# angular velocity output of IMU

I am reading the paper

On-Manifold Preintegration for Real-Time Visual-Inertial Odometry.

There is one paragraph about IMU model. I have two questions.

The first one: An IMU commonly includes a 3-axis accelerometer and a 3-axis gyroscope and allows measuring the rotation rate and the acceleration of the sensor with respect to an inertial frame what does an inertial frame mean?

The second one: The vector(the second quantity from the first equation) is the instantaneous angular velocity of B relative to W expressed in coordinate frame B. The sentence is difficult for me, especially the highlighted part.

• That's simple. Let's say you know the $i_{th}$ IMU body frame $^w \textbf{T}_{B_i}$. Then, your raw angular velocity $^{B_{i}} \textbf{v}$ in Body frame is represented in the $B_i$ frame as a vector in that frame, which means you can transfrom it into the world coordinate like ${^w \textbf{v}_i}={^w \textbf{T}_{B_i}} {^{B_{i}} \textbf{v}}$. Aug 23, 2018 at 1:43