Mean Relative Gap

Hello, I am a project manager in ITTI. We are developing a tool based on Orekit 9.3. We have implemented a feature of orbit improvement basing on optical observations. We can do it and acquire state vectors (PV) at any moment. To determine the accuracy of the estimation and prediction we have to calculate Mean Relative Gap (a Cartesian distance between predicted and observed position of the satellite). We have no problem to derive predicted positions in (x,y,z) out of the propagation but having only passive optical measurements (angular) we cannot determine the observed point in Cartesian space to calculate the distance between them. We lack one dimension (we do not know the distance to the object). I guess it would be much easier if we had a laser measurements but we haven’t. Is there any method to perform this comparison basing on telescope observations? I will be obliged for any help with this.

Hi @Andrzej

It depends the eccentricity of the orbit. If the orbit is close to circular, you can assume the altitude of the observed point is the same as the predicted point. With your predicted position, you can create a SpacecraftState and then access the altitude.


Hi @Andrzej,

In your problem, there are 3 states that can be compared:

  • the predicted position, from a catalog (a TLE ?)
  • the observed position, from your telescope observations
  • the estimated position, from an orbit determination over your observations

As you said, you lack a dimension in the observations to have the observed position. However, you can perform an orbit determination over your measurements to have an estimated position, that you can compare to the predicted position at the date you want.


Thank you for your advice. I will try to do it so.