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I have an IMU that includes an accelerometer and a gyroscope. The IMU is moving through 3D space while rotating around it's z axis(yaw). Here's what I know so far:

Below is a 2D diagram that will hopefully help with understanding what I am trying to accomplish. My end goal though is in 3D space.

**Velocity Vector**: I have a 3D velocity vector (x, y, z) that was integrated from a resting position using the accelerometer data.**Orientation**: I also have an orientation in the form of euler angles, which has been integrated from the gyroscope data, starting from a rest position.**Unknown Initial Yaw**: The initial yaw around the Z-axis is unknown.

**Pitch**and**Roll**angles relative to the velocity vector.**My question is:**How can I determine the pitch and roll angles of the IMU relative to its velocity vector given this information? Are there specific formulas or methods that account for the unknown initial yaw?Below is a 2D diagram that will hopefully help with understanding what I am trying to accomplish. My end goal though is in 3D space.

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