Random Attitudes

ahrs.common.quaternion.random_attitudes(n: int = 1, representation: str = 'quaternion') → ndarray

Generate random attitudes

To generate a random quaternion a mapping in SO(3) is first created and then transformed as explained originally by [Sho92] and summarized in [Kuf04].

First, three uniform random values are sampled from the interval [0, 1]:

\[u_1, u_2, u_3 \sim U(0, 1)\]

Then, two random angles are generated from these values:

\[\begin{split}\begin{array}{rl} s_1 &= \sqrt{1-u_1} \\ s_2 &= \sqrt{u_1} \\ t_1 &= 2\pi u_2 \\ t_2 &= 2\pi u_3 \end{array}\end{split}\]

Finally, the quaternion is built as:

\[\begin{split}\mathbf{q} = \begin{bmatrix} s_2\cos t_2 \\ s_1\sin t_1 \\ s_1\cos t_1 \\ s_2\sin t_2 \end{bmatrix}\end{split}\]

Parameters:

• n (int, default: 1) – Number of random attitudes to generate. Default is 1.

• representation (str, default: 'quaternion') – Attitude representation. Options are 'quaternion' or 'rotmat'.

Returns:

Q – Array of n random quaternions.

Return type:

numpy.ndarray

Examples

>>> random_attitudes()
array([ 0.17607048, -0.42133834, -0.42445916, -0.78186163])
>>> random_attitudes(1)
array([ 0.50391486,  0.15642284, -0.04152787, -0.84845574])
>>> random_attitudes(3)
array([[-0.78506768, -0.21469241,  0.57654945, -0.07187942],
    [ 0.35614954,  0.78811481,  0.45912792, -0.20306182],
    [-0.2474619 ,  0.21632585,  0.50492025,  0.79813613]])
>>> random_attitudes(3, 'rotmat')
array([[[-0.43297822,  0.69987831, -0.56806708],
        [-0.07346304, -0.65550383, -0.75161021],
        [-0.89840583, -0.28369892,  0.33523407]],

       [[ 0.1082323 , -0.55111441,  0.82738061],
        [-0.55001356,  0.66008952,  0.51163162],
        [-0.82811283, -0.51044562, -0.23167739]],

       [[ 0.19915247,  0.86104088, -0.46791762],
        [-0.13040079, -0.44995169, -0.88348124],
        [-0.97125379,  0.2369643 ,  0.02267142]]])