I have flight test data where the IMU is junk. The roll and yaw are obviously wrong, while the pitch seems to be correct. [I know the yaw is wrong because it doesn't match the changes in headings, and I know the roll is wrong because the it stays near 0° during horizontal loops where it should be closer to 20°.] The pitch seems ok because it is stays near 5° most of the time, which was the angle of attack for most of the flight.
I also have GPS data that gives me position at a high update rate. I was able to use the position to compute the yaw values. With the position updates I can also estimate speed. With the position I can get a turn radius, and the change in position gives a velocity which can lead to a linear and/or angular momentum.
Now, I'd like to get an estimate of the roll (I say estimate because I figure the computation will require some simplifying assumptions). The resolution for roll that I need is much less than the position data (by a factor of about 1000).
My question is this: given the position of the aircraft, how can I estimate the roll?
The purpose of this is for analysis of flight test data for a product that was tested on the aircraft. The product had (what turned out to be) a poor IMU, and we cannot do another flight test. I need the attitude and position to complete my analysis.