This topic is about PID auto tuning algorithm that can tune your Quadcopter from PIDs ZERO as a start value.
Introduction
Adjusting PIDs is a problem for many of Quadcopter’ pilots, it would be nice to get your quadcopter to adjust PIDs for itself. I made some investigation in this area, and found many complex algorithms that are related to Adaptive PIDs, and Fuzzy Logic. Although my background is engineering but I don’t like complex math when you can make simple solutions

I started with multiwii version 2.3, I chose it because its code is not that complex, while it has many GUI tools and debug facilities to trace, and it has one of the largest community that can test and verify the results. Anyway I have developed a new mode that I called G_TUNE, which enables quadcopter to calculate flyable PIDs values for ACRO mode. i.e. PIDs for GYRO.
How to Use
G_Tune mode starts by resetting all Gyro' PIDs for Roll, Pitch & Yaw to Zero’s. Then pilot needs to takeoff !! yes it will take off as the algorithm will start instantly to correct errors and update PIDs parameters accordingly. Pilot should try not to make aggressive maneuvers. That is because the error in multiwii is calculated as (RC_Stick - Gyroreading) as stick position acts as rotation speed target i.e. the target rpm, so moving stick suddenly generates false errors.
The algorithm mainly works as our human eye. what you do is that if you find your quad tilt you give thrust to motor to adjust this tilt.
Caution
1- This is a test mode that I tested only on my quadcopter with Simonk ESC, 10x4.5 props and Turnigy 1100 KV. It should work on other configuration, but I have not try it myself.
2- Moving ELE & ALE sticks just before changing from G_TUNE to ACRO mode could corrupt the values, so please try to fly as stable as possible and switch to ACRO while sticks are almost released for best results.
3- Switching back from GYRO to G_Tune mode in AIR could be dangerous -however the correction is very fast and it normally works- because PIDs are reset to ZEROs in AIR.