How can I calculate a drone camera’s height above the ground from the measured distances to the top and bottom of a known target?

Question

I’m trying to estimate a drone’s height using only its camera. The target is a square platform that is always upright, with a known vertical size of 0.2 m. From the image, I can estimate the camera-to-target distance to the top edge and the bottom edge. The camera’s field of view is 82.6°.

If I know the distance from the camera to the bottom of the platform and the distance from the camera to the top of the platform, can I calculate the drone’s height above the ground? If so, what is the formula?

user75947 · Accepted Answer

Assuming your distances are accurate, you have two right triangles:

Drone, point on ground below drone (\$H\$), bottom corner of platform
Drone, point 20 cm above ground below drone (\$H-h\$), top corner of platform

Using Pythagoras theorem, with \$D\$ the distance between ground track of drone and platform:

$$\begin{align} ext{eq. 1:} && H^2+D^2 &= (\mathrm{distance2})^2 \ ext{eq. 2:} &&(H-h)^2+D^2 &= (\mathrm{distance1})^2 \end{align}$$

Subtracting eq. 2 from eq. 1:

$$ equire{cancel}\begin{align} 2Hh - h^2 &= (\mathrm{distance2})^2 - (\mathrm{distance2})^2 \ H &= \frac{(\mathrm{distance2})^2 - (\mathrm{distance2})^2 + h^2}{2h} \end{align}$$

But I would be surprised if your distance were accurate enough.

How can I calculate a drone camera’s height above the ground from the measured distances to the top and bottom of a known target?

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