# Satellite's EO sensor footprint on ground

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?

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