A way to calculate height offsets

Good afternoon everyone!

I'm currently in a competition where we are to design a quad copter that can fulfill specific tasks. One requirement of this completion is you need to create your own "useful" feature. My team and I decided that we would have our data stream over an access point and display this data in a 3D perspective so the user could get a better idea on what the data means. We've gotten everything finished but the final hurdle I am having problems is finding the height of the quadcopter in comparison to the last check that was made.

For example, the quadcopter moved 0.4feet since 0.5 seconds ago or something.

Right now I am using a pressure sensors and converting it to altitudes the problem with this is the range is widely innacurate. For example without moving the sensor the paste altitude measurement could be like +- 2 feet, which when the data is streamed to the computer the quadcopter's icon flies up and down sporadically.

What I'm trying to ask is if anyone knows a good way to find the height of the quadcopter in comparison to when it first started (which should be 0 feet.) I don't need the altitude just a way to know whether or not the quadcopter has gained height or lost height.

Please don't suggest an ultrasonic sensor since we are using it to find the height below the quadcopter (To map out objects that may be under it, such as a table)

Thank you in advance!

Ill just note here that I have been using the MPU6050 to get the x and y axis in terms of velocity. But z is a strange mistress. With this sensor it seems as though it gets acceleration through tilt of the device and the way that quad-copters gain height (Can be still on the x and y axis), getting the z velocity using this device wont work for me it seems.

Wootenstien:
Please don't suggest an ultrasonic sensor since we are using it to find the height below the quadcopter (To map out objects that may be under it, such as a table)

Couldn't you use that in conjunction with your other sensor - for example pressure and acceleration.

If the ultrasonic altitude changes but the other sensors suggest no change then you can assume that the ground has come closer. But if there is a significant change in the other sensors you could assume that the ground has not changed and the actual altitude of the 'copter has.

I know my suggestion is far from perfect but it may be the best you are going to get.

...R

Oh wow, I didn't think of trying that. Yeah your suggestion probably is the best case scenario for me if I choose to use the sensors I have now.

The problem I do see in this is how quad copters can also gain height whist moving, but using some sort of threshold might work (and piloting the copter in a certain way.)

Of course if anyone else has a suggestion I am open, pretty much on the final stretch of the competition (it happens in 2 weeks) so I'm looking for anything that would help make relative height more smooth and less sporadic.