoidal threat volumes of the objects and the range between the objects. Then, you'll apply covariance data to the analysis. The first analysis is linear and the second is nonlinear.

What you will learn

Upon completion of this tutorial, you will understand how to:

  • Use the High-Precision Orbit Propagator (HPOP)
  • Use the Conjunction Analysis capability
  • Use the Nonlinear Probability Tool
  • Create custom reports using the Report & Graph Manager

Video guidance

Watch the following video. Then follow the steps below, which incorporate the systems and missions you work on (sample inputs provided).

Create a new scenario

Create a new scenario.

  1. Launch STK ().
  2. Click the Create a Scenario () button.
  3. Enter the following in the STK: New Scenario Wizard:
    4. Option Value
    Name Conjunction_Analysis
    Start 1 Jun 2019 16:00:00.000 UTCG
    Stop 4 Jun 2019 16:00:00.000 UTCG
  4. Click OK.
  5. When the scenario loads, click Save (). A folder with the same name as your scenario is created for you.
  6. In the Save As window, verify the scenario name and location and click Save.

Save often!

Removing unneeded windows

The Timeline View and the 2D Graphics window are not required for this scenario, so you can remove them from your workspace.

  1. Close the Timeline View.
  2. Close the 2D Graphics window.

Creating satellites

Two satellites are required in the analysis. One satellite, Primary, is prebuilt and saved as an ephemeris file. The data in the ephemeris file also contains covariance data.

An ephemeris file is an ASCII text file formatted for compatibility with STK that ends in a *.e extension. You can generate an STK *.e file with the High-precision Orbital Propagator (HPOP) using a frame defined by a Conjunction Data Message (CDM). The CDM specification allows many possible frames, but having all the data in *.e files where the frame is specified in the metadata allows for the appropriate comparisons.

If you have your ephemerides converted to *.e files (regardless of the frame), STK will handle all the conversions internally for whatever analysis it needs to perform. The bottom line is that STK needs *.e files, manually entered satellite properties, or Two Line Element (TLE) sets to run CAT, and any frame is acceptable.

Creating a primary satellite

Primary is your satellite. The satellite was built using the HPOP and was saved as an ephemeris file.

  1. Using the Insert STK Objects tool, insert a Satellite () object using the Insert Default () method.
  2. In the Object Browser, rename the Satellite () object "Primary."
  3. Open Primary's () properties ().
  4. On the Basic - Orbit page, change the Propagator to StkExternal.
  5. Click the Filename ellipsis () button.
  6. When the Select Ephemeris File window opens, browse to the location of the ephemeris file, typically <Install Dir>\Data\Resources\stktraining\text.
  7. Select Primary.e.
  8. Click Open.
  9. Click OK.

Viewing Primary

  1. Bring the 3D Graphics window to the front.
  2. In the Object Browser, right-click Primary ().
  3. Select Zoom To.

Primary Satellite

Creating a secondary satellite

After propagating Primary, you can now manually build the second satellite. There are various ways to enter data for the satellite. For this scenario, you will manually enter orbit coordinates and transfer covariance data using a Connect command. The Connect command is entered using the API Demo Utility, but the covariance data could be sent from outside of STK using other means (e.g., Excel, Script, etc.). If you don't want to enter this data, a second ephemeris is available for the secondary satellite.

Build Secondary using orbital parameters obtained from a source, such as a CDM.

If you don't want to manually insert Secondary, skip this section and start at Insert the Secondary Satellite Using an Ephemeris. However, this section contains important information that STK users should read.

  1. Using the Insert STK Objects tool, insert a Satellite () object using the Insert Default () method.
  2. In the Object Browser, rename the Satellite () object "Secondary."
  3. Open Secondary's () properties ().

Setting up the High-precision Orbit Propagator

The High-precision Orbit Propagator (HPOP) uses numerical integration of the differential equations of motions to generate ephemeris. HPOP can handle the following orbit types:

  • circular
  • elliptical
  • parabolic
  • hyperbolic

around any central body and at distance ranges from the lower atmosphere of the Earth, to the Moon, and beyond.

  1. On the Basic - Orbit page, change the Propagator to HPOP.

    2. When entering the following data, it would be a good idea to copy and paste the Cartesian Coordinates from this tutorial into STK.

  2. Set the following:
    3. Option Value
    Step Size 6 sec
    Coord Type Cartesian
    X -7669168.8042875 m
    Y -7859650.1453306 m
    Z -23040324.781931 m
    X Velocity 2232.2151237860 m/sec
    Y Velocity -3239.6197689674 m/sec
    Z Velocity 358.11070444968 m/sec
  3. Click Apply.

