I need linear acceleration along the 3 axis of a smartphone.
I already used the device orientation to project and subtract gravity from accelerometer input. with a correct filter it works well.
However when applying a rotation (without any translation) the output is biased. I believe this is resulting from the tangential (maybe centripetal) acceleration component of the rotation. Using the gyroscope one can calculate those components.
What do you think about that? How should the combination be done. I am a beginner with Kalman filtering (which sound good for this) so any help, ideas, references are very welcome.
Are you removing the gravity from the output ? If yes you could be right and the acceleration that you are still detecting is due to the centripetal forces on the smart phone. Do you have also gyros on the smartphone ?
Hi Emanuele, indeed i removed gravity using the quaternion vector representing device orientation. i do have Gyroscope reading, i am thinking of calculating the general angular velocity (sqrt of squared sum) and using it to calculate centripetal acceleration (wondering if i should add tangential to) and then project it using the quaternion vector.
However centripetal acceleration (and tangential) are related to linear by the radius (i imagine it is the distance of the accelerometer from the center of rotation) which is an unknown value (depending on the device to).
any ideas ? i feel a bit stuck with this.
Hi Elie,
Your problem is known in literature as “lever arm” effect and is generally addressed in inertial navigation system.
If you search on the web you can find different references.
The problem is exactly what you mentioned and is generated by the distance among the centre of rotation and the position of you accelerometers ( r )
The “fictitious” acceleration that you are reading is given by
Af = dw/dt x r + wx(wxr). In the previous equation you have the angular velocity (w), the accelerometer position wrt the centre of rotation ( r ) and the angular acceleration (dw/dt).
Your problem is to determine the ( r ). What you could do is simple imposing a centre of rotation joining your smart phone through whatever mechanical device providing rotation and invert the previous equation to fit the measurement you get from the acc, and gyros. Rotating slowly could be enough to neglect the first term (dw/dt x r) in the equation.
Let me know your opinion
Just a last thing, the equation is a vectorial equation
Hi Elie,
If you have access to the quaternions or the rotation matrices, this python code below can help you
from scipy.spatial.transform import Rotation as R
import numpy as np
N = len(your dataset)
acc_data = 3D acceleration data, shape: N x [Acc_X, Acc_Y, Acc_Z]
quat_data = 4D quaternions, shape: N x [q0, q1, q2, q3]
linear_acc = np.zeros((N, 3))
for t in range(N):
r = R.from_quat(quat_data[t]).as_matrix() # convert the quaternion to rotation matrix
r = r * [[0, 1, 1], [1, 0, 1], [1, 1, 0]] # to remove the gravity component
linear_acc[t] = np.matmul(r.T, acc_data[t])
You may also check the Kaggle for more info.
https://www.kaggle.com/hrshtt/kalman-filters-and-imus-starter/notebook
Best of Luck
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