From 83b422099fd676b68bdcbdde2c793e59228df629 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 4 Dec 2025 15:02:19 +0100
Subject: [PATCH 01/42] coning alg

---
 src/smsfusion/_coning_sculling.py | 88 +++++++++++++++++++++++++++++++
 1 file changed, 88 insertions(+)
 create mode 100644 src/smsfusion/_coning_sculling.py

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
new file mode 100644
index 00000000..86f52903
--- /dev/null
+++ b/src/smsfusion/_coning_sculling.py
@@ -0,0 +1,88 @@
+import numpy as np
+from numpy.typing import ArrayLike
+
+from ._vectorops import _cross
+
+
+class ConingScullingAlgorithm:
+    """
+    Coning and sculling algorithm.
+    """
+
+    def __init__(self, fs: float, bias_gyro=None, bias_acc=None):
+        self._fs = fs
+        self._dt = 1.0 / fs
+        self._bg = bias_gyro or np.zeros(3)
+        self._ba = bias_acc or np.zeros(3)
+
+        # Coning params
+        self._theta = np.zeros(3)
+        self._dtheta = np.zeros(3)
+        self._dtheta_prev = np.zeros(3)
+        self._w_prev = np.zeros(3)
+
+    def _coning_update(self, w):
+        """
+        Update the coning integrals using new gyroscope measurements, w[l+1].
+
+        Coning algorithm:
+
+            phi := beta + dbeta
+
+        where,
+
+            dtheta[l] = dt * (w[l+1] - w[l])
+            dbeta[l+1] = dbeta[l] + 0.5 * cross((beta[l] + (1/6) * dtheta[l-1]), dtheta[l])
+            beta[l+1] = beta[l] + dtheta[l]
+
+        with initial conditions,
+            beta[0] = [0, 0, 0]
+            dbeta[0] = [0, 0, 0]
+
+        Parameters
+        ----------
+        f_imu : array-like, shape (3,)
+            Specific force measurements (i.e., accelerations + gravity), given
+            as [f_x, f_y, f_z]^T where f_x, f_y and f_z are
+            acceleration measurements in x-, y-, and z-direction, respectively.
+        w_imu : array-like, shape (3,)
+            Angular rate measurements, given as [w_x, w_y, w_z]^T where
+            w_x, w_y and w_z are angular rates about the x-, y-,
+            and z-axis, respectively.
+        degrees : bool, default False
+            Specify whether the angular rates are given in degrees or radians.
+        """
+        dtheta = (w - self._w_prev) * self._dt
+        self._dbeta += 0.5 * _cross(self._dbeta + (1.0 / 6.0) * self._dtheta_prev, dtheta)
+        self._beta += dtheta
+
+        self._w_prev = w
+        self._dtheta_prev = dtheta
+
+    def update(self, f_imu: ArrayLike, w_imu: ArrayLike, degrees: bool = False):
+        """
+        Update.
+
+        Parameters
+        ----------
+        f_imu : array-like, shape (3,)
+            Specific force measurements (i.e., accelerations + gravity), given
+            as [f_x, f_y, f_z]^T where f_x, f_y and f_z are
+            acceleration measurements in x-, y-, and z-direction, respectively.
+        w_imu : array-like, shape (3,)
+            Angular rate measurements, given as [w_x, w_y, w_z]^T where
+            w_x, w_y and w_z are angular rates about the x-, y-,
+            and z-axis, respectively.
+        degrees : bool, default False
+            Specify whether the angular rates are given in degrees or radians.
+        """
+        f_imu = np.asarray(f_imu, dtype=float)
+        w_imu = np.asarray(w_imu, dtype=float)
+
+        if degrees:
+            w_imu = (np.pi / 180.0) * w_imu
+
+        f_ins = f_imu - self._ba
+        w_ins = w_imu - self._bg
+
+        self._coning_update(w_ins)

From 87f96d2d8c2814cf97a1a8a5fc48add9460a7be4 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 4 Dec 2025 15:24:40 +0100
Subject: [PATCH 02/42] sculling

---
 src/smsfusion/_coning_sculling.py | 45 ++++++++++++++++++++++++-------
 1 file changed, 35 insertions(+), 10 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 86f52903..d99f693b 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -21,6 +21,11 @@ def __init__(self, fs: float, bias_gyro=None, bias_acc=None):
         self._dtheta_prev = np.zeros(3)
         self._w_prev = np.zeros(3)
 
+        # Sculling params
+        self._gamma1 = np.zeros(3, dtype=float)
+        self._u = np.zeros(3, dtype=float)
+        self._f_prev = np.zeros(3, dtype=float)
+
     def _coning_update(self, w):
         """
         Update the coning integrals using new gyroscope measurements, w[l+1].
@@ -41,16 +46,8 @@ def _coning_update(self, w):
 
         Parameters
         ----------
-        f_imu : array-like, shape (3,)
-            Specific force measurements (i.e., accelerations + gravity), given
-            as [f_x, f_y, f_z]^T where f_x, f_y and f_z are
-            acceleration measurements in x-, y-, and z-direction, respectively.
-        w_imu : array-like, shape (3,)
-            Angular rate measurements, given as [w_x, w_y, w_z]^T where
-            w_x, w_y and w_z are angular rates about the x-, y-,
-            and z-axis, respectively.
-        degrees : bool, default False
-            Specify whether the angular rates are given in degrees or radians.
+        w : numpy.ndarray
+            Bias corrected angular rate measurements.
         """
         dtheta = (w - self._w_prev) * self._dt
         self._dbeta += 0.5 * _cross(self._dbeta + (1.0 / 6.0) * self._dtheta_prev, dtheta)
@@ -59,6 +56,15 @@ def _coning_update(self, w):
         self._w_prev = w
         self._dtheta_prev = dtheta
 
+    def _sculling_update(self, f):
+        """
+        Update the sculling integrals using new accelerometer measurements, f[l+1].
+        """
+        dvel = (f - self._f_prev) * self._dt
+        self._gamma1 += np.cross(self._beta + 0.5 * self._dtheta, dvel)
+        self._u += dvel
+
+
     def update(self, f_imu: ArrayLike, w_imu: ArrayLike, degrees: bool = False):
         """
         Update.
@@ -85,4 +91,23 @@ def update(self, f_imu: ArrayLike, w_imu: ArrayLike, degrees: bool = False):
         f_ins = f_imu - self._ba
         w_ins = w_imu - self._bg
 
+        self._sculling_update(f_ins)
         self._coning_update(w_ins)
+
+    def dtheta(self):
+        """
+        Coning integral.
+        """
+        return self._beta + self._dbeta
+    
+    def dvel(self):
+        """
+        Sculling integral.
+        """
+        return self._u + self._gamma1
+    
+    def reset(self):
+        self._beta = np.zeros(3, dtype=float)
+        self._dbeta = np.zeros(3, dtype=float)
+        self._gamma1 = np.zeros(3, dtype=float)
+        self._u = np.zeros(3, dtype=float)
\ No newline at end of file

From 2da4c217ddf4319abd696140eaf6e9a674cff646 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 4 Dec 2025 16:02:27 +0100
Subject: [PATCH 03/42] some fixes

---
 src/smsfusion/_coning_sculling.py | 22 ++++++++++++----------
 1 file changed, 12 insertions(+), 10 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index d99f693b..7f2d071a 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -1,7 +1,7 @@
 import numpy as np
 from numpy.typing import ArrayLike
 
-from ._vectorops import _cross
+from smsfusion._vectorops import _cross
 
 
 class ConingScullingAlgorithm:
@@ -16,8 +16,8 @@ def __init__(self, fs: float, bias_gyro=None, bias_acc=None):
         self._ba = bias_acc or np.zeros(3)
 
         # Coning params
-        self._theta = np.zeros(3)
-        self._dtheta = np.zeros(3)
+        self._beta = np.zeros(3)
+        self._dbeta = np.zeros(3)
         self._dtheta_prev = np.zeros(3)
         self._w_prev = np.zeros(3)
 
@@ -49,21 +49,23 @@ def _coning_update(self, w):
         w : numpy.ndarray
             Bias corrected angular rate measurements.
         """
-        dtheta = (w - self._w_prev) * self._dt
-        self._dbeta += 0.5 * _cross(self._dbeta + (1.0 / 6.0) * self._dtheta_prev, dtheta)
+        dtheta = w * self._dt
+        # dtheta = 0.5 * (w + self._w_prev) * self._dt
+        self._dbeta += 0.5 * np.cross((self._beta + (1.0 / 6.0) * self._dtheta_prev), dtheta)
         self._beta += dtheta
 
-        self._w_prev = w
-        self._dtheta_prev = dtheta
+        self._w_prev = w.copy()
+        self._dtheta_prev = dtheta.copy()
 
     def _sculling_update(self, f):
         """
         Update the sculling integrals using new accelerometer measurements, f[l+1].
         """
-        dvel = (f - self._f_prev) * self._dt
-        self._gamma1 += np.cross(self._beta + 0.5 * self._dtheta, dvel)
+        dvel = f * self._dt
+        # dvel = 0.5 * (f + self._f_prev) * self._dt
+        self._gamma1 += np.cross(self._beta + 0.5 * self._dtheta_prev, dvel)
         self._u += dvel
-
+        self._f_prev = f
 
     def update(self, f_imu: ArrayLike, w_imu: ArrayLike, degrees: bool = False):
         """

From 1b7c4eab203753a1df79086687ab44dfbb6c8bad Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Fri, 5 Dec 2025 09:53:04 +0100
Subject: [PATCH 04/42] small fix

---
 src/smsfusion/_coning_sculling.py | 7 ++-----
 1 file changed, 2 insertions(+), 5 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 7f2d071a..1cb5b3d1 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -90,11 +90,8 @@ def update(self, f_imu: ArrayLike, w_imu: ArrayLike, degrees: bool = False):
         if degrees:
             w_imu = (np.pi / 180.0) * w_imu
 
-        f_ins = f_imu - self._ba
-        w_ins = w_imu - self._bg
-
-        self._sculling_update(f_ins)
-        self._coning_update(w_ins)
+        self._sculling_update(f_imu - self._ba)
+        self._coning_update(w_imu - self._bg)
 
     def dtheta(self):
         """

From 79ab49725ad29b5064072f2ff63a9d36a4c36849 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Fri, 5 Dec 2025 10:05:22 +0100
Subject: [PATCH 05/42] some changes

---
 src/smsfusion/_coning_sculling.py | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 1cb5b3d1..7e2b36a6 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -49,20 +49,20 @@ def _coning_update(self, w):
         w : numpy.ndarray
             Bias corrected angular rate measurements.
         """
-        dtheta = w * self._dt
-        # dtheta = 0.5 * (w + self._w_prev) * self._dt
-        self._dbeta += 0.5 * np.cross((self._beta + (1.0 / 6.0) * self._dtheta_prev), dtheta)
+        # dtheta = w * self._dt
+        dtheta = 0.5 * (w + self._w_prev) * self._dt
+        self._dbeta += 0.5 * np.cross(self._beta + (1.0 / 6.0) * self._dtheta_prev, dtheta)
         self._beta += dtheta
 
