Difference between gyroscope angular displacement and Euler angles

[ZekDe]

Hi guys, I'm trying to understand between gyroscope angular displacement and euler angles?
for example { Δx = Δx + h * Rx * SCx);} this is gyroscope output about anguler displacement.This value can be used to determine angle that
device created.Why we should euler angles to fly.(I know quaternions.I just try to understand the difference)

 

[FactChecker]

Gyroscopes on airplanes are usually hard-mounted on the frame and give you the rotation rates, not the total displacement. The rates are integrated external to the gyroscope hardware to keep track of the angles.
As an airplane rolls, pitches, and yaws, a particular gyroscope angular rate represents rotations in different directions. It is necessary to keep track of the airplane orientation to know how the gyroscope rates should be interpreted in Euler angles.

 

[ZekDe]

What about DCM,firstly we need to convert body-frame to inertial-frame.What is the purpose?.it that how degree we got displacement according to inertial-frame?

 

[FactChecker]

There are a lot of coordinate systems used in an Inertial Navigation System (INS): INS mount, body-frame, locally-level, Earth-Centered-Earth-Fixed (ECEF), Latitude Longitude Altitude (LLA). And there is a reason for each one. For one thing, body-frame coordinates wouldn't tell the airplane which way gravity is pointing, which is important for interpreting the accelerometer measurements. For another thing, the rotation of the Earth shows up in modern gyro outputs, so it is necessary to know what direction that is into interpret the gyro readings. The mathematics of a modern INS is quite complicated. There are all sorts of Direction Cosine Matrices and integrals used. The long-term drift of the integrals is periodically corrected using fixes on known positions (these days, GPS inputs). The errors of the merged inputs are minimized using Kalman filters. So many of the inputs are communicated in different coordinate systems that DCMs are all over the place. I have not looked at it in detail, but this looks like a good simplified introduction (especially if you have access to MATLAB)

 

[ZekDe]

FactChecker
thank you for your interest,I thought about it and solved the massy information in my mind.Excatly that is what did you say.