IMU -> rotation angle -> quaternions

[ritchie888]

I'm trying to determine the link between an IMU I have (tri-axis accelerometer, gyroscope, and magnetometer) and determining its rotation using quaternions.

I've spent a while reading up on the IMU's properties, and quaternions, but I can't get my head around how the two meet.

So, scenario: I have my IMU collecting accelerometer data (in G's) and gyroscope data (in degrees/s) at 64Hz (for example, we're also ignoring magnetometer here). My IMU is sitting on a desk with x pointing away from me, y pointing to the left, and z point up to the sky. The accelerometer data will read x = 0, y = 0, z = 1 (due to gravity). I turn my IMU by 90° to the left (x pointing to the left, y pointing towards me, z still pointing up, data remains the same) and then put it on its side (x still pointing left, y pointing to the ground, z pointing towards me, data now x = 0, y = -1, z = 0. Gyroscope data of course changes during the movements.

Now, I know I need to do some form of double integration to get the acceleration to velocity and then position. But what exactly I'm not too sure. I assume once the necessary calculations have been performed they will be in an angular form which I can put into the quaternion equation.

Could someone please help me break down the task/math so that I can work out the rotation, please.

Thank you!

 

[LightHero]

The best way to approach this is by using an Extended Kalman Filter (EKF). An EKF fuses together the accelerometer and gyroscope data, and then uses the quaternion equation to determine the orientation of the IMU. The EKF will take in the accelerometer and gyroscope data as inputs. The accelerometer data will be used to calculate the linear acceleration of the IMU, while the gyroscope data will be used to calculate the angular velocity. From this, you can integrate to get the linear and angular positions of the IMU. You can then use the linear and angular position data to calculate the quaternion describing the orientation of the IMU. Specifically, you would use the following equations:Quat = [cos(θ/2), ax*sin(θ/2), ay*sin(θ/2), az*sin(θ/2)]Where θ is the angle of rotation, and ax, ay, and az are the components of the axis of rotation. Once you have the quaternion, you can then use it to determine the orientation of the IMU.