-        self._w_prev = w.copy()
-        self._dtheta_prev = dtheta.copy()
+        self._w_prev = w
+        self._dtheta_prev = dtheta
 
     def _sculling_update(self, f):
         """
         Update the sculling integrals using new accelerometer measurements, f[l+1].
         """
-        dvel = f * self._dt
-        # dvel = 0.5 * (f + self._f_prev) * self._dt
+        # dvel = f * self._dt
+        dvel = 0.5 * (f + self._f_prev) * self._dt
         self._gamma1 += np.cross(self._beta + 0.5 * self._dtheta_prev, dvel)
         self._u += dvel
         self._f_prev = f

From 2e230b78f60ae156382962dd26ea51dde9d212c9 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Fri, 5 Dec 2025 10:19:43 +0100
Subject: [PATCH 06/42] some changes

---
 src/smsfusion/__init__.py         |  2 ++
 src/smsfusion/_coning_sculling.py | 12 +++++++-----
 2 files changed, 9 insertions(+), 5 deletions(-)

diff --git a/src/smsfusion/__init__.py b/src/smsfusion/__init__.py
index fb68cdbb..48ec7ea4 100644
--- a/src/smsfusion/__init__.py
+++ b/src/smsfusion/__init__.py
@@ -1,4 +1,5 @@
 from . import benchmark, calibrate, constants, noise
+from ._coning_sculling import ConingScullingAlg
 from ._ins import AHRS, VRU, AidedINS, FixedNED, StrapdownINS, gravity
 from ._smoothing import FixedIntervalSmoother
 from ._transforms import quaternion_from_euler
@@ -16,4 +17,5 @@
     "StrapdownINS",
     "VRU",
     "quaternion_from_euler",
+    "ConingScullingAlg",
 ]
diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 7e2b36a6..31c8ee5b 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -4,7 +4,7 @@
 from smsfusion._vectorops import _cross
 
 
-class ConingScullingAlgorithm:
+class ConingScullingAlg:
     """
     Coning and sculling algorithm.
     """
@@ -51,7 +51,9 @@ def _coning_update(self, w):
         """
         # dtheta = w * self._dt
         dtheta = 0.5 * (w + self._w_prev) * self._dt
-        self._dbeta += 0.5 * np.cross(self._beta + (1.0 / 6.0) * self._dtheta_prev, dtheta)
+        self._dbeta += 0.5 * np.cross(
+            self._beta + (1.0 / 6.0) * self._dtheta_prev, dtheta
+        )
         self._beta += dtheta
 
         self._w_prev = w
@@ -98,15 +100,15 @@ def dtheta(self):
         Coning integral.
         """
         return self._beta + self._dbeta
-    
+
     def dvel(self):
         """
         Sculling integral.
         """
         return self._u + self._gamma1
-    
+
     def reset(self):
         self._beta = np.zeros(3, dtype=float)
         self._dbeta = np.zeros(3, dtype=float)
         self._gamma1 = np.zeros(3, dtype=float)
-        self._u = np.zeros(3, dtype=float)
\ No newline at end of file
+        self._u = np.zeros(3, dtype=float)

From 0eacaebad3471edbbcbc59c4d9786027f7d3e525 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Fri, 5 Dec 2025 10:27:26 +0100
Subject: [PATCH 07/42] use private cross

---
 src/smsfusion/_coning_sculling.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 31c8ee5b..3175cdfa 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -51,7 +51,7 @@ def _coning_update(self, w):
         """
         # dtheta = w * self._dt
         dtheta = 0.5 * (w + self._w_prev) * self._dt
-        self._dbeta += 0.5 * np.cross(
+        self._dbeta += 0.5 * _cross(
             self._beta + (1.0 / 6.0) * self._dtheta_prev, dtheta
         )
         self._beta += dtheta

From b19e73a74c0b8b1d3eb59baaaf05df5732a6db35 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Fri, 5 Dec 2025 11:29:38 +0100
Subject: [PATCH 08/42] docstring

---
 src/smsfusion/_coning_sculling.py | 125 +++++++++++++++++-------------
 1 file changed, 69 insertions(+), 56 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 3175cdfa..44ad5068 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -7,6 +7,34 @@
 class ConingScullingAlg:
     """
     Coning and sculling algorithm.
+
+    Integrates an IMU's specific force and angular rate measurements to coning and
+    sculling corrected velocity (dvel) and attitude (dtheta) changes.
+
+    For use in a strapdown algorithm as:
+
+        vel[m+1] = vel[m] + R(q[m]) @ dvel[m] + dvel_corr
+        q[m+1] = q[m] ⊗ h(dtheta[m])
+
+    where,
+
+        dvel_corr = [0, 0, g] (if NED)
+        dvel_corr = [0, 0, -g] (if ENU)
+
+    and,
+
+    - dvel[m] is the sculling integral, i.e., the velocity vector change (no gravity
+      correction) from time step m to m+1.
+    - dtheta[m] is the coning integral, i.e., the rotation vector change from time
+      step m to m+1.
+    - h(dtheta[m]) is the unit quaternion representation of the rotation increment
+      over the interval [m, m+1].
+
+    The coning and sculling integrals are computed according to ref [1]_.
+
+    References
+    ----------
+    .. [1] https://apps.dtic.mil/sti/tr/pdf/ADP003621.pdf
     """
 
     def __init__(self, fs: float, bias_gyro=None, bias_acc=None):
@@ -19,70 +47,26 @@ def __init__(self, fs: float, bias_gyro=None, bias_acc=None):
         self._beta = np.zeros(3)
         self._dbeta = np.zeros(3)
         self._dtheta_prev = np.zeros(3)
-        self._w_prev = np.zeros(3)
+        self._w_prev = None
 
         # Sculling params
         self._gamma1 = np.zeros(3, dtype=float)
         self._u = np.zeros(3, dtype=float)
-        self._f_prev = np.zeros(3, dtype=float)
-
-    def _coning_update(self, w):
-        """
-        Update the coning integrals using new gyroscope measurements, w[l+1].
-
-        Coning algorithm:
-
-            phi := beta + dbeta
-
-        where,
-
-            dtheta[l] = dt * (w[l+1] - w[l])
-            dbeta[l+1] = dbeta[l] + 0.5 * cross((beta[l] + (1/6) * dtheta[l-1]), dtheta[l])
-            beta[l+1] = beta[l] + dtheta[l]
-
-        with initial conditions,
-            beta[0] = [0, 0, 0]
-            dbeta[0] = [0, 0, 0]
-
-        Parameters
-        ----------
-        w : numpy.ndarray
-            Bias corrected angular rate measurements.
-        """
-        # dtheta = w * self._dt
-        dtheta = 0.5 * (w + self._w_prev) * self._dt
-        self._dbeta += 0.5 * _cross(
-            self._beta + (1.0 / 6.0) * self._dtheta_prev, dtheta
-        )
-        self._beta += dtheta
-
-        self._w_prev = w
-        self._dtheta_prev = dtheta
-
-    def _sculling_update(self, f):
-        """
-        Update the sculling integrals using new accelerometer measurements, f[l+1].
-        """
-        # dvel = f * self._dt
-        dvel = 0.5 * (f + self._f_prev) * self._dt
-        self._gamma1 += np.cross(self._beta + 0.5 * self._dtheta_prev, dvel)
-        self._u += dvel
-        self._f_prev = f
+        self._f_prev = None
 
     def update(self, f_imu: ArrayLike, w_imu: ArrayLike, degrees: bool = False):
         """
-        Update.
+        Update the coning (dtheta) and sculling (dvel) integrals using new IMU measurements.
 
         Parameters
         ----------
         f_imu : array-like, shape (3,)
-            Specific force measurements (i.e., accelerations + gravity), given
-            as [f_x, f_y, f_z]^T where f_x, f_y and f_z are
-            acceleration measurements in x-, y-, and z-direction, respectively.
+            Specific force (acceleration + gravity) measurements [f_x, f_y, f_z],
+            where f_x, f_y and f_z are specific forces along the x-, y-, and z-axis,
+            respectively.
         w_imu : array-like, shape (3,)
-            Angular rate measurements, given as [w_x, w_y, w_z]^T where
-            w_x, w_y and w_z are angular rates about the x-, y-,
-            and z-axis, respectively.
+            Angular rate measurements [w_x, w_y, w_z], where w_x, w_y and w_z are
+            angular rates about the x-, y-, and z-axis, respectively.
         degrees : bool, default False
             Specify whether the angular rates are given in degrees or radians.
         """
@@ -92,22 +76,51 @@ def update(self, f_imu: ArrayLike, w_imu: ArrayLike, degrees: bool = False):
         if degrees:
             w_imu = (np.pi / 180.0) * w_imu
 
-        self._sculling_update(f_imu - self._ba)
-        self._coning_update(w_imu - self._bg)
+        f = f_imu - self._ba
+        w = w_imu - self._bg
+
+        # Accelerometer and gyro pulse vector counts from l to l+1
+        if self._f_prev is not None or self._w_prev is not None:  # first sample
+            dvel = f * self._dt  # backward Euler
+            dtheta = w * self._dt  # backward Euler
+        else:
+            dvel = 0.5 * (f + self._f_prev) * self._dt  # trapezoidal
+            dtheta = 0.5 * (w + self._w_prev) * self._dt  # trapezoidal
+
+        # Sculling update
+        self._gamma1 += np.cross(self._beta + 0.5 * dtheta, dvel)
+        self._u += dvel
+
+        # Coning update
+        self._dbeta += 0.5 * _cross(
+            self._beta + (1.0 / 6.0) * self._dtheta_prev, dtheta
+        )
+        self._beta += dtheta
+
+        self._f_prev = f
+        self._w_prev = w
+        self._dtheta_prev = dtheta
 
     def dtheta(self):
         """
-        Coning integral.
+        The accumulated 'body attitude change' vector. I.e., the rotation vector
+        describing the total rotation over all samples since initialization (or
+        last reset).
         """
         return self._beta + self._dbeta
 
     def dvel(self):
         """
-        Sculling integral.
+        The accumulated specific force velocity vector change. I.e., 
+        the total change in velocity (no gravity correction) over all samples since
+        initialization (or last reset).
         """
         return self._u + self._gamma1
 
     def reset(self):
+        """
+        Reset the coning (dtheta) and sculling (dvel) integrals to zero.
+        """
         self._beta = np.zeros(3, dtype=float)
         self._dbeta = np.zeros(3, dtype=float)
         self._gamma1 = np.zeros(3, dtype=float)

From 658666564ec4ec5f0a1b955b6e55842d336f7fcd Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Fri, 5 Dec 2025 11:59:28 +0100
Subject: [PATCH 09/42] reference equations

---
 src/smsfusion/_coning_sculling.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 44ad5068..2e5102ea 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -30,7 +30,8 @@ class ConingScullingAlg:
     - h(dtheta[m]) is the unit quaternion representation of the rotation increment
       over the interval [m, m+1].
 