Force models

You can use Force models to define a precise representation of a satellite's force environment for use in HPOP analysis. The focus of this tutorial is Advanced CAT, but you'll make some changes to the force models to align them with the models used to generate ephemeris for the primary satellite.

  1. Click Force Models... on the Basic - Orbit properties page.
  2. When the Force Model Properties window opens, ensure the Gravity tab is selected and set the following Central Body Gravity values:
    3. Option Value
    Gravity File WGS84_EGM96.grv
    Maximum Degree 0
    Maximum Order 0
  3. Clear the Truncate to Gravity Field Size check box in the Solid Tides field.
  4. Clear the Use check boxes for Sun and Moon in the Third Body Gravity field.
  5. Select the Drag tab.
  6. Disable the Use Drag option.
  7. Select the SRP tab.
  8. Clear the Use SRP check box.
  9. Click OK to close the Force Model Properties window.

Propagating covariance

HPOP is capable of propagating the state error covariance matrix as it is propagating ephemeris. The state error covariance matrix represents the uncertainty in the vehicle's position and velocity. You can then have STK report and graph the vehicle's position covariance submatrix and display it in the 3D Graphics window over time.

State error covariance growth is usually dominated by the initial position and velocity covariance, which is typically generated by orbit determination software. Any errors between the estimated state and the actual state tend to grow over time, especially in the along-velocity direction. This is a direct effect of the dominant two-body force, since the period of the orbital motion is on its initial state. Eccentric orbits also show a oscillation in uncertainty superposing the growth trend, which has a larger amplitude for larger eccentricity. Uncertainty increases near perigee, where the speed of the vehicle is largest in its orbital cycle. Uncertainty will actually decrease near apogee, where the speed is the smallest.

A second contributor to state error covariance growth is force model mismodeling. The force model environment modeled by the software, chosen by you to best represent the force environment, does not precisely model the actual forces experienced by the vehicle. In orbit determination software that uses Kalman or related filters, force model mismodeling contributes to covariance growth through process noise models that aim to characterize the uncertainty of the modeling itself. Because HPOP does not have all the data needed to do this sophisticated analysis, it uses a simpler scheme to account for some force model mismodeling called "consider analysis."

A consider analysis adds contributions of force model mismodeling to the state error covariance propagation by treating constant parameters in the force model as being instead uncertain themselves. The uncertainty in the parameter value leads to uncertainty in the force evaluation, which then contributes to the state error covariance.

In the absence of an external ephemeris file, the HPOP propagator is used to propagate satellite position, velocity, and associated covariances. The Covariance page enables you to enter your initial state error covariance matrix. Because the matrix is symmetric, you only need to enter the lower triangle.

Cartesian covariance units are m2, m2/s, m2/s2.

  1. Click Covariance... on the Basic - Orbit properties page.

    2. Default Cartesian Covariance Units

    You could manually enter the Cartesian covariance units from the CDM. To save time, you'll use a preconstructed Connect command to enter the data.

  2. Click Cancel to close the HPOP Covariance window.
  3. Click OK to close Secondary's () properties ().

Using the HPOP Covariance command

The HPOP Covariance command enables you to enter an initial state error covariance matrix. In this instance, set the position velocity (PosVel) parameters.

To enter the Connect command, use the API Demo Utility.

  1. In the View menu, open the Web Browser.
  2. When the Web Browser window opens, look at the top of the window and click the Browse () button.
  3. When the Open window appears, go to the following filepath: Windows (C:) > ProgramFiles > AGI > STK 12 > Data > HtmlUtilities > STK Automation > API Demo.
  4. Select API Demo Utility.htm.
  5. Click Open.
  6. Enter the 21 values representing the lower triangle of the 6x6 position velocity submatrix. Copy and paste the completed HPOP Connect command into the API Demo Utility Code Sandbox. You could type the parameters in if needed.

    7. Syntax: PosVel <xx> <yx> <yy> <zx> <zy> <zz> <Vxx> <Vxy> <Vxz> <VxVx> <Vyx> <Vyy> <Vyz> <VyVx> <VyVy> <Vzx> <Vzy> <Vzz> <VzVx> <VzVy> <VzVz>

    hpop */Satellite/Secondary Covariance PosVel 0.55964154920517E-01 -0.23168820659027E-01 0.73624971281146E-01 0.25611038576040E-02 -0.37169368664612E-02 0.40410873798337E-01 0 0 0 0.10000000000000E-07 0 0 0 0.70962140501337E-24 0.10000000000000E-07 0 0 0 0.35340968553901E-25 -0.24799262505252E-24 0.10000000000000E-07
  7. Click Run Code.
  8. Close the API Demo Utility.

