Hello
I'm using a 3-axis accelerometer along with a gyroscope and magnetometer to estimate the current attitude of an object, using quaternions.
For that, I need an initial attitude estimation using the accelerometer. I get the acceleration vectors norms from its 3 axes.
I want to determine the direction of one of these vectors in 3D space as coordinates as the direction of one of these vector will be the same than my object's.
I am using a coordinates system with the z axis as "up" and the y and x axes defining the horizontal plane in a terrestrial referential.
I only need its direction "relative to the up direction", as I can rotate the vector using the magnetometer afterwards or just define it as rotation 0 : we can consider the calculated vector to be on the same plane as the referential z axis and any of the horizontal axes.
I don't have much experience in 3D space math so I'm a bit lost and can't figure it out 
I know the normalized total acceleration vector has coordinates of (x = 0, y = 0, z = -1) since it's pointing straight down and other relation between acceleromter axes but couldn't get a solution.
Can anyone that tried this before help ? I think it can be done, but if there's an easier alternative I would be happy too : )
(Sorry if this the wrong thread to post this in as I'm more asking a math question than a sensor question, and also for bad english.)
EDIT : Stumbled accross this old account and thought I'd post the finished project - my attempt at a quaternion based ADAHRS :
https://drive.google.com/drive/u/0/folders/1kYKDX41ThOkm7UC58phY4ZwCFXjqwfW7