-    The coning and sculling integrals are computed according to ref [1]_.
+    The coning and sculling integrals are computed according to Eq. (26) and Eq. (55)
+    in ref [1]_.
 
     References
     ----------

From 32f43fd2458be28909890f7e664af6d279311042 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Fri, 5 Dec 2025 12:10:44 +0100
Subject: [PATCH 10/42] some changes

---
 src/smsfusion/_coning_sculling.py | 46 +++++++++++++++++--------------
 1 file changed, 25 insertions(+), 21 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 2e5102ea..f64f4979 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -38,16 +38,14 @@ class ConingScullingAlg:
     .. [1] https://apps.dtic.mil/sti/tr/pdf/ADP003621.pdf
     """
 
-    def __init__(self, fs: float, bias_gyro=None, bias_acc=None):
+    def __init__(self, fs: float):
         self._fs = fs
         self._dt = 1.0 / fs
-        self._bg = bias_gyro or np.zeros(3)
-        self._ba = bias_acc or np.zeros(3)
 
         # Coning params
-        self._beta = np.zeros(3)
-        self._dbeta = np.zeros(3)
-        self._dtheta_prev = np.zeros(3)
+        self._beta = np.zeros(3, dtype=float)
+        self._dbeta = np.zeros(3, dtype=float)
+        self._dtheta_prev = np.zeros(3, dtype=float)
         self._w_prev = None
 
         # Sculling params
@@ -55,33 +53,30 @@ def __init__(self, fs: float, bias_gyro=None, bias_acc=None):
         self._u = np.zeros(3, dtype=float)
         self._f_prev = None
 
-    def update(self, f_imu: ArrayLike, w_imu: ArrayLike, degrees: bool = False):
+    def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
         """
         Update the coning (dtheta) and sculling (dvel) integrals using new IMU measurements.
 
         Parameters
         ----------
-        f_imu : array-like, shape (3,)
+        f : array-like, shape (3,)
             Specific force (acceleration + gravity) measurements [f_x, f_y, f_z],
             where f_x, f_y and f_z are specific forces along the x-, y-, and z-axis,
             respectively.
-        w_imu : array-like, shape (3,)
+        w : array-like, shape (3,)
             Angular rate measurements [w_x, w_y, w_z], where w_x, w_y and w_z are
             angular rates about the x-, y-, and z-axis, respectively.
         degrees : bool, default False
             Specify whether the angular rates are given in degrees or radians.
         """
-        f_imu = np.asarray(f_imu, dtype=float)
-        w_imu = np.asarray(w_imu, dtype=float)
+        f = np.asarray(f, dtype=float)
+        w = np.asarray(w, dtype=float)
 
         if degrees:
-            w_imu = (np.pi / 180.0) * w_imu
-
-        f = f_imu - self._ba
-        w = w_imu - self._bg
+            w = (np.pi / 180.0) * w
 
         # Accelerometer and gyro pulse vector counts from l to l+1
-        if self._f_prev is not None or self._w_prev is not None:  # first sample
+        if self._f_prev is None or self._w_prev is None:  # first sample
             dvel = f * self._dt  # backward Euler
             dtheta = w * self._dt  # backward Euler
         else:
@@ -98,17 +93,26 @@ def update(self, f_imu: ArrayLike, w_imu: ArrayLike, degrees: bool = False):
         )
         self._beta += dtheta
 
-        self._f_prev = f
-        self._w_prev = w
-        self._dtheta_prev = dtheta
+        self._f_prev = f.copy()
+        self._w_prev = w.copy()
+        self._dtheta_prev = dtheta.copy()
 
-    def dtheta(self):
+    def dtheta(self, degrees=False):
         """
         The accumulated 'body attitude change' vector. I.e., the rotation vector
         describing the total rotation over all samples since initialization (or
         last reset).
+
+        Parameters
+        ----------
+        degrees : bool, default False
+            Specifies whether the returned rotation vector should be in degrees
+            or radians (default).
         """
-        return self._beta + self._dbeta
+        dtheta = self._beta + self._dbeta
+        if degrees:
+            dtheta *= (180.0 / np.pi)
+        return dtheta
 
     def dvel(self):
         """

From e9116eca7e495afec53c0ca6a38da78953a189ba Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Mon, 8 Dec 2025 13:35:12 +0100
Subject: [PATCH 11/42] some changesw

---
 src/smsfusion/_coning_sculling.py | 91 +++++++++++++++++++++++++++++--
 1 file changed, 85 insertions(+), 6 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index f64f4979..279c0f00 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -53,6 +53,82 @@ def __init__(self, fs: float):
         self._u = np.zeros(3, dtype=float)
         self._f_prev = None
 
+    # def _coning_update(self, w):
+    #     """
+    #     Update the coning integrals using new gyroscope measurements, w[l+1].
+
+    #     Coning algorithm:
+
+    #         phi := beta + dbeta
+
+    #     where,
+
+    #         dtheta[l] = dt * (w[l+1] - w[l])
+    #         dbeta[l+1] = dbeta[l] + 0.5 * cross((beta[l] + (1/6) * dtheta[l-1]), dtheta[l])
+    #         beta[l+1] = beta[l] + dtheta[l]
+
+    #     with initial conditions,
+    #         beta[0] = [0, 0, 0]
+    #         dbeta[0] = [0, 0, 0]
+
+    #     Parameters
+    #     ----------
+    #     w : numpy.ndarray
+    #         Bias corrected angular rate measurements.
+    #     """
+    #     # if self._w_prev is None:  # first sample
+    #     #     dtheta = w * self._dt  # backward Euler
+    #     # else:
+    #     #     dtheta = 0.5 * (w + self._w_prev) * self._dt  # trapezoidal
+    #     dtheta = w * self._dt  # backward Euler
+    #     self._dbeta += 0.5 * _cross(
+    #         self._beta + (1.0 / 6.0) * self._dtheta_prev, dtheta
+    #     )
+    #     self._beta += dtheta
+
+    #     self._w_prev = w
+    #     self._dtheta_prev = dtheta
+
+    # def _sculling_update(self, f):
+    #     """
+    #     Update the sculling integrals using new accelerometer measurements, f[l+1].
+    #     """
+    #     # dvel = f * self._dt
+    #     # if self._f_prev is None:  # first sample
+    #     #     dvel = f * self._dt  # backward Euler
+    #     # else:
+    #     #     dvel = 0.5 * (f + self._f_prev) * self._dt  # trapezoidal
+    #     dvel = f * self._dt  # backward Euler
+    #     self._gamma1 += np.cross(self._beta + 0.5 * self._dtheta_prev, dvel)
+    #     self._u += dvel
+    #     self._f_prev = f
+
+    # def update(self, f_imu: ArrayLike, w_imu: ArrayLike, degrees: bool = False):
+    #     """
+    #     Update.
+
+    #     Parameters
+    #     ----------
+    #     f_imu : array-like, shape (3,)
+    #         Specific force measurements (i.e., accelerations + gravity), given
+    #         as [f_x, f_y, f_z]^T where f_x, f_y and f_z are
+    #         acceleration measurements in x-, y-, and z-direction, respectively.
+    #     w_imu : array-like, shape (3,)
+    #         Angular rate measurements, given as [w_x, w_y, w_z]^T where
+    #         w_x, w_y and w_z are angular rates about the x-, y-,
+    #         and z-axis, respectively.
+    #     degrees : bool, default False
+    #         Specify whether the angular rates are given in degrees or radians.
+    #     """
+    #     f_imu = np.asarray(f_imu, dtype=float)
+    #     w_imu = np.asarray(w_imu, dtype=float)
+
+    #     if degrees:
+    #         w_imu = (np.pi / 180.0) * w_imu
+
+    #     self._sculling_update(f_imu)
+    #     self._coning_update(w_imu)
+
     def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
         """
         Update the coning (dtheta) and sculling (dvel) integrals using new IMU measurements.
@@ -76,12 +152,15 @@ def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
             w = (np.pi / 180.0) * w
 
         # Accelerometer and gyro pulse vector counts from l to l+1
-        if self._f_prev is None or self._w_prev is None:  # first sample
-            dvel = f * self._dt  # backward Euler
-            dtheta = w * self._dt  # backward Euler
-        else:
-            dvel = 0.5 * (f + self._f_prev) * self._dt  # trapezoidal
-            dtheta = 0.5 * (w + self._w_prev) * self._dt  # trapezoidal
+        # if self._f_prev is None or self._w_prev is None:  # first sample
+        #     dvel = f * self._dt  # backward Euler
+        #     dtheta = w * self._dt  # backward Euler
+        # else:
+        #     dvel = 0.5 * (f + self._f_prev) * self._dt  # trapezoidal
+        #     dtheta = 0.5 * (w + self._w_prev) * self._dt  # trapezoidal
+
+        dvel = f * self._dt  # backward Euler
+        dtheta = w * self._dt  # backward Euler
 
         # Sculling update
         self._gamma1 += np.cross(self._beta + 0.5 * dtheta, dvel)

From 843c43d3e33cf4e90af8920f267ad7c749bdd84d Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Mon, 8 Dec 2025 13:35:34 +0100
Subject: [PATCH 12/42] delete commented out code

---
 src/smsfusion/_coning_sculling.py | 76 -------------------------------
 1 file changed, 76 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 279c0f00..412e8484 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -53,82 +53,6 @@ def __init__(self, fs: float):
         self._u = np.zeros(3, dtype=float)
         self._f_prev = None
 
-    # def _coning_update(self, w):
-    #     """
-    #     Update the coning integrals using new gyroscope measurements, w[l+1].
-
-    #     Coning algorithm:
-
-    #         phi := beta + dbeta
-
-    #     where,
-
-    #         dtheta[l] = dt * (w[l+1] - w[l])
-    #         dbeta[l+1] = dbeta[l] + 0.5 * cross((beta[l] + (1/6) * dtheta[l-1]), dtheta[l])
-    #         beta[l+1] = beta[l] + dtheta[l]
-
-    #     with initial conditions,
-    #         beta[0] = [0, 0, 0]
-    #         dbeta[0] = [0, 0, 0]
-
-    #     Parameters
-    #     ----------
-    #     w : numpy.ndarray
-    #         Bias corrected angular rate measurements.
-    #     """
-    #     # if self._w_prev is None:  # first sample
-    #     #     dtheta = w * self._dt  # backward Euler
-    #     # else:
-    #     #     dtheta = 0.5 * (w + self._w_prev) * self._dt  # trapezoidal
-    #     dtheta = w * self._dt  # backward Euler
-    #     self._dbeta += 0.5 * _cross(
-    #         self._beta + (1.0 / 6.0) * self._dtheta_prev, dtheta
-    #     )
-    #     self._beta += dtheta
-
-    #     self._w_prev = w
-    #     self._dtheta_prev = dtheta
-
-    # def _sculling_update(self, f):
-    #     """
-    #     Update the sculling integrals using new accelerometer measurements, f[l+1].
-    #     """
-    #     # dvel = f * self._dt
-    #     # if self._f_prev is None:  # first sample
-    #     #     dvel = f * self._dt  # backward Euler
-    #     # else:
-    #     #     dvel = 0.5 * (f + self._f_prev) * self._dt  # trapezoidal
-    #     dvel = f * self._dt  # backward Euler
-    #     self._gamma1 += np.cross(self._beta + 0.5 * self._dtheta_prev, dvel)
-    #     self._u += dvel
-    #     self._f_prev = f
-
-    # def update(self, f_imu: ArrayLike, w_imu: ArrayLike, degrees: bool = False):
-    #     """
-    #     Update.
-
-    #     Parameters
-    #     ----------
-    #     f_imu : array-like, shape (3,)
-    #         Specific force measurements (i.e., accelerations + gravity), given
-    #         as [f_x, f_y, f_z]^T where f_x, f_y and f_z are
-    #         acceleration measurements in x-, y-, and z-direction, respectively.
-    #     w_imu : array-like, shape (3,)
-    #         Angular rate measurements, given as [w_x, w_y, w_z]^T where
-    #         w_x, w_y and w_z are angular rates about the x-, y-,
-    #         and z-axis, respectively.
-    #     degrees : bool, default False
-    #         Specify whether the angular rates are given in degrees or radians.
-    #     """
-    #     f_imu = np.asarray(f_imu, dtype=float)
-    #     w_imu = np.asarray(w_imu, dtype=float)
-
-    #     if degrees:
-    #         w_imu = (np.pi / 180.0) * w_imu
-
-    #     self._sculling_update(f_imu)
-    #     self._coning_update(w_imu)
-
     def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
         """
         Update the coning (dtheta) and sculling (dvel) integrals using new IMU measurements.