Enabling covariance

  1. Open Secondary's () properties ().
  2. On the Basic - Orbit page, click Covariance....
  3. When the HPOP Covariance window opens, select the Compute Covariance check box.
  4. In the Gravity field, set both Maximum Degree and Maximum Order to 0 (zero). You're matching the force model gravity values set earlier in the scenario.

    5. The Cartesian covariance units have been populated with the values sent from the Connect command.

    Inserted Cartesian Covariance Units

  5. Click OK to close the HPOP Covariance window.
  6. Click Apply in the Secondary satellite properties.

Viewing Secondary

To properly view Secondary's orbit, make two changes to its 3D Graphics properties.

  1. Go to the 3D Graphics - Pass page.
  2. In the Leading/Trailing field, under Orbit Track, set Lead Type to All. This tells the 3D Graphics window to display the track spanning the entire vehicle ephemeris.
  3. Select the 3D Graphics - Orbit System page.
  4. Clear the Show check box for the Inertial by Window option.
  5. Click Add VVLH System.... This is an object-centered Vehicle Velocity Local Horizontal reference frame with the Z axis opposite the position vector and the X axis toward the inertial velocity vector.
  6. When the Select Object VVLH System window appears, select Primary.
  7. Click OK to close the Select Object VVLH System window.
  8. Click OK to accept property changes and close Primary's ()properties window.
  9. Skip to the View Both Satellites section.

Insert the Secondary satellite using an ephemeris

  1. Using the Insert STK Objects tool, insert a Satellite () object using the From External Ephemeris File (*.e) () method.
  2. When the Select Ephemeris File window opens, browse to the location of the ephemeris file, typically <Install Dir>\Data\Resources\stktraining\text.
  3. Select Secondary.e.
  4. Click Open.
  5. In the Object Browser, rename the Satellite () object "Secondary."
  6. Open Secondary's () properties ().
  7. On the Basic - Orbit page, click Reload Ephemeris.
  8. Click OK.

Viewing Secondary

To properly view Secondary's orbit, make two changes to its 3D Graphics properties.

  1. Go to the 3D Graphics - Pass page.
  2. In the Leading/Trailing field, under Orbit Track, set Lead Type to All. This tells the 3D Graphics window to display the track spanning the entire vehicle ephemeris.
  3. Select the 3D Graphics - Orbit System page.
  4. Clear the Show check box for the Inertial by Window option.
  5. Click Add VVLH System.... This is an object-centered Vehicle Velocity Local Horizontal reference frame with the Z axis opposite the position vector and the X axis toward the inertial velocity vector.
  6. When the Select Object VVLH System window appears, select Primary.
  7. Click OK to close the Select Object VVLH System window.
  8. Click OK to accept property changes and close Primary's ()properties window.
  9. Skip to the View Both Satellites section.

Viewing both satellites

The motion of the secondary satellite is relative to the primary satellite; that is why it is being shown in the VVLH frame of the first satellite. Each loop corresponds to one orbit revolution.

  1. Bring the 3D Graphics window to the front.
  2. In the Object Browser, right-click Primary and select Zoom To.
  3. Use your mouse to refine your view until you can see both satellites.

    4. Primary and Secondary

  4. Using the Animation Toolbar, Increase () the Time Step to 300 sec.
  5. Start () the animation.
  6. When finished, reset () the scenario.

Using Advanced CAT for conjunction analysis

You will complete a linear and a nonlinear analysis. Start with a linear analysis using the Conjunction Analysis capability.

  1. Bring the Insert STK Objects tool to the front. If you have the AdvCAT scenario object available, move to step 5 (five). Otherwise, continue with step 2 (two).
  2. Click Edit Preferences….
  3. In the New Object field, enable AdvCAT.
  4. Click OK to close the Preferences window.
  5. Using the Insert STK Objects tool, insert an AdvCat () object using the Insert Default () method.

Setting Advanced CAT properties

The Main page under Advanced CAT Basic properties contains fields for defining general parameters and selecting and defining analysis objects.

