Quaternion distance of inner products

ahrs.utils.metrics.qeip(q1: ndarray, q2: ndarray) → float

Euclidean distance of inner products between two unit quaternions \(\mathbf{q}_1\) and :mathbf{q}_2` as defined in [Huy09] and [Kuf04]:

\[d(\mathbf{q}_1, \mathbf{q}_2) = 1 - |\mathbf{q}_1\cdot\mathbf{q}_2|\]

The error lies within [0, 1], where \(d\) is equal to zero if the quaternions represent the same attitude, and to one if they are completely divergent.

Parameters:

• q1 (numpy.ndarray) – First quaternion, or set of quaternions, to compare.

• q2 (numpy.ndarray) – Second quaternion, or set of quaternions, to compare.

Returns:

d – Euclidean distance of inner products between given unit quaternions.

Return type:

float

Raises:

• ValueError – If the quaternions are not of the same shape.

• TypeError – If the quaternions are not of type list or numpy.ndarray.

Examples

>>> q1 = ahrs.Quaternion(random=True)
>>> q1.view()
Quaternion([ 0.94185064,  0.04451339, -0.00622856,  0.33301221])
>>> q2 = ahrs.Quaternion(random=True)
>>> q2.view()
Quaternion([-0.51041283, -0.38336653,  0.76929238, -0.0264211 ])
>>> ahrs.utils.qeip(q1, q2)
0.48861226940378377
>>> ahrs.utils.qeip(q1, -q1)
0.0