From 088aeaede26ee8b2421bb8b08873bf8eea3b56e4 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 11 Dec 2025 10:31:27 +0100
Subject: [PATCH 13/42] comment out trapezoid integral

---
 src/smsfusion/_coning_sculling.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 412e8484..c4a172c4 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -46,12 +46,12 @@ def __init__(self, fs: float):
         self._beta = np.zeros(3, dtype=float)
         self._dbeta = np.zeros(3, dtype=float)
         self._dtheta_prev = np.zeros(3, dtype=float)
-        self._w_prev = None
+        # self._w_prev = None
 
         # Sculling params
         self._gamma1 = np.zeros(3, dtype=float)
         self._u = np.zeros(3, dtype=float)
-        self._f_prev = None
+        # self._f_prev = None
 
     def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
         """
@@ -96,8 +96,8 @@ def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
         )
         self._beta += dtheta
 
-        self._f_prev = f.copy()
-        self._w_prev = w.copy()
+        # self._f_prev = f.copy()
+        # self._w_prev = w.copy()
         self._dtheta_prev = dtheta.copy()
 
     def dtheta(self, degrees=False):

From 153ad481ed6719b61169ffb039fbafd27008cb41 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 11 Dec 2025 10:34:19 +0100
Subject: [PATCH 14/42] docstrign

---
 src/smsfusion/_coning_sculling.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index c4a172c4..51a37ecc 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -11,15 +11,15 @@ class ConingScullingAlg:
     Integrates an IMU's specific force and angular rate measurements to coning and
     sculling corrected velocity (dvel) and attitude (dtheta) changes.
 
-    For use in a strapdown algorithm as:
+    Can be used in a strapdown algorithm as:
 
         vel[m+1] = vel[m] + R(q[m]) @ dvel[m] + dvel_corr
         q[m+1] = q[m] ⊗ h(dtheta[m])
 
     where,
 
-        dvel_corr = [0, 0, g] (if NED)
-        dvel_corr = [0, 0, -g] (if ENU)
+        dvel_corr = [0, 0, g] (if 'NED')
+        dvel_corr = [0, 0, -g] (if 'ENU')
 
     and,
 

From e3b4fc5a8dcca9a3c90bd7f7969f536e5fed63c7 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 11 Dec 2025 10:56:28 +0100
Subject: [PATCH 15/42] wnd order sculling

---
 src/smsfusion/_coning_sculling.py | 16 ++++++++++++----
 1 file changed, 12 insertions(+), 4 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 51a37ecc..a1526c10 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -51,6 +51,7 @@ def __init__(self, fs: float):
         # Sculling params
         self._gamma1 = np.zeros(3, dtype=float)
         self._u = np.zeros(3, dtype=float)
+        self._dvel_prev = np.zeros(3, dtype=float)
         # self._f_prev = None
 
     def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
@@ -86,8 +87,14 @@ def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
         dvel = f * self._dt  # backward Euler
         dtheta = w * self._dt  # backward Euler
 
-        # Sculling update
-        self._gamma1 += np.cross(self._beta + 0.5 * dtheta, dvel)
+        # Sculling update 1st order
+        # self._gamma1 += np.cross(self._beta + 0.5 * dtheta, dvel)
+        # self._u += dvel
+
+        # Sculling update 2nd order
+        self._gamma1 += np.cross(self._beta + 0.5 * dtheta, dvel) + (1.0 / 12.0) * (
+            np.cross(self._dtheta_prev, dvel) + np.cross(self._dvel_prev, dtheta)
+        )
         self._u += dvel
 
         # Coning update
@@ -98,6 +105,7 @@ def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
 
         # self._f_prev = f.copy()
         # self._w_prev = w.copy()
+        self._dvel_prev = dvel.copy()
         self._dtheta_prev = dtheta.copy()
 
     def dtheta(self, degrees=False):
@@ -114,12 +122,12 @@ def dtheta(self, degrees=False):
         """
         dtheta = self._beta + self._dbeta
         if degrees:
-            dtheta *= (180.0 / np.pi)
+            dtheta *= 180.0 / np.pi
         return dtheta
 
     def dvel(self):
         """
-        The accumulated specific force velocity vector change. I.e., 
+        The accumulated specific force velocity vector change. I.e.,
         the total change in velocity (no gravity correction) over all samples since
         initialization (or last reset).
         """

From 48ec92b625e4ad7a5daf13d5d5d06b0b7c8a2ae1 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 11 Dec 2025 14:32:11 +0100
Subject: [PATCH 16/42] S2 version

---
 src/smsfusion/_coning_sculling.py | 20 +++++++++++++-------
 1 file changed, 13 insertions(+), 7 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index a1526c10..b3ceca6e 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -49,9 +49,10 @@ def __init__(self, fs: float):
         # self._w_prev = None
 
         # Sculling params
-        self._gamma1 = np.zeros(3, dtype=float)
+        self._gamma2 = np.zeros(3, dtype=float)
+        # self._gamma1 = np.zeros(3, dtype=float)
         self._u = np.zeros(3, dtype=float)
-        self._dvel_prev = np.zeros(3, dtype=float)
+        # self._dvel_prev = np.zeros(3, dtype=float)
         # self._f_prev = None
 
     def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
@@ -91,12 +92,16 @@ def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
         # self._gamma1 += np.cross(self._beta + 0.5 * dtheta, dvel)
         # self._u += dvel
 
-        # Sculling update 2nd order
-        self._gamma1 += np.cross(self._beta + 0.5 * dtheta, dvel) + (1.0 / 12.0) * (
-            np.cross(self._dtheta_prev, dvel) + np.cross(self._dvel_prev, dtheta)
-        )
+        # Sculling update 1st order
+        self._gamma2 += 0.5 * (np.cross(self._beta, dvel) + np.cross(self._u, dtheta))
         self._u += dvel
 
+        # # Sculling update 2nd order
+        # self._gamma1 += np.cross(self._beta + 0.5 * dtheta, dvel) + (1.0 / 12.0) * (
+        #     np.cross(self._dtheta_prev, dvel) + np.cross(self._dvel_prev, dtheta)
+        # )
+        # self._u += dvel
+
         # Coning update
         self._dbeta += 0.5 * _cross(
             self._beta + (1.0 / 6.0) * self._dtheta_prev, dtheta
@@ -131,7 +136,7 @@ def dvel(self):
         the total change in velocity (no gravity correction) over all samples since
         initialization (or last reset).
         """
-        return self._u + self._gamma1
+        return self._u + 0.5 * np.cross(self._beta, self._u) + self._gamma2
 
     def reset(self):
         """
@@ -140,4 +145,5 @@ def reset(self):
         self._beta = np.zeros(3, dtype=float)
         self._dbeta = np.zeros(3, dtype=float)
         self._gamma1 = np.zeros(3, dtype=float)
+        self._gamma2 = np.zeros(3, dtype=float)
         self._u = np.zeros(3, dtype=float)

From 2a649f77ee654a29ce75d03c1ce1e9947660cdf0 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 11 Dec 2025 14:37:32 +0100
Subject: [PATCH 17/42] 2nd order S2 version

---
 src/smsfusion/_coning_sculling.py | 10 +++++++---
 1 file changed, 7 insertions(+), 3 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index b3ceca6e..8faa21f7 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -52,7 +52,7 @@ def __init__(self, fs: float):
         self._gamma2 = np.zeros(3, dtype=float)
         # self._gamma1 = np.zeros(3, dtype=float)
         self._u = np.zeros(3, dtype=float)
-        # self._dvel_prev = np.zeros(3, dtype=float)
+        self._dvel_prev = np.zeros(3, dtype=float)
         # self._f_prev = None
 
     def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
@@ -92,8 +92,12 @@ def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
         # self._gamma1 += np.cross(self._beta + 0.5 * dtheta, dvel)
         # self._u += dvel
 
-        # Sculling update 1st order
-        self._gamma2 += 0.5 * (np.cross(self._beta, dvel) + np.cross(self._u, dtheta))
+        # # Sculling update 1st order
+        # self._gamma2 += 0.5 * (np.cross(self._beta, dvel) + np.cross(self._u, dtheta))
+        # self._u += dvel
+
+        # Sculling update 2nd order
+        self._gamma2 += 0.5 * (np.cross(self._beta + (1.0 / 6.0) * self._dtheta_prev, dvel) + np.cross(self._u + (1.0 / 6.0) * self._dvel_prev, dtheta))
         self._u += dvel
 
         # # Sculling update 2nd order

From ab3e55072c5513293297176bef58837ef10f8fea Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Fri, 12 Dec 2025 09:11:25 +0100
Subject: [PATCH 18/42] renaming, refactoring and deleting old code

---
 src/smsfusion/_coning_sculling.py | 75 +++++++++++--------------------
 1 file changed, 26 insertions(+), 49 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 8faa21f7..04be0011 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -43,17 +43,14 @@ def __init__(self, fs: float):
         self._dt = 1.0 / fs
 
         # Coning params
-        self._beta = np.zeros(3, dtype=float)
-        self._dbeta = np.zeros(3, dtype=float)
+        self._theta = np.zeros(3, dtype=float)
+        self._dtheta_con = np.zeros(3, dtype=float)
         self._dtheta_prev = np.zeros(3, dtype=float)
-        # self._w_prev = None
 
