Principle of operation of a Gyroscope-Free IMU What is the principle of operation of a Gyroscope-Free IMU, or how can angular accelerations and velocities be measured with accelerometers?
 A: Answering my own question here.
The paper [1] is really useful and shows how an accelerometer in a rotating mount frame measures the specific force on the mount frame, plus the Euler force, plus the Centrifugal force. It discusses also the advantages and disadvantages of accelerometer-only arrays.
#Edit
A triad accelerometer measures: $\mathbf{a}_{i} -  \mathbf{g}  + \boldsymbol{\alpha} \times \mathbf{r} + \boldsymbol{\omega} \times ( \boldsymbol{\omega} \times \mathbf{r} )$
where:

*

*$\mathbf{a}_{i}$ is the inertial acceleration vector

*$\mathbf{g}$ is the gravitational acceleration vector

*$\boldsymbol{\omega}$ is the angular velocity vector

*$\boldsymbol{\alpha}$ is the angular acceleration vector

*$\mathbf{r}$ is a vector from the rotation axis to the mount point of the accelerometer triad

Additionally the Wikipedia page for "Rigid body" very useful, specifically the "Kinematic Equations" section and the "Acceleration of two points fixed on a rigid body" subsection.  Also the Wikipedia page on "Centrifugal force", the section Derivation / Acceleration. And note that an accelerometer would be fixed to the mounting frame, thus the Coriolis force is zero ( dr/dt = 0 ).
[1] "Inertial Sensor Arrays – A Literature Review" by John-Olof Nilsson and Isaac Skog http://www.openshoe.org/wp-content/uploads/2016/09/survey.pdf
