Update sudmodules' and filters' docstrings to use bibtex.

ahrs/common/dcm.py

@@ -58,10 +58,11 @@
 rotation matrix in :math:`SO(3)`.
 
 `Direction cosines <https://en.wikipedia.org/wiki/Direction_cosine>`_ are
-cosines of angles between a vector and a base coordinate frame [WikipediaDCM]_.
-In this case, the direction cosines describe the differences between orthogonal
-vectors :math:`\\mathbf{r}_i` and the base frame. The matrix containing these
-differences is commonly named the **Direction Cosine Matrix**.
+cosines of angles between a vector and a base coordinate frame
+:cite:p:`Wiki_DirectionCosine`. In this case, the direction cosines describe
+the differences between orthogonal vectors :math:`\\mathbf{r}_i` and the base
+frame. The matrix containing these differences is commonly named the
+**Direction Cosine Matrix**.
 
 These matrices are used for two main purposes:
 
@@ -72,32 +73,12 @@
 Because of the latter, the DCM is also known as the **rotation matrix**.
 
 DCMs are, therefore, the most common representation of rotations
-[WikipediaRotMat]_, especially in real applications of spacecraft tracking and
-location.
+:cite:p:`Wolfram_RotationMatrix`, especially in real applications of spacecraft
+tracking and location.
 
 Throughout this package they will be used to represent the attitudes with
 respect to the global frame.
 
-References
-----------
-.. [WikipediaDCM] Wikipedia: Direction Cosine.
-    (https://en.wikipedia.org/wiki/Direction_cosine)
-.. [WikipediaRotMat] Wikipedia: Rotation Matrix
-    (https://mathworld.wolfram.com/RotationMatrix.html)
-.. [Ma] Yi Ma, Stefano Soatto, Jana Kosecka, and S. Shankar Sastry. An
-    Invitation to 3-D Vision: From Images to Geometric Models. Springer
-    Verlag. 2003.
-    (https://www.eecis.udel.edu/~cer/arv/readings/old_mkss.pdf)
-.. [Huyhn] Huynh, D.Q. Metrics for 3D Rotations: Comparison and Analysis. J
-    Math Imaging Vis 35, 155–164 (2009).
-.. [Curtis] Howard D Curtis. Orbital Mechanics for Engineering Students (Third
-    Edition) Butterworth-Heinemann. 2014.
-.. [Kuipers] Kuipers, Jack B. Quaternions and Rotation Sequences: A Primer with
-    Applications to Orbits, Aerospace and Virtual Reality. Princeton;
-    Oxford: Princeton University Press, 1999.
-.. [Diebel] Diebel, James. Representing Attitude; Euler Angles, Unit
-    Quaternions, and Rotation. Stanford University. 20 October 2006.
-
 """
 
 from typing import Tuple
@@ -1039,14 +1020,14 @@ def to_quaternion(self, method: str='shepperd', **kw) -> np.ndarray:
         There are five methods available to obtain a quaternion from a
         Direction Cosine Matrix:
 
-        * ``'shepperd'`` as described in [Chiaverini]_.
-        * ``'hughes'`` as described in [Hughes]_.
-        * ``'itzhack'`` as described in [Bar-Itzhack]_ using version ``3`` by
+        * ``'chiaverini'`` as described in :cite:p:`Chiaverini1999`.
+        * ``'hughes'`` as described in :cite:p:`hughes1986spacecraft17`.
+        * ``'itzhack'`` as described in :cite:p:`BarItzhack2000` using version ``3`` by
           default. Possible options are integers ``1``, ``2`` or ``3``.
-        * ``'sarabandi'`` as described in [Sarabandi]_ with a threshold equal
+        * ``'sarabandi'`` as described in :cite:p:`sarabandi2019` with a threshold equal
           to ``0.0`` by default. Possible threshold values are floats between
           ``-3.0`` and ``3.0``.
-        * ``'shepperd'`` as described in [Shepperd]_.
+        * ``'shepperd'`` as described in :cite:p:`shepperd1978`.
 