         # Sculling params
-        self._gamma2 = np.zeros(3, dtype=float)
-        # self._gamma1 = np.zeros(3, dtype=float)
-        self._u = np.zeros(3, dtype=float)
-        self._dvel_prev = np.zeros(3, dtype=float)
-        # self._f_prev = None
+        self._vel = np.zeros(3, dtype=float)
+        self._dvel_scul = np.zeros(3, dtype=float)
+        self._dv_prev = np.zeros(3, dtype=float)
 
     def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
         """
@@ -77,44 +74,23 @@ def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
         if degrees:
             w = (np.pi / 180.0) * w
 
-        # Accelerometer and gyro pulse vector counts from l to l+1
-        # if self._f_prev is None or self._w_prev is None:  # first sample
-        #     dvel = f * self._dt  # backward Euler
-        #     dtheta = w * self._dt  # backward Euler
-        # else:
-        #     dvel = 0.5 * (f + self._f_prev) * self._dt  # trapezoidal
-        #     dtheta = 0.5 * (w + self._w_prev) * self._dt  # trapezoidal
-
-        dvel = f * self._dt  # backward Euler
+        dv = f * self._dt  # backward Euler
         dtheta = w * self._dt  # backward Euler
 
-        # Sculling update 1st order
-        # self._gamma1 += np.cross(self._beta + 0.5 * dtheta, dvel)
-        # self._u += dvel
-
-        # # Sculling update 1st order
-        # self._gamma2 += 0.5 * (np.cross(self._beta, dvel) + np.cross(self._u, dtheta))
-        # self._u += dvel
-
         # Sculling update 2nd order
-        self._gamma2 += 0.5 * (np.cross(self._beta + (1.0 / 6.0) * self._dtheta_prev, dvel) + np.cross(self._u + (1.0 / 6.0) * self._dvel_prev, dtheta))
-        self._u += dvel
-
-        # # Sculling update 2nd order
-        # self._gamma1 += np.cross(self._beta + 0.5 * dtheta, dvel) + (1.0 / 12.0) * (
-        #     np.cross(self._dtheta_prev, dvel) + np.cross(self._dvel_prev, dtheta)
-        # )
-        # self._u += dvel
+        self._dvel_scul += 0.5 * (
+            np.cross(self._theta + (1.0 / 6.0) * self._dtheta_prev, dv)
+            + np.cross(self._vel + (1.0 / 6.0) * self._dv_prev, dtheta)
+        )
+        self._vel += dv
 
         # Coning update
-        self._dbeta += 0.5 * _cross(
-            self._beta + (1.0 / 6.0) * self._dtheta_prev, dtheta
+        self._dtheta_con += 0.5 * _cross(
+            self._theta + (1.0 / 6.0) * self._dtheta_prev, dtheta
         )
-        self._beta += dtheta
+        self._theta += dtheta
 
-        # self._f_prev = f.copy()
-        # self._w_prev = w.copy()
-        self._dvel_prev = dvel.copy()
+        self._dv_prev = dv.copy()
         self._dtheta_prev = dtheta.copy()
 
     def dtheta(self, degrees=False):
@@ -129,10 +105,12 @@ def dtheta(self, degrees=False):
             Specifies whether the returned rotation vector should be in degrees
             or radians (default).
         """
-        dtheta = self._beta + self._dbeta
-        if degrees:
-            dtheta *= 180.0 / np.pi
-        return dtheta
+        dtheta = self._theta + self._dtheta_con
+        return np.degrees(dtheta) if degrees else dtheta
+
+    @property
+    def _dvel_rot(self):
+        return 0.5 * np.cross(self._theta, self._vel)
 
     def dvel(self):
         """
@@ -140,14 +118,13 @@ def dvel(self):
         the total change in velocity (no gravity correction) over all samples since
         initialization (or last reset).
         """
-        return self._u + 0.5 * np.cross(self._beta, self._u) + self._gamma2
+        return self._vel + self._dvel_rot + self._dvel_scul
 
     def reset(self):
         """
         Reset the coning (dtheta) and sculling (dvel) integrals to zero.
         """
-        self._beta = np.zeros(3, dtype=float)
-        self._dbeta = np.zeros(3, dtype=float)
-        self._gamma1 = np.zeros(3, dtype=float)
-        self._gamma2 = np.zeros(3, dtype=float)
-        self._u = np.zeros(3, dtype=float)
+        self._theta = np.zeros(3, dtype=float)
+        self._dtheta_con = np.zeros(3, dtype=float)
+        self._dvel_scul = np.zeros(3, dtype=float)
+        self._vel = np.zeros(3, dtype=float)

From f0dde5bbff019b6837606bfe6664ba9094658b2b Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Fri, 12 Dec 2025 09:21:19 +0100
Subject: [PATCH 19/42] update references

---
 src/smsfusion/_coning_sculling.py | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 04be0011..cdda6cf0 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -30,12 +30,13 @@ class ConingScullingAlg:
     - h(dtheta[m]) is the unit quaternion representation of the rotation increment
       over the interval [m, m+1].
 
-    The coning and sculling integrals are computed according to Eq. (26) and Eq. (55)
-    in ref [1]_.
+    The coning and sculling integrals are computed using a 2nd order algorithm as
+    described in [1]_ and [2]_.
 
     References
     ----------
     .. [1] https://apps.dtic.mil/sti/tr/pdf/ADP003621.pdf
+    .. [2] https://strapdownassociates.com/Strapdown%20Analytics%20II%20Part%201.pdf
     """
 
     def __init__(self, fs: float):
@@ -77,14 +78,14 @@ def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
         dv = f * self._dt  # backward Euler
         dtheta = w * self._dt  # backward Euler
 
-        # Sculling update 2nd order
+        # (2nd order) sculling update, see (Eq. 7.2.2.2.2-15) in ref [2]_
         self._dvel_scul += 0.5 * (
             np.cross(self._theta + (1.0 / 6.0) * self._dtheta_prev, dv)
             + np.cross(self._vel + (1.0 / 6.0) * self._dv_prev, dtheta)
         )
         self._vel += dv
 
-        # Coning update
+        # Coning update, see (Eq. 26) in ref [1]_
         self._dtheta_con += 0.5 * _cross(
             self._theta + (1.0 / 6.0) * self._dtheta_prev, dtheta
         )

From df3767c860ad926e5110886b8cf149ae0f86b22e Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Fri, 12 Dec 2025 09:23:50 +0100
Subject: [PATCH 20/42] fix eq comment

---
 src/smsfusion/_coning_sculling.py | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index cdda6cf0..287678bc 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -78,14 +78,15 @@ def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
         dv = f * self._dt  # backward Euler
         dtheta = w * self._dt  # backward Euler
 
-        # (2nd order) sculling update, see (Eq. 7.2.2.2.2-15) in ref [2]_
+        # (2nd order) sculling update
+        # See Eq. (7.2.2.2.2-15) in ref [2]_ and Eq. (56) in ref [1]_
         self._dvel_scul += 0.5 * (
             np.cross(self._theta + (1.0 / 6.0) * self._dtheta_prev, dv)
             + np.cross(self._vel + (1.0 / 6.0) * self._dv_prev, dtheta)
         )
         self._vel += dv
 
-        # Coning update, see (Eq. 26) in ref [1]_
+        # Coning update, see Eq. (26) in ref [1]_
         self._dtheta_con += 0.5 * _cross(
             self._theta + (1.0 / 6.0) * self._dtheta_prev, dtheta
         )

From 94e7d87637567ab5a9740d2fd46f4a5c95521062 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Fri, 12 Dec 2025 09:27:42 +0100
Subject: [PATCH 21/42] small fix

---
 src/smsfusion/_coning_sculling.py | 15 ++++++++-------
 1 file changed, 8 insertions(+), 7 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 287678bc..8f40b576 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -86,14 +86,15 @@ def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
         )
         self._vel += dv
 
-        # Coning update, see Eq. (26) in ref [1]_
+        # Coning update
+        # See Eq. (26) in ref [1]_
         self._dtheta_con += 0.5 * _cross(
             self._theta + (1.0 / 6.0) * self._dtheta_prev, dtheta
         )
         self._theta += dtheta
 
-        self._dv_prev = dv.copy()
-        self._dtheta_prev = dtheta.copy()
+        self._dv_prev[:] = dv
+        self._dtheta_prev[:] = dtheta
 
     def dtheta(self, degrees=False):
         """
@@ -126,7 +127,7 @@ def reset(self):
         """
         Reset the coning (dtheta) and sculling (dvel) integrals to zero.
         """
-        self._theta = np.zeros(3, dtype=float)
-        self._dtheta_con = np.zeros(3, dtype=float)
-        self._dvel_scul = np.zeros(3, dtype=float)
-        self._vel = np.zeros(3, dtype=float)
+        self._theta[:] = np.zeros(3, dtype=float)
+        self._dtheta_con[:] = np.zeros(3, dtype=float)
+        self._dvel_scul[:] = np.zeros(3, dtype=float)
+        self._vel[:] = np.zeros(3, dtype=float)

From 4104debe96578c18900ac1e9294697467f438340 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Fri, 12 Dec 2025 09:44:09 +0100
Subject: [PATCH 22/42] small fix

---
 src/smsfusion/_coning_sculling.py | 28 +++++++++++++++++-----------
 1 file changed, 17 insertions(+), 11 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 8f40b576..57d9d20d 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -75,26 +75,32 @@ def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
         if degrees:
             w = (np.pi / 180.0) * w
 
+        # View for readability
+        theta = self._theta
+        dtheta_con = self._dtheta_con
+        dtheta_prev = self._dtheta_prev
+        vel = self._vel
+        dvel_scul = self._dvel_scul
+        dv_prev = self._dv_prev
+
         dv = f * self._dt  # backward Euler
         dtheta = w * self._dt  # backward Euler
 
         # (2nd order) sculling update
         # See Eq. (7.2.2.2.2-15) in ref [2]_ and Eq. (56) in ref [1]_
-        self._dvel_scul += 0.5 * (
-            np.cross(self._theta + (1.0 / 6.0) * self._dtheta_prev, dv)
-            + np.cross(self._vel + (1.0 / 6.0) * self._dv_prev, dtheta)
+        dvel_scul += 0.5 * (
+            _cross(theta + (1.0 / 6.0) * dtheta_prev, dv)
+            + _cross(vel + (1.0 / 6.0) * dv_prev, dtheta)
         )
-        self._vel += dv
+        vel += dv
 
         # Coning update
         # See Eq. (26) in ref [1]_
-        self._dtheta_con += 0.5 * _cross(
-            self._theta + (1.0 / 6.0) * self._dtheta_prev, dtheta
-        )
-        self._theta += dtheta
+        dtheta_con += 0.5 * _cross(theta + (1.0 / 6.0) * dtheta_prev, dtheta)
+        theta += dtheta
 
-        self._dv_prev[:] = dv
-        self._dtheta_prev[:] = dtheta
+        dv_prev[:] = dv
+        dtheta_prev[:] = dtheta
 
     def dtheta(self, degrees=False):
         """
@@ -113,7 +119,7 @@ def dtheta(self, degrees=False):
 
     @property
     def _dvel_rot(self):
-        return 0.5 * np.cross(self._theta, self._vel)
+        return 0.5 * _cross(self._theta, self._vel)
 
     def dvel(self):
         """

From 722a45a38260959818fbe615fd429ac877519b0f Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Fri, 12 Dec 2025 10:00:57 +0100
Subject: [PATCH 23/42] docstring fix

---
 src/smsfusion/_coning_sculling.py | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 57d9d20d..86f51f62 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -29,6 +29,10 @@ class ConingScullingAlg:
       step m to m+1.
     - h(dtheta[m]) is the unit quaternion representation of the rotation increment
       over the interval [m, m+1].
+    - R(q[m]) is the rotation matrix (body-to-nav) corresponding to the attitude
+      quaternion q[m].
+
+    Here, ⊗ denotes quaternion multiplication (Hamilton product) and R(q).
 
