Angular distance

ahrs.utils.metrics.angular_distance(R1: ndarray, R2: ndarray) → float

The angular distance between two rotations \(\mathbf{R}_1\) and \(\mathbf{R}_2\) in SO(3), as defined in [HTDL13]:

\[d(\mathbf{R}_1, \mathbf{R}_2) = \|\log(\mathbf{R}_1\mathbf{R}_2^T)\|\]

where \(\|\mathbf{x}\|\) represents the usual euclidean norm of the vector \(\mathbf{x}\).

Parameters:

• R1 (numpy.ndarray) – 3-by-3 rotation matrix.

• R2 (numpy.ndarray) – 3-by-3 rotation matrix.

Returns:

d – Angular distance between rotation matrices

Return type:

float

Examples

>>> import ahrs
>>> R1 = ahrs.DCM(rpy=[0.0, 0.0, 0.0])
>>> R2 = ahrs.DCM(rpy=[90.0, 90.0, 90.0])
>>> ahrs.utils.angular_distance(R1, R2)
1.5707963267948966
>>> R1 = ahrs.DCM(rpy=[10.0, -20.0, 30.0])
>>> R2 = ahrs.DCM(rpy=[-10.0, 20.0, -30.0])
>>> ahrs.utils.angular_distance(R1, R2)
1.282213683073497