I'm a student and I'm trying to compute the footprint of a generic EO sensor starting from sensor's characteristics and position and velocity vector of my satellite in ECEF coordinates. I followed this tutorial of Stephen Hartzell to compute the satellite line-of-sight intersection with Earth and validate the results comparing with the ones from STK.

It seems to work well when the satellite is Nadir pointing: the results (slant range, point on earth coordinates) differs about $10^{-8}$ from the STK ones. However, when I apply a pitch or roll rotation to the sensor boresight, the slant computed differs 27 meters from the STK ones with consequent significant errors (0.1°) to the latitude and longitude points computed from the intersection point coordinates.

To describe the procedure in detail, I've defined a unit vector pointing toward the Earth $(z = \frac{\llap{-}r}{|r|})$ from my ECEF coordinate. Therefore, I've moved that from ECEF to the satellite body coordinate system with the appropriate rotation matrix, and then I've applied my pitch/roll rotations around the proper axis. At this point, I converted the rotated pointing vector in ECEF coordinates, and I’ve applied the intersection procedure shown above.

Do you think this procedure is correct or there is another one more effective?

Thanks in advance.

  • $\begingroup$ Do you calculate the influence of the atmosphere to the light from Earth surface to the sensor? $\endgroup$
    – Uwe
    May 25, 2022 at 9:42
  • 3
    $\begingroup$ Please define your acronyms. EO can mean electro-optical, Earth observing, or maybe something else. $\endgroup$ May 25, 2022 at 10:00
  • $\begingroup$ No, moreover I'm considering a propagation with only the effects of J2 . $\endgroup$
    – Frank
    May 25, 2022 at 10:16
  • $\begingroup$ You're right, I mean electro-optical (with a rectangular footprint) but I'm also considering an Earth observation mission. $\endgroup$
    – Frank
    May 25, 2022 at 10:17
  • 1
    $\begingroup$ Are you assuming the same ellipsoid as your reference? 27 metre is much less than 0.1°. $\endgroup$
    – gerrit
    May 25, 2022 at 12:29

1 Answer 1


I solved my problem: it must be taken into account a yaw angle for the yaw steering maneuver.

  • $\begingroup$ can you please describe your approach? Are you applying the intersection method for nadir as well as unit vectors corresponding to FOV or BeamWidth to compute the footprint? $\endgroup$
    – jkt
    Sep 15, 2022 at 15:56

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