     The coning and sculling integrals are computed using a 2nd order algorithm as
     described in [1]_ and [2]_.

From 72ff53cdd115a1c3b79651a08552b056ebc54b39 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Fri, 12 Dec 2025 10:07:26 +0100
Subject: [PATCH 24/42] docstring

---
 src/smsfusion/_coning_sculling.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 86f51f62..76bfa8e3 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -71,7 +71,7 @@ def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
             Angular rate measurements [w_x, w_y, w_z], where w_x, w_y and w_z are
             angular rates about the x-, y-, and z-axis, respectively.
         degrees : bool, default False
-            Specify whether the angular rates are given in degrees or radians.
+            Specifies whether the angular rates are given in degrees or radians (default).
         """
         f = np.asarray(f, dtype=float)
         w = np.asarray(w, dtype=float)

From 20d5ff00ea4f69dcdab4da160696a360f79e7028 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Fri, 12 Dec 2025 10:08:43 +0100
Subject: [PATCH 25/42] docstring fix

---
 src/smsfusion/_coning_sculling.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 76bfa8e3..6e55d159 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -90,7 +90,7 @@ def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
         dv = f * self._dt  # backward Euler
         dtheta = w * self._dt  # backward Euler
 
-        # (2nd order) sculling update
+        # Sculling update (2nd order)
         # See Eq. (7.2.2.2.2-15) in ref [2]_ and Eq. (56) in ref [1]_
         dvel_scul += 0.5 * (
             _cross(theta + (1.0 / 6.0) * dtheta_prev, dv)

From dc001892692392d8d4dc77c0ab6b049c6d589a02 Mon Sep 17 00:00:00 2001
From: Ali Cetin <ali.cetin@4subsea.com>
Date: Thu, 18 Dec 2025 10:06:40 +0100
Subject: [PATCH 26/42] small updates to docstring

---
 src/smsfusion/_coning_sculling.py | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 6e55d159..ade67223 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -8,18 +8,18 @@ class ConingScullingAlg:
     """
     Coning and sculling algorithm.
 
-    Integrates an IMU's specific force and angular rate measurements to coning and
+    Integrates the specific force and angular rate measurements to coning and
     sculling corrected velocity (dvel) and attitude (dtheta) changes.
 
     Can be used in a strapdown algorithm as:
 
         vel[m+1] = vel[m] + R(q[m]) @ dvel[m] + dvel_corr
-        q[m+1] = q[m] ⊗ h(dtheta[m])
+        q[m+1] = q[m] ⊗ dq(dtheta[m])
 
     where,
 
-        dvel_corr = [0, 0, g] (if 'NED')
-        dvel_corr = [0, 0, -g] (if 'ENU')
+        dvel_corr = [0, 0, g * dt] (if 'NED')
+        dvel_corr = [0, 0, -g * dt] (if 'ENU')
 
     and,
 
@@ -27,20 +27,20 @@ class ConingScullingAlg:
       correction) from time step m to m+1.
     - dtheta[m] is the coning integral, i.e., the rotation vector change from time
       step m to m+1.
-    - h(dtheta[m]) is the unit quaternion representation of the rotation increment
+    - dq(dtheta[m]) is the unit quaternion representation of the rotation increment
       over the interval [m, m+1].
     - R(q[m]) is the rotation matrix (body-to-nav) corresponding to the attitude
       quaternion q[m].
 
-    Here, ⊗ denotes quaternion multiplication (Hamilton product) and R(q).
+    Here, ⊗ denotes quaternion multiplication (Hamilton product).
 
     The coning and sculling integrals are computed using a 2nd order algorithm as
     described in [1]_ and [2]_.
 
     References
     ----------
-    .. [1] https://apps.dtic.mil/sti/tr/pdf/ADP003621.pdf
-    .. [2] https://strapdownassociates.com/Strapdown%20Analytics%20II%20Part%201.pdf
+    .. [1] Savage, Paul G., Strapdown System Algorithms, AD-P003 621, https://apps.dtic.mil/sti/tr/pdf/ADP003621.pdf
+    .. [2] Savage, Paul G., Strapdown Analytics, 2nd Edition, Part 1, 2007, https://strapdownassociates.com/Strapdown%20Analytics%20II%20Part%201.pdf
     """
 
     def __init__(self, fs: float):

From d45ae00e527fa1d77202e21a8cb0fee6e25510df Mon Sep 17 00:00:00 2001
From: Ali Cetin <ali.cetin@4subsea.com>
Date: Thu, 18 Dec 2025 10:06:53 +0100
Subject: [PATCH 27/42] small updates to docstring

---
 src/smsfusion/_coning_sculling.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index ade67223..ce30ae16 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -59,7 +59,7 @@ def __init__(self, fs: float):
 
     def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
         """
-        Update the coning (dtheta) and sculling (dvel) integrals using new IMU measurements.
+        Update the coning (dtheta) and sculling (dvel) integrals using new measurements.
 
         Parameters
         ----------

From b7086d510b87c54edd894054cd894b1abf587617 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 18 Dec 2025 11:05:34 +0100
Subject: [PATCH 28/42] test init

---
 tests/test_coning_sculling.py | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)
 create mode 100644 tests/test_coning_sculling.py

diff --git a/tests/test_coning_sculling.py b/tests/test_coning_sculling.py
new file mode 100644
index 00000000..69fd51c3
--- /dev/null
+++ b/tests/test_coning_sculling.py
@@ -0,0 +1,17 @@
+import numpy as np
+import smsfusion as sf
+
+
+class Test_ConingScullingAlg:
+
+    def test__init__(self):
+        alg = sf.ConingScullingAlg(256.0)
+
+        alg._fs == 256.0
+        alg._dt == 1.0 / 256.0
+        np.testing.assert_allclose(alg._theta, np.zeros(3))
+        np.testing.assert_allclose(alg._dtheta_con, np.zeros(3))
+        np.testing.assert_allclose(alg._dtheta_prev, np.zeros(3))
+        np.testing.assert_allclose(alg._vel, np.zeros(3))
+        np.testing.assert_allclose(alg._dvel_scul, np.zeros(3))
+        np.testing.assert_allclose(alg._dv_prev, np.zeros(3))

From 586c0ec2028ad301fd215a9ab6e3c43fbfde98af Mon Sep 17 00:00:00 2001
From: Ali Cetin <ali.cetin@4subsea.com>
Date: Thu, 18 Dec 2025 13:16:49 +0100
Subject: [PATCH 29/42] add flush, remove reset

---
 src/smsfusion/_coning_sculling.py | 25 ++++++++++++++++++++++---
 1 file changed, 22 insertions(+), 3 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index ce30ae16..aa4a50a8 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -127,17 +127,36 @@ def _dvel_rot(self):
 
     def dvel(self):
         """
-        The accumulated specific force velocity vector change. I.e.,
+        The accumulated specific force velocity change vector. I.e.,
         the total change in velocity (no gravity correction) over all samples since
         initialization (or last reset).
         """
         return self._vel + self._dvel_rot + self._dvel_scul
 
-    def reset(self):
+    def flush(self, degrees=False):
         """
-        Reset the coning (dtheta) and sculling (dvel) integrals to zero.
+        Return dtheta (the accumulated 'body attitude change' vector) and
+        dvel (the accumulated specific force velocity change vector), and reset
+        the coning (dtheta) and sculling (dvel) integrals to zero.
+
+        Parameters
+        ----------
+        degrees : bool, default False
+            Specifies whether the returned rotation vector should be in degrees
+            or radians (default).
+
+        Returns
+        -------
+        dtheta : ndarray, shape (3,)
+            The accumulated 'body attitude change' vector, see :meth:`dtheta`.
+        dvel : ndarray, shape (3,)
+            The accumulated specific force velocity change vector, see :meth:`dvel`.
         """
+        dtheta = self.dtheta(degrees=degrees)
+        dvel = self.dvel()
+
         self._theta[:] = np.zeros(3, dtype=float)
         self._dtheta_con[:] = np.zeros(3, dtype=float)
         self._dvel_scul[:] = np.zeros(3, dtype=float)
         self._vel[:] = np.zeros(3, dtype=float)
+        return dtheta, dvel
\ No newline at end of file

From eae10dd558b4708af49b3b1906da934f941e1403 Mon Sep 17 00:00:00 2001
From: Ali Cetin <ali.cetin@4subsea.com>
Date: Thu, 18 Dec 2025 13:18:26 +0100
Subject: [PATCH 30/42] docstring

---
 src/smsfusion/_coning_sculling.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index aa4a50a8..839c2b0e 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -108,9 +108,9 @@ def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
 
     def dtheta(self, degrees=False):
         """
-        The accumulated 'body attitude change' vector. I.e., the rotation vector
-        describing the total rotation over all samples since initialization (or
-        last reset).
+        Peek at the accumulated 'body attitude change' vector. I.e., the rotation
+        vector describing the total rotation over all samples since
+        initialization (or last reset).
 
