I have a question about something that seems like it would be pretty basic, but so fair I haven't been able to find a whole lot of discussion on the issue. It's possible I'm not not familiar enough with the terminology.
I have a rigid body with an accelerometer/gyro IC dev board nailed to it. I would like to know what the accelerometer would measure at another point on this board, in this case, the sensor of a camera that is also nailed to it.
My thinking is that I can use the accelerator, gyroscope and differentiated gyroscope data and the equation $a_t = a_m + \omega' \times r + \omega \times (\omega \times r)$, where
$a_t$ = transformed acceleration
$a_m$ = measure acceleration
$\omega$ = measured gyroscope reading
$\omega'$ = first derivative of the gyroscope reading
$r$ = the vector between the accelerometer/gyro and the point I want transformed to.
My plan is to get $\omega'$ with a Savitzky-Golay filter, though this makes implementation a lot less convenient, because I have to buffer my data, and try to figure out how the filter effects the noise variance of the sensor.
Does this plan make sense? Is there a better accepted way that I don't know about? I'm surprised that ROS or tf2 doesn't have a built in function for this. Is there something I am missing? Thanks!