MATLAB: Rotate acceleration vector using rotation matrix

Question

Hello, first time question asker here.

I am trying to orient a smartphone whlist it is in a persons pocket. I collected accelerometer, gyroscope, and magnetometer data from the phone. Next i used the ahrsfilter to output quaternions relative to the NED reference frame.

Next i created a rotation matrix using rotationMatrix = quat2rotm(orientation). this gave me my rotation matrix.

Now here is the problem. My acceleration data which i want to rotate is in a 940×3 (X Y Z) array and my rotation matrix is in a 3x3x940 multidimensional array. So, how can i multiply each of my acceleration points with the appropriate rotation matrix. I suspect i will have to use a loop, however i am unsure about how to do this. How would you go about doing this?

Thank you

Answer 1

You can use a loop, e.g.

acc = your 940x3 matrix
r = your 3x3x940 array
result = zeros(size(acc));
for k=1:size(acc,1)
    result(k,:) = r(:,:,k) * acc(k,:)';
end

Depending on how r is defined (you didn't specify) you might need this instead:

result(k,:) = acc(k,:) * r(:,:,k);

Or you can explore using one of these FEX submissions (some of which require a C/C++ compiler to create mex routines):

https://www.mathworks.com/matlabcentral/fileexchange/37515-mmx

https://www.mathworks.com/matlabcentral/fileexchange/25977-mtimesx-fast-matrix-multiply-with-multi-dimensional-support

https://www.mathworks.com/matlabcentral/fileexchange/8773-multiple-matrix-multiplications-with-array-expansion-enabled