  1. Open AdvCat's () properties (). Click HERE to see detailed information about the Basic - Main page.

    2. Note the default threshold of ten (10) km. This is the threat volume, and you can change it if required. Advanced CAT assigns to each primary and secondary satellite a threat volume, comprising an ellipsoidal shape enclosing the object. This shape possibly represents the degree of uncertainty regarding an object's position at any given time. When the range between ellipsoids falls below the user-selected threshold, STK issues a warning . A collision event occurs whenever the range between the two threat volumes becomes zero or negative.

    As you move down the page, primary objects are the satellites of interest to you, such as those that you own or wish to use. Secondary objects are those that present a potential risk of collision with, or unacceptably close approach to, your primary objects.

  2. In the Primary List, move () Satellite/Primary to the Chosen list.
  3. In the Secondary List, move () Satellite/Secondary to the Chosen list.

Setting fixed definition ellipsoid values

Begin by using a fixed definition, which is the default. Fixed specifies the dimensions of the threat volume ellipsoid on the basis of values you enter.

  1. Set the following for both the Primary and Secondary satellites:
    2. Option Value
    Tangential 10 km
    CrossTrack 5 km
    Normal 5 km
    • The X axis is in the tangential direction, i.e., parallel to the object's velocity vector.
    • The Y axis is in the cross-track direction, i.e., parallel to the orbit normal vector, or the cross product of the radius and velocity vectors.
    • The Z axis is in the normal direction, i.e., parallel to the cross product of the X and Y axes.
    • The X and Z axes are in, and the Y axis is perpendicular to, the orbit plane.
  2. Set HardBodyRadius to a value of .002 (2 meters). This would be set based on your satellite.

    3. Proper Settings

  3. Click Apply.

Reviewing advanced options

  1. Select the Basic - Advanced page.
  2. Note the various fields and settings. For detailed information about this page, click HERE.
  3. You will use the default settings on this page.

On the Basic - Main page, the Threshold: is set to ten (10) km. On the Basic - Main page, default Pre-Filters are set to Apogee/Perigee 30 km and Time 30 km. If you make any changes to the Pre-Filters, make sure they are equal to or greater than the threshold.

For advanced technical information, read "Operating Characteristic Approach To Effective Satellite Conjunction Filtering" (Salvatore Alfano and David Finkleman).

Computing a linear conjunction analysis

  1. Select the Basic - Main page.
  2. At the top of the page, click Compute.
  3. In the Object Browser, right-click AdvCat () and select the Report & Graph Manager.

Choosing analysis type

Advanced CAT provides numerous data provider elements for Events by Min Range. Understanding these choices enables you to determine which elements are needed in your analysis. To quickly understand the collision probability elements, look at graphs that depict each choice. Incursions into operational decision will be key into choosing a data provider element.

Collision Probability (Analytic)

This shows the probability of collision computed using an analytic method based upon Ken Chan's paper. Chan (Aerospace) transforms the two-dimensional Gaussian probability density function (pdf) to a one-dimensional Rician pdf and uses the concept of equivalent areas.

Analytic Graph

Collision Probability (Numeric)

The probability of collision is computed using a numeric method based upon Sal Alfano's paper. Collision Probability (Numeric) returns -1.0 as an error indicator when encounter plane's sigma X or sigma Z value is too small (less than 0.1 mm).

Numeric Graph

Collision Probability (Patera 2005)

The probability of collision is computed using an analytic method based upon Russell Patera's paper that appeared in the Journal of Guidance, Control and Dynamics, vol. 28 (6), 2005.

Patera 2005 Graph

Collision Probability (Maha)

The probability of collision computed based on the Mahalanobis distance method. The Mahalanobis distance is the distance between two points in multivariate space. The Mahalanobis distance is a measure of the distance between a point P and a distribution D, introduced by P. C. Mahalanobis in 1936. No graph is available.

Making a decision

All four methods are sufficiently accurate for analysis of satellite conjunctions. Chan’s method is by far the fastest, but is also the most restrictive due to relative object size limitations. Patera’s method produces good results, especially with his more-recent object-oriented formulation. Alfano’s method determines the number of integrations steps on a case-by-case basis. You must decide what level of accuracy is required.

  • Chan’s method can go down to a collision probability (P)<10e-300. If the miss distance is within 2 sigma, you might not want to use Chan’s method, due to its Rician distribution (versus Gaussian) .
  • Alfano’s method is clipped at P=10e-12. It is somewhat faster than Patera’s and is well within the standard decision making region (10e-1 < P < 10e-7).
  • Patera’s method is capable of going down to P<10e-300, if you are interested in looking at incredibly tiny numbers.

Creating a custom report

For the purposes of this tutorial, you will use all four methods.

