# Orientation 3-axis accelerometer from x y z only

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Francesco Lucarelli on 22 Jul 2021
Answered: Prabhan Purwar on 28 Jul 2021
Hi all,
i was wondering if it's possible to get an estimation of the orientation of the accelerometer, from x y z
I have a 3-axis accelerometer, with x(t), y(t) and z(t).
From just those 3 components, is it possible to determine the orientation of my accelerometer, eventually with respect to gravity?
Please find attached also a copy of x, y and z
Regards
Mathieu NOE on 23 Jul 2021
if you take the mean of x,y,z data , you will have the projection of the gravity vector on your local X Y Z coordinate system.
from there you should be able to compute the Euler's angles
transformation matrix is :
you can start by computing theta as the 3,3 term of this matrix can be used in a straigthforward way
then, phi can be also computed by using term 3,1
etc...
Francesco Lucarelli on 23 Jul 2021
you mean form the left side i have the gravity vector [x',y',z'] (mean of x y and z) and from the right side i have my [x,y,z]
so [x',y',z']=A[x,y,z]
computing the math i can have the three angles. Is it okay?
Thanks again

Prabhan Purwar on 28 Jul 2021
Hi Francesco
Rough estimate of the Position and orientation of the device can be predicted by making use of Kinematic equations.
It's under the assumtion that there is no collision taking place and the sampling rate is high to assume a linear motion model.
% Motion Equation
s = @(dt,u,a) u*dt + 0.5*a*dt^2;
v = @(dt,u,a) u + a*dt;
Once velocity components are obtained make use of the following code to get orientation and visualization
velocityAngle = atan2d(velocityY,velocityX);
w = zeros(size(u,1),1);
% Visualization
figure
% Trajectory obtained using motion model
plot3(trajectoryX, trajectoryY, trajectoryZ);
hold on
% Orientation
quiver3(trajectoryX, trajectoryY, trajectoryZ,u,v,w,'LineWidth',0.75,'AutoScaleFactor',1)
view(0,90)
axis equal
hold off
title('Velocity plot')
Some manual adjustments will need to be made according to the setup condition assumed.
Hope it helps!!
Thanks