         Parameters
         ----------
@@ -127,7 +127,7 @@ def _dvel_rot(self):
 
     def dvel(self):
         """
-        The accumulated specific force velocity change vector. I.e.,
+        Peek at the accumulated specific force velocity change vector. I.e.,
         the total change in velocity (no gravity correction) over all samples since
         initialization (or last reset).
         """

From 40d4f591edadec7716a5913f1f76f3e9a196c04c Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 18 Dec 2025 13:27:19 +0100
Subject: [PATCH 31/42] test update

---
 tests/test_coning_sculling.py                 |   80 +
 ...coning_sculling_sim_highfreq_20251218A.csv | 2001 +++++++++++++++++
 .../coning_sculling_sim_lowfreq_20251218A.csv |  100 +
 3 files changed, 2181 insertions(+)
 create mode 100644 tests/testdata/coning_sculling/coning_sculling_sim_highfreq_20251218A.csv
 create mode 100644 tests/testdata/coning_sculling/coning_sculling_sim_lowfreq_20251218A.csv

diff --git a/tests/test_coning_sculling.py b/tests/test_coning_sculling.py
index 69fd51c3..e7d380cd 100644
--- a/tests/test_coning_sculling.py
+++ b/tests/test_coning_sculling.py
@@ -1,5 +1,55 @@
+from pathlib import Path
+from turtle import down
 import numpy as np
 import smsfusion as sf
+import pytest
+
+
+TEST_PATH = Path(__file__).parent
+
+
+@pytest.fixture
+def data_ag():
+    data = np.genfromtxt(
+        TEST_PATH / "testdata/coning_sculling/coning_sculling_sim_highfreq_20251218A.csv",
+        delimiter=",",
+        names=True,
+        dtype=float,
+    )
+
+    gx = data["Gx_rads"]
+    gy = data["Gy_rads"]
+    gz = data["Gz_rads"]
+    ax = data["Ax_ms2"]
+    ay = data["Ay_ms2"]
+    az = data["Az_ms2"]
+
+    w = np.column_stack((gx, gy, gz))
+    f = np.column_stack((ax, ay, az))
+
+    return f, w
+
+
+@pytest.fixture
+def data_dtheta_dvel():
+    data = np.genfromtxt(
+        TEST_PATH / "testdata/coning_sculling/coning_sculling_sim_lowfreq_20251218A.csv",
+        delimiter=",",
+        names=True,
+        dtype=float,
+    )
+
+    dtheta_x = data["dThetaX_rad"]
+    dtheta_y = data["dThetaY_rad"]
+    dtheta_z = data["dThetaZ_rad"]
+    dvel_x = data["dVelX_ms"]
+    dvel_y = data["dVelY_ms"]
+    dvel_z = data["dVelZ_ms"]
+
+    dtheta = np.column_stack((dtheta_x, dtheta_y, dtheta_z))
+    dvel = np.column_stack((dvel_x, dvel_y, dvel_z))
+
+    return dvel, dtheta
 
 
 class Test_ConingScullingAlg:
@@ -15,3 +65,33 @@ def test__init__(self):
         np.testing.assert_allclose(alg._vel, np.zeros(3))
         np.testing.assert_allclose(alg._dvel_scul, np.zeros(3))
         np.testing.assert_allclose(alg._dv_prev, np.zeros(3))
+
+    def test_update(self, data_ag, data_dtheta_dvel):
+        f, w = data_ag
+        dvel_ref, dtheta_ref = data_dtheta_dvel
+
+        fs_highfreq = 200.0
+        fs_lowfreq = 10.0
+        step = int(fs_highfreq / fs_lowfreq)
+        alg = sf.ConingScullingAlg(200.0)
+
+        dtheta_out = []
+        dvel_out = []
+        for i, (w_i, f_i) in enumerate(zip(w, f)):
+            # w_i = (np.pi / 180.0) * w_i
+
+            alg.update(f_i, w_i)
+
+            # Store downsampled coning integral, phi    
+            if (i != 0) and (i % step == 0.0):
+                dtheta_out.append(alg.dtheta())
+                dvel_out.append(alg.dvel())
+
+                # Reset
+                alg.reset()
+
+        dtheta_out = np.array(dtheta_out)
+        dvel_out = np.array(dvel_out)
+
+        np.testing.assert_allclose(dvel_out, dvel_ref, atol=1e-8)
+        np.testing.assert_allclose(dtheta_out, dtheta_ref, atol=1e-8)
diff --git a/tests/testdata/coning_sculling/coning_sculling_sim_highfreq_20251218A.csv b/tests/testdata/coning_sculling/coning_sculling_sim_highfreq_20251218A.csv
new file mode 100644
index 00000000..3b8dcc18
--- /dev/null
+++ b/tests/testdata/coning_sculling/coning_sculling_sim_highfreq_20251218A.csv
@@ -0,0 +1,2001 @@
+Time_s,PosX_m,PosY_m,PosZ_m,VelX_ms,VelY_ms,VelZ_ms,Roll_rad,Pitch_rad,Yaw_rad,Gx_rads,Gy_rads,Gz_rads,Ax_ms2,Ay_ms2,Az_ms2
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+0.005,0.0003141463462364135,0.014362525955263777,0.019997532649633214,0.06282410166200973,0.04372549058627086,-0.000986919853488383,0.0013707220187338782,0.06266834170562417,0.08725569675279128,0.2743915448561796,0.1907823741277897,-0.0045593107799900496,0.6111135077798423,-0.154629976322687,-9.985144169627052
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diff --git a/tests/testdata/coning_sculling/coning_sculling_sim_lowfreq_20251218A.csv b/tests/testdata/coning_sculling/coning_sculling_sim_lowfreq_20251218A.csv
new file mode 100644
index 00000000..ee2d3b58
--- /dev/null
+++ b/tests/testdata/coning_sculling/coning_sculling_sim_lowfreq_20251218A.csv
@@ -0,0 +1,100 @@
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+9.3,-0.017478536774872645,-0.0009759323203755039,0.019361946316642443,-0.07084052025327564,0.07054820125734991,-0.962056763180714
+9.4,-0.010208539790379412,0.006739761054670443,0.024935776202191794,-0.06704842696744852,0.08829591622676308,-0.965911166532619
+9.5,-0.0021884480843604543,0.013868520646767447,0.028218342575144988,-0.056699852889772716,0.09747570890020228,-0.9715854420294538
+9.6,0.005831532662016484,0.0198482766342747,0.02868867859740395,-0.04081414705083497,0.09717355474182444,-0.9785720151659273
+9.700000000000001,0.013214428285030368,0.02410431298315191,0.02614030400021066,-0.020954362280696064,0.08737716812167218,-0.9859469115341128
+9.8,0.019442546722257637,0.026094595918155435,0.020769845071471154,0.0009282945069032371,0.06900835983621943,-0.9925568819175945
+9.9,0.024089404589295194,0.025411089903691557,0.013188594098913126,0.022688065638058415,0.04386161435247243,-0.9972967166715755

From 6df28ecf389e72cdb74279dc53c6baf9a5ce4bb4 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 18 Dec 2025 13:31:00 +0100
Subject: [PATCH 32/42] fix tests

---
 src/smsfusion/_coning_sculling.py |  2 +-
 tests/test_coning_sculling.py     | 27 +++++++++++++++++----------
 2 files changed, 18 insertions(+), 11 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 839c2b0e..58648a95 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -159,4 +159,4 @@ def flush(self, degrees=False):
         self._dtheta_con[:] = np.zeros(3, dtype=float)
         self._dvel_scul[:] = np.zeros(3, dtype=float)
         self._vel[:] = np.zeros(3, dtype=float)
-        return dtheta, dvel
\ No newline at end of file
+        return dtheta, dvel
diff --git a/tests/test_coning_sculling.py b/tests/test_coning_sculling.py
index e7d380cd..21ecd629 100644
--- a/tests/test_coning_sculling.py
+++ b/tests/test_coning_sculling.py
@@ -1,17 +1,23 @@
 from pathlib import Path
 from turtle import down
+
 import numpy as np
-import smsfusion as sf
 import pytest
 
+import smsfusion as sf
 
 TEST_PATH = Path(__file__).parent
 
 
 @pytest.fixture
 def data_ag():
+    """
+    200 Hz AG data.
+    """
+
     data = np.genfromtxt(
-        TEST_PATH / "testdata/coning_sculling/coning_sculling_sim_highfreq_20251218A.csv",
+        TEST_PATH
+        / "testdata/coning_sculling/coning_sculling_sim_highfreq_20251218A.csv",
         delimiter=",",
         names=True,
         dtype=float,
@@ -32,8 +38,13 @@ def data_ag():
 
 @pytest.fixture
 def data_dtheta_dvel():
+    """
+    10 Hz coning/sculling reference data.
+    """
+
     data = np.genfromtxt(
-        TEST_PATH / "testdata/coning_sculling/coning_sculling_sim_lowfreq_20251218A.csv",
+        TEST_PATH
+        / "testdata/coning_sculling/coning_sculling_sim_lowfreq_20251218A.csv",
         delimiter=",",
         names=True,
         dtype=float,
@@ -78,17 +89,13 @@ def test_update(self, data_ag, data_dtheta_dvel):
         dtheta_out = []
         dvel_out = []
         for i, (w_i, f_i) in enumerate(zip(w, f)):
-            # w_i = (np.pi / 180.0) * w_i
 
             alg.update(f_i, w_i)
 
-            # Store downsampled coning integral, phi    
             if (i != 0) and (i % step == 0.0):
-                dtheta_out.append(alg.dtheta())
-                dvel_out.append(alg.dvel())
-
-                # Reset
-                alg.reset()
+                dtheta_i, dvel_i = alg.flush()
+                dtheta_out.append(dtheta_i)
+                dvel_out.append(dvel_i)
 
         dtheta_out = np.array(dtheta_out)
         dvel_out = np.array(dvel_out)

From 27d6468ff9596ca774b76aab227ecf2cda3d78fb Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 18 Dec 2025 13:32:33 +0100
Subject: [PATCH 33/42] docstring fix

---
 src/smsfusion/_coning_sculling.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/smsfusion/_coning_sculling.py b/src/smsfusion/_coning_sculling.py
index 58648a95..b4c676cd 100644
--- a/src/smsfusion/_coning_sculling.py
+++ b/src/smsfusion/_coning_sculling.py
@@ -109,8 +109,8 @@ def update(self, f: ArrayLike, w: ArrayLike, degrees: bool = False):
     def dtheta(self, degrees=False):
         """
         Peek at the accumulated 'body attitude change' vector. I.e., the rotation
-        vector describing the total rotation over all samples since
-        initialization (or last reset).
+        vector describing the total rotation over all samples since initialization
+        (or last reset).
 