  1. In the Report & Graph Manager's Installed Styles list, right-click Close Approach By Min Range and select Properties.
  2. In the Report Contents list, locate and select Events by Min Range Time Out in the Report Contents field. This takes you to the location of the element.
  3. In the. Data Providers list, locate the element Time at Min Sep (TMS) and move () it to the Report Contents list.
  4. In the Report Contents list, select Events by Min Range-Min Range.
  5. Click New Section.
  6. Click New Line.
  7. In the Data Providers list, move () the following elements to Line 2:
    • Collision Probability (Analytic)
    • Collision Probability (Numeric)
    • Collision Probability (Patera 2005)
    • Collision Probability (Maha)
  8. Click OK.
  9. Read the Warning and then click OK.

Generating a report

  1. In the Styles list, expand () My Styles.
  2. Rename the report "Close Approach and Collision Probability".
  3. Click Generate....

Understanding the Data

As you scroll down through the report, focus on the last two lines. Your report's values may be different from the image (different data entered, etc.). The purpose of the image is to explain the data provider elements.

Linear Data

  1. Leave the Report open.
  2. Close the Report & Graph Manager.

Computing a nonlinear conjunction analysis

Now you will take covariance into consideration.

  1. Return to AdvCAT's () properties.
  2. Change the Class for both the primary and secondary satellites to Covariance.
  3. Click Apply.
  4. Click Compute.
  5. Click OK to close AdvCAT's () properties ().
  6. Bring the report to the front and refresh () the report. Note the collision probability changes. They've increased substantially. However, the minimum range is still the same.
  7. When finished, close the report.

Using the Nonlinear Probability Tool

The Nonlinear Probability Tool can be used to compute conjunction probability for nonlinear relative motion. The tool enables you to test for linear relative motion and provides two methods for computing conjunction probability: adjoining parallelepipeds (bundles) and adjoining tubes (cylinders).

The previously mentioned methods (Chan, Alfano, Patera, and Maha) all assume linear relative motion; that is to say the secondary satellite moves past the primary satellite in a straight line. Under certain circumstances (GEO orbits, rendezvous, formation flying, etc.) this assumption is violated, as seen in the 3D Graphics window (Primary and Secondary orbits). The Advanced CAT tool provides you with a test to determine when the linear assumption is not valid. If invalid, you should use adjoining parallelepipeds (bundles) and/or adjoining tubes (cylinders) to obtain a proper probability of collision.

Addressing Nonlinear Motion using Cylinders

Analyzing Non Linear Motion Using Cylinders

Computing probability of collision using cylinders is done by breaking the collision tube into small sections, computing the probability associated with each section, and then summing. This process can take a while to analyze.

Cylinders

Nonlinear motion causes gaps and overlaps where the tube sections meet. If the relative motion track bends towards the covariance ellipsoid center, then the overlapping sections will occur in regions of greater probability density with the gaps occurring in regions of lesser probability density. Although the gap and overlapping volumes are almost equal, their probability densities are not. The resulting summation causes an overinflation of the probability. If the relative motion track bends away from the covariance ellipsoid center, then the probability for cylindrical tubes will be underestimated because the gap is in a region of higher probability density. The amount of error will vary based on the degree of bending/overlap relative to probability density.

Addressing nonlinear motion using bundles

The gaps and overlaps created by adjoining right-circular cylinders can be reduced by sectioning the cylinder into component pieces. The gaps and overlaps of all the sections will be considerably smaller than the unsectioned cylinder. If there is sufficient movement in the probability density space, the aforementioned discs can be linked to form a bent collision tube. The right cylinders described in the previous section are replaced by bundles of abutting parallelepipeds. Each parallelepiped end is adjusted such that the bundle forms a compound miter where neighboring tubes meet, thereby reducing the gaps and overlaps of the previous method. The implicit assumption is that the one-dimensional probability along the central axis of each parallelepiped adequately represents that dimension’s probability for any point on the face of the parallelepiped. Analysis will take much longer than when using cylinders.

Opening the Nonlinear Probability Tool

  1. In the Object Browser, select AdvCat ().
  2. In the menu bar, click AdvCat and select Nonlinear Probability.

    3. At the top of the Nonlinear Probability Tool are Primary Object, Secondary Object, and Time of Closest Approach lists. If you were working with more than one satellite, the lists display them. If all three fields are blank, click the Compute AdvCAT button. This could be the case if you shut down STK and restart your scenario at a later time.

  3. If required, click Compute AdvCAT.

    4. Objects and TCA

    The End Sigma field holds a default value of 4.000. This enables you to set your probability density.

