Some potential ideas you could use are:
- GPS + IMU
Probably the easiest solution and depending on how much you want to pay you can adjust for accuracy. You just measure the GPS coordinate of the center pitch, and then just do some simple subtraction to get relative pose.
Another advantage of this combination is that it is a simple system to build yourself. The math is also very well known, and you can find multiple open source projects on github.
- Transmitter and Receiver Localization + IMU
There are solutions that work with a transmitter and receiver. So you have some sort of device on the object and beacons around the field. If you want to research them I would look up IPS(Indoor Positioning System) Possible options are:
- Ultra WideBand(UWB)
Probably the most accurate one of these is UWB.
However, for all of these you probably have to buy a solution. Making your own is not really an option unless you have a lot of time to develop the hardware and software. It could also be quite expensive to have enough beacons to cover the soccer field.
- Embed beacons in the field + IMU:
Similar to the transmitter and receiver option. But instead of having a few beacons surrounding the field you have a ton of beacons embedded in the field. When the object passes by the beacon gets triggered. You can improve results using prediction and interpolation.
Possible options for this could be pressure plates or RFID tags.
Problems are somewhat obvious:
- Have to actually modify the field.
- Object must stay close enough to the beacons. So if it flies above the field then it won't be detected.
For all options you should if possible always have an IMU on the object. That way you can do some sensor fusion to always improve the results.
Regarding which one is best is up to you. I recommend Option 1, and if it doesn't work for some reason then rethink your camera limitation. Options 2/3 are going to require either money or an extraordinary amount of effort.