How to Calculate When an STK Object (satellite) is Within a Volume

Objective 

Find the time intervals when an actor satellite approaches a target point offset from a parent satellite, within a specified tolerance. 
In this specific case, the target point is offset from the parent satellite by 100 km in the parent's in-track direction. The tolerances are centered on the target point specified in the parent's RIC reference frame center: R = +/- 10 km, I = +/- 50 km, and C = +/-10 km.

Solution

Use STK's Analysis Workbench capability to create a volume around the target point that is based on the specified tolerance. You can then determine the time intervals when the actor satellite is within the target volume.

Add a Target Point

1. Open the Analysis Workbench ().
2. Click the Vector Geometry tab.
3. Select the TargetParent () satellite.
4. Create a Target point () on the parent satellite.
5. Set the Name to TargetPointVol.
6. Click the ellipsis () button beside the Reference System.
7. Select the RIC system.
8. Set the Cartesian Y to 100 km.
9. Click OK.

Add a Target System

1. Select TargetPointVol () in the Components For list.
2. Create a new Target System ().
3. Set the Name to TargetSystemVol.
4. Ensure the Type is set to Assembled.
5. Set the Origin Point to TargetPointVol.
6. Set the Reference Axes to RIC for the TargetParent.

Spatial Analysis tab

1. Select the Spatial Analysis tab.
2. Click the Create new Volume Grid () button.
3. Ensure the Type is set to Cartesian.
4. Set the Name to VolumeGridParent.
5. Ensure the Parent field is set to Satellite/TargetParent.
6. Set the Reference System to TargetSystemVol (). This is centered around the target point.
7. Click the Get Grid Values... button.
8. Set the following options:

Title	X	Y	Z
Minimum	-10	-50	-10
Maximum	10	50	10
Number of Steps	1	1	1

You set the number of steps because you are only interested in the defined volume and not in evaluating the grid points.

Spatial condition

1. Click the Create the new Condition () button.
2. Set the Type to Grid Bounding Volume.
3. Set the Name to GridBound.
4. Set the VolumeGrid to TargetParent VolumeGridParent, which is the volume grid set in the Spatial Analysis tab.
5. Set the Edge Type to Coordinate Edge.
6. Click OK.

Trajectory within the volume

You would like to know when the actor satellite is within the volume bounds you just created. Set up a calculation that ensures the center point of the actor satellite is within the bounds.

1. Select the Calculation tab.
2. Create a spatial Condition ().
3. Set the Type to Trajectory Within Volume.
4. Set the Name to WithinTrajectory.
5. Set the Trajectory Point to the Center point of the actor satellite.
6. Set the Spatial Condition to GridBound, which is the bound volume from the Spatial Condition section.
7. Click OK.

Create a Satisfaction Intervals report

1. Expand the WithinTrajectory Calculation Condition.
2. Right-click SatisfactionIntervals.
3. Select the Report... option.

Create the visualization

You would like to visualize the tolerance volume. Do this by creating a Volumetric object.

1. Create a Volumetric Object () using the Object Browser.
2. Open the Volumetric's () properties ().
3. Select the Basic - Definition page.
4. Set the Volume Grid to VolumeGridParent.
5. Click OK.
6. Right-click the Volumetric () object in the Object Browser. 
7. Expand the Volumetric menu.
8. Select the Compute option.

See the attached scenario for a completed version using STK 12.