    3D sigmas contain the following probability densities:

    • 1 sigma ≥ 19.87%
    • 2 sigma ≥ 73.85%
    • 3 sigma ≥ 97.07%
    • 4 sigma ≥ 99.89%
    • 5 sigma ≥ 99.998%
    • 6 sigma ≥ 99.99999%

    You can see that you do not gain much beyond four (4) sigma. This is operator defined based operational requirements. Keep the default value.

    Fractional Limit of Probability is the acceptable difference between linear and nonlinear computations. This is operator defined based on operational requirements. Keep the default.

  4. Click Compute Linearity Test.
  5. Read the Warning and click OK. Your conjunction is nonlinear.

    6. Dilution, Maximum and Linear

    • Dilution distance should be compared to the predicted miss distance. If miss distance is less than dilution distance, then you are in the dilution region. This is an indicator that you should try to get better data, perhaps an update and/or prioritized tracking.
    • The maximum probability computation scales and reorients the original covariance at time-of-closest-approach (TCA) to produce a maximum. This is a “worst case” number if you do not have confidence in your covariance or if covariance is not provided (such as with TLEs).
    • The linear probability is the estimated actual probability assuming linear relative motion at TCA. It can be used to compare/contrast with the nonlinear results, which you'll see later.
  6. Review the results in the TCA Rel Val and Approx Min Rel Val fields to evaluate whether a nonlinear computation is warranted.
  • TCA Rel Vel is the velocity of Secondary relative to Primary.
  • Approx Min Rel Vel is the relative speed that must be matched or exceeded for the conjunction to be considered linear based on the Fractional Limit of Probability threshold. If there is an X here, your conjunction is nonlinear.

You have determined that the conjunction is nonlinear. Look at the following fields:

  • Integration Duration: Recommend one quarter of orbital period foward/backward from TCA. The default setting of zero (0) sec automatically sets this for you.
  • Max Time Step: Sets the sectional time step upper limit. Leave the default.
  • Max Angular Bend: Limits the angular difference between abutting cylinders. A higher number could create larger cylinder gaps. Leave the default.
  • Max Sigma Step: Limits individual cylinder length based on the traversed Mahalanobis distance. Leave the default.

Computing collision probability using cylinders

For the purposes of this tutorial, we'll say that a probability of ≥e -4 meets some form of reporting criteria. Based on the reporting criteria, a value ≥than 0.0001 requires action.

  1. Click Compute Prob (Cylinders).
  2. Take a look at the results.

Be patient. This can take several minutes.

The probability of collision is rather high. Remember, cylinders contain gaps and overlaps which can produce an overinflation of the probability.

Computing collision probability using bundles

Using cylinders, the probability of collision exceeded the criteria for reporting a possibility of collision. For the purposes of this tutorial, a probability of ≥e -4 meets some form of reporting criteria. Based on the reporting criteria, a value ≥than 0.0001 requires action.

  • Resolution: You can specify how many parallelepipeds are needed to adequately represent the combined object space. The Resolution field defines this granularity for the two-dimensional probability computation by determining grid size.
  1. Click Compute Prob (Bundles).

    2. Be patient. This could take much longer than using Cylinders.

  2. When finished, close the Nonlinear Probability Tool.

The probability of collision is higher, which was expected. However, the value using cylinders was well with range of taking some form of action. You could have used those numbers. You might consider using bundles if the cylinder value was very close to the threshold of 0.0001.

Summary

You began by loading a prebuilt ephemeris file for the primary satellite and manually loading properties for the secondary satellite. You could load your values into a Satellite () object's properties from outside of STK using a script or STK Integration and an application such as Excel, Python, MATLAB, etc. To test for a nonlinear conjunction, you could bypass setting up ellipsoids, but there is a benefit from seeing the difference of creating a threat volume and using covariance data. Your choice of collision calculation is based on your operational needs. Using the Nonlinear Probability Tool is time consuming but it could be required due to, again, operational requirements. Using covariance data, the satellites had a high probability of collision.

Save your work

  1. Save () your work.
  2. Close STK.

On your own

If you have your own data, enter it into STK, running both linear and nonlinear analyses. Use TLEs to create conjunctions. Keep in mind, you will be missing covariance data. Dive deeper into the Help files to better understand the Advanced CAT tool, cylinders, bundles, etc. Replace the primary satellite with a manually entered satellite. You can change force models for both the new satellite and match them in the secondary satellite to see the effects of refining your analysis.