         Parameters
         ----------

ahrs/common/orientation.py

@@ -104,7 +104,6 @@ def q_random(size: int = 1) -> np.ndarray:
         return q[0]
     return q
 
-
 def q_norm(q: np.ndarray) -> np.ndarray:
     """
     Normalize quaternion [WQ1]_ :math:`\\mathbf{q}_u`, also known as a versor
@@ -1085,7 +1084,7 @@ def slerp(q0: np.ndarray, q1: np.ndarray, t_array: np.ndarray, threshold: float
     arc of a great circle passing through any two existing quaternion endpoints
     lying on the unit radius hypersphere.
 
-    Based on the method detailed in [Wiki_SLERP]_
+    Based on the method detailed in :cite:p:`Wiki_SLERP`.
 
     Parameters
     ----------
@@ -1106,10 +1105,6 @@ def slerp(q0: np.ndarray, q1: np.ndarray, t_array: np.ndarray, threshold: float
     q : numpy.ndarray
         New quaternion representing the interpolated rotation.
 
-    References
-    ----------
-    .. [Wiki_SLERP] https://en.wikipedia.org/wiki/Slerp
-
     """
     qdot = q0@q1
     # Ensure SLERP takes the shortest path
@@ -1132,7 +1127,7 @@ def slerp(q0: np.ndarray, q1: np.ndarray, t_array: np.ndarray, threshold: float
 def chiaverini(dcm: np.ndarray) -> np.ndarray:
     """
     Quaternion from a Direction Cosine Matrix with Chiaverini's algebraic
-    method [Chiaverini]_.
+    method :cite:p:`Chiaverini1999`.
 
     Defining the unit quaternion as:
 
@@ -1218,7 +1213,8 @@ def chiaverini(dcm: np.ndarray) -> np.ndarray:
 
 def hughes(C: np.ndarray) -> np.ndarray:
     """
-    Quaternion from a Direction Cosine Matrix with Hughes' method [Hughes]_.
+    Quaternion from a Direction Cosine Matrix with trigonometric Hughes' method
+    :cite:p:`hughes1986spacecraft17`.
 
     Defining the quaternion (reluctantly called "Euler Parameters" in Hughes'
     book) as:
@@ -1320,7 +1316,7 @@ def hughes(C: np.ndarray) -> np.ndarray:
 def sarabandi(dcm: np.ndarray, eta: float = 0.0) -> np.ndarray:
     """
     Quaternion from a Direction Cosine Matrix using Sarabandi's method
-    [Sarabandi]_.
+    :cite:p:`sarabandi2019`.
 
     A rotation matrix :math:`\\mathbf{R}` can be expressed as:
 
@@ -1521,7 +1517,7 @@ def sarabandi(dcm: np.ndarray, eta: float = 0.0) -> np.ndarray:
 def itzhack(dcm: np.ndarray, version: int = 3) -> np.ndarray:
     """
     Quaternion from a Direction Cosine Matrix with Bar-Itzhack's method
-    [Bar-Itzhack]_.
+    :cite:p:`BarItzhack2000`.
 
     This method to compute the quaternion from a Direction Cosine Matrix (DCM)
     is based on the eigenvalue decomposition of the matrix :math:`\\mathbf{K}`,
@@ -1775,13 +1771,14 @@ def itzhack(dcm: np.ndarray, version: int = 3) -> np.ndarray:
             q = eigvec[:, np.where(np.isclose(eigval, 1.0))[0]].flatten().real
         else:
             q = eigvec[:, eigval.argmax()]
-    q = np.roll(q, 1)       # Original implementation uses [qx, qy, qz, qw]
+    q = np.roll(q, 1)       # Re-arrange quaternion to [qw, qx, qy, qz]
     q[0] *= -1              # Original implementation computes inverse rotation
     return q / np.linalg.norm(q)
 
 def shepperd(dcm: np.ndarray) -> np.ndarray:
     """
-    Quaternion from a Direction Cosine Matrix with Shepperd's method [Shepperd]_.
+    Quaternion from a Direction Cosine Matrix with Shepperd's method
+    :cite:p:`Shepperd1978`.
 
     Since it was proposed in 1978, the Shepperd method has been widely used
     in the aerospace industry.