Real time location sensor for following a kite in the air
If the rope length is constant, then how about simple directional and angle sensing? Then with some simple trigonometery you have your kite position.

For example, you attach the kite string to a rotary encoder for the rotation, and on the rotary encoder you have another 180 degree encoder for the angle. You could probably hack this together for less than $10 or spare parts from various consumer items.  

For the calculations, say your kite string is 50m long, and the measured angle is 45 degrees. Now we are assuming reasonably flat ground here so the opposite angle is ~90 degrees (however even if the ground is not flat under the kite you still know the height from your base position if you imagine a right angle triangle)   

So using the above numbers, calculating for height we get (sin calculated in degrees here):

\$ 50m \cdot sin(45^\circ) = 35.36m \$ 

For the direction, you simply need a north reference and use the encoder reading to see how far offset it is.

EDIT - about the rope length/bending:

If you are concerned about the rope length and bending you could have a second thin string (e.g. fishing nylon, strong but very light) that could be used on a lightly tensioned bobbin to keep it straight and have yet another encoder on the bobbin to calculate length. I know it's a hack but you say you want to do this cheaply using consumer hardware. I can think of other options but they are liable to be quite expensive and complex for possibly not too much benefit (depending on the accuracy/precision you need)