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The start-up I work for is planning to capture remote sensing imagery from cameras on-board our stratospheric balloons. We would like to be able to georeference the images we capture.

If it is possible to accomplish this knowing the GPS, bearing and altitude of our balloons (and the camera specs), what is the formula to calculate it?

From my research it seems like georeferencing is typically done with control points, but this is difficult for us to do as the images we will capturing are typically of forests and oceans.

How do satellites handle this problem?

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If you have an accurate location of your balloon, as well as accurate yaw, pitch, and roll (YPR) for the camera, calculating the direct vector between the lens and the ground is a matter of trigonometry. With that vector, an elevation model, and the camera specs, you can calculate the expected footprint of your image. You can look at this description from PIX4D about YPR and OPR and with details on how to convert from YPR to OPK. The main concern is getting consistent and accurate measurements of YPR for every image taken, as even small uncertainties will result in large errors in georeferencing / footprint.

Satellites can do it in a similar way, however, they have less uncertainty around YPR, as there is less interaction with the environment that can cause things to jostle around.

The usage of ground control points is generally required to go from a spatial accuracy of 10s of meters, down to pixel scale accuracy.

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