         Parameters
         ----------

From 8a438e403f0d40bad466078ffdcef9d29bfecb02 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 18 Dec 2025 13:40:11 +0100
Subject: [PATCH 34/42] test puyre pitch

---
 tests/test_coning_sculling.py | 32 ++++++++++++++++++++++++++++++++
 1 file changed, 32 insertions(+)

diff --git a/tests/test_coning_sculling.py b/tests/test_coning_sculling.py
index 21ecd629..60575741 100644
--- a/tests/test_coning_sculling.py
+++ b/tests/test_coning_sculling.py
@@ -102,3 +102,35 @@ def test_update(self, data_ag, data_dtheta_dvel):
 
         np.testing.assert_allclose(dvel_out, dvel_ref, atol=1e-8)
         np.testing.assert_allclose(dtheta_out, dtheta_ref, atol=1e-8)
+
+    def test_update_pure_roll(self):
+        fs = 100.0
+        alg = sf.ConingScullingAlg(fs)
+
+        f = np.array([0.0, 0.0, 0.0])  # m/s^2
+        w = np.array([np.radians(90.0), 0.0, 0.0])  # rad/s
+
+        for i in range(int(fs * 1.0)):  # 1 second
+            alg.update(f, w)
+
+        dtheta_out, dvel_out = alg.flush()
+
+        dtheta_expect = np.array([np.radians(90.0), 0.0, 0.0])
+        np.testing.assert_allclose(dtheta_out, dtheta_expect)
+        np.testing.assert_allclose(dvel_out, np.zeros(3))
+
+    def test_update_pure_pitch(self):
+        fs = 100.0
+        alg = sf.ConingScullingAlg(fs)
+
+        f = np.array([0.0, 0.0, 0.0])  # m/s^2
+        w = np.array([0.0, np.radians(90.0), 0.0])  # rad/s
+
+        for i in range(int(fs * 1.0)):  # 1 second
+            alg.update(f, w)
+
+        dtheta_out, dvel_out = alg.flush()
+
+        dtheta_expect = np.array([0.0, np.radians(90.0), 0.0])
+        np.testing.assert_allclose(dtheta_out, dtheta_expect)
+        np.testing.assert_allclose(dvel_out, np.zeros(3))

From 48a58691df05f2a86326a9351e41c7f2c60860e0 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 18 Dec 2025 13:40:49 +0100
Subject: [PATCH 35/42] test pure yaw

---
 tests/test_coning_sculling.py | 16 ++++++++++++++++
 1 file changed, 16 insertions(+)

diff --git a/tests/test_coning_sculling.py b/tests/test_coning_sculling.py
index 60575741..a7bb3ff3 100644
--- a/tests/test_coning_sculling.py
+++ b/tests/test_coning_sculling.py
@@ -134,3 +134,19 @@ def test_update_pure_pitch(self):
         dtheta_expect = np.array([0.0, np.radians(90.0), 0.0])
         np.testing.assert_allclose(dtheta_out, dtheta_expect)
         np.testing.assert_allclose(dvel_out, np.zeros(3))
+
+    def test_update_pure_yaw(self):
+        fs = 100.0
+        alg = sf.ConingScullingAlg(fs)
+
+        f = np.array([0.0, 0.0, 0.0])  # m/s^2
+        w = np.array([0.0, 0.0, np.radians(90.0)])  # rad/s
+
+        for i in range(int(fs * 1.0)):  # 1 second
+            alg.update(f, w)
+
+        dtheta_out, dvel_out = alg.flush()
+
+        dtheta_expect = np.array([0.0, 0.0, np.radians(90.0)])
+        np.testing.assert_allclose(dtheta_out, dtheta_expect)
+        np.testing.assert_allclose(dvel_out, np.zeros(3))

From 9cad7028b7d96bab8fa55eb1cd5a8c189c1707ba Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 18 Dec 2025 13:41:51 +0100
Subject: [PATCH 36/42] test pure sway

---
 tests/test_coning_sculling.py | 32 ++++++++++++++++++++++++++++++++
 1 file changed, 32 insertions(+)

diff --git a/tests/test_coning_sculling.py b/tests/test_coning_sculling.py
index a7bb3ff3..8ffdca69 100644
--- a/tests/test_coning_sculling.py
+++ b/tests/test_coning_sculling.py
@@ -150,3 +150,35 @@ def test_update_pure_yaw(self):
         dtheta_expect = np.array([0.0, 0.0, np.radians(90.0)])
         np.testing.assert_allclose(dtheta_out, dtheta_expect)
         np.testing.assert_allclose(dvel_out, np.zeros(3))
+
+    def test_pure_surge(self):
+        fs = 100.0
+        alg = sf.ConingScullingAlg(fs)
+
+        f = np.array([1.0, 0.0, 0.0])  # m/s^2
+        w = np.array([0.0, 0.0, 0.0])  # rad/s
+
+        for i in range(int(fs * 1.0)):  # 1 second
+            alg.update(f, w)
+
+        dtheta_out, dvel_out = alg.flush()
+
+        dvel_expect = np.array([1.0, 0.0, 0.0])
+        np.testing.assert_allclose(dvel_out, dvel_expect)
+        np.testing.assert_allclose(dtheta_out, np.zeros(3))
+
+    def test_pure_sway(self):
+        fs = 100.0
+        alg = sf.ConingScullingAlg(fs)
+
+        f = np.array([0.0, 1.0, 0.0])  # m/s^2
+        w = np.array([0.0, 0.0, 0.0])  # rad/s
+
+        for i in range(int(fs * 1.0)):  # 1 second
+            alg.update(f, w)
+
+        dtheta_out, dvel_out = alg.flush()
+
+        dvel_expect = np.array([0.0, 1.0, 0.0])
+        np.testing.assert_allclose(dvel_out, dvel_expect)
+        np.testing.assert_allclose(dtheta_out, np.zeros(3))

From 2197fe33e8114172c12433f9543806157d619a93 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 18 Dec 2025 13:42:20 +0100
Subject: [PATCH 37/42] test pure heave

---
 tests/test_coning_sculling.py | 16 ++++++++++++++++
 1 file changed, 16 insertions(+)

diff --git a/tests/test_coning_sculling.py b/tests/test_coning_sculling.py
index 8ffdca69..5a7e0b74 100644
--- a/tests/test_coning_sculling.py
+++ b/tests/test_coning_sculling.py
@@ -182,3 +182,19 @@ def test_pure_sway(self):
         dvel_expect = np.array([0.0, 1.0, 0.0])
         np.testing.assert_allclose(dvel_out, dvel_expect)
         np.testing.assert_allclose(dtheta_out, np.zeros(3))
+
+    def test_pure_heave(self):
+        fs = 100.0
+        alg = sf.ConingScullingAlg(fs)
+
+        f = np.array([0.0, 0.0, 1.0])  # m/s^2
+        w = np.array([0.0, 0.0, 0.0])  # rad/s
+
+        for i in range(int(fs * 1.0)):  # 1 second
+            alg.update(f, w)
+
+        dtheta_out, dvel_out = alg.flush()
+
+        dvel_expect = np.array([0.0, 0.0, 1.0])
+        np.testing.assert_allclose(dvel_out, dvel_expect)
+        np.testing.assert_allclose(dtheta_out, np.zeros(3))

From d96cf4fa7ec49d168a9e9ce67eb00da711e713ca Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 18 Dec 2025 13:44:58 +0100
Subject: [PATCH 38/42] test rot and acc

---
 tests/test_coning_sculling.py | 51 +++++++++++++++++++++++++++++++++++
 1 file changed, 51 insertions(+)

diff --git a/tests/test_coning_sculling.py b/tests/test_coning_sculling.py
index 5a7e0b74..cc28c862 100644
--- a/tests/test_coning_sculling.py
+++ b/tests/test_coning_sculling.py
@@ -198,3 +198,54 @@ def test_pure_heave(self):
         dvel_expect = np.array([0.0, 0.0, 1.0])
         np.testing.assert_allclose(dvel_out, dvel_expect)
         np.testing.assert_allclose(dtheta_out, np.zeros(3))
+
+    def test_roll_and_surge(self):
+        fs = 100.0
+        alg = sf.ConingScullingAlg(fs)
+
+        f = np.array([1.0, 0.0, 0.0])  # m/s^2
+        w = np.array([np.radians(90.0), 0.0, 0.0])  # rad/s
+
+        for i in range(int(fs * 1.0)):  # 1 second
+            alg.update(f, w)
+
+        dtheta_out, dvel_out = alg.flush()
+
+        dtheta_expect = np.array([np.radians(90.0), 0.0, 0.0])
+        dvel_expect = np.array([1.0, 0.0, 0.0])
+        np.testing.assert_allclose(dtheta_out, dtheta_expect, atol=1e-8)
+        np.testing.assert_allclose(dvel_out, dvel_expect, atol=1e-8)
+
+    def test_pitch_and_sway(self):
+        fs = 100.0
+        alg = sf.ConingScullingAlg(fs)
+
+        f = np.array([0.0, 1.0, 0.0])  # m/s^2
+        w = np.array([0.0, np.radians(90.0), 0.0])  # rad/s
+
+        for i in range(int(fs * 1.0)):  # 1 second
+            alg.update(f, w)
+
+        dtheta_out, dvel_out = alg.flush()
+
+        dtheta_expect = np.array([0.0, np.radians(90.0), 0.0])
+        dvel_expect = np.array([0.0, 1.0, 0.0])
+        np.testing.assert_allclose(dtheta_out, dtheta_expect, atol=1e-8)
+        np.testing.assert_allclose(dvel_out, dvel_expect, atol=1e-8)
+
+    def test_yaw_and_heave(self):
+        fs = 100.0
+        alg = sf.ConingScullingAlg(fs)
+
+        f = np.array([0.0, 0.0, 1.0])  # m/s^2
+        w = np.array([0.0, 0.0, np.radians(90.0)])  # rad/s
+
+        for i in range(int(fs * 1.0)):  # 1 second
+            alg.update(f, w)
+
+        dtheta_out, dvel_out = alg.flush()
+
+        dtheta_expect = np.array([0.0, 0.0, np.radians(90.0)])
+        dvel_expect = np.array([0.0, 0.0, 1.0])
+        np.testing.assert_allclose(dtheta_out, dtheta_expect, atol=1e-8)
+        np.testing.assert_allclose(dvel_out, dvel_expect, atol=1e-8)

From fa8e3b40d54f450cf37452e5d317089b35096edd Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 18 Dec 2025 13:51:04 +0100
Subject: [PATCH 39/42] all linear test

---
 tests/test_coning_sculling.py | 16 ++++++++++++++++
 1 file changed, 16 insertions(+)

diff --git a/tests/test_coning_sculling.py b/tests/test_coning_sculling.py
index cc28c862..2d310b0d 100644
--- a/tests/test_coning_sculling.py
+++ b/tests/test_coning_sculling.py
@@ -249,3 +249,19 @@ def test_yaw_and_heave(self):
         dvel_expect = np.array([0.0, 0.0, 1.0])
         np.testing.assert_allclose(dtheta_out, dtheta_expect, atol=1e-8)
         np.testing.assert_allclose(dvel_out, dvel_expect, atol=1e-8)
+
+    def test_surge_sway_heave(self):
+        fs = 100.0
+        alg = sf.ConingScullingAlg(fs)
+
+        f = np.array([1.0, -2.0, 3.0])  # m/s^2
+        w = np.array([0.0, 0.0, 0.0])  # rad/s
+
+        for i in range(int(fs * 1.0)):  # 1 second
+            alg.update(f, w)
+
+        dtheta_out, dvel_out = alg.flush()
+
+        dvel_expect = np.array([1.0, -2.0, 3.0])
+        np.testing.assert_allclose(dvel_out, dvel_expect)
+        np.testing.assert_allclose(dtheta_out, np.zeros(3))

From 5b5a59ff91f9b33c5a8576aa0c57778d214c0078 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 18 Dec 2025 13:52:13 +0100
Subject: [PATCH 40/42] test all rots

---
 tests/test_coning_sculling.py | 18 ++++++++++++++++++
 1 file changed, 18 insertions(+)

diff --git a/tests/test_coning_sculling.py b/tests/test_coning_sculling.py
index 2d310b0d..f7551156 100644
--- a/tests/test_coning_sculling.py
+++ b/tests/test_coning_sculling.py
@@ -250,6 +250,24 @@ def test_yaw_and_heave(self):
         np.testing.assert_allclose(dtheta_out, dtheta_expect, atol=1e-8)
         np.testing.assert_allclose(dvel_out, dvel_expect, atol=1e-8)
 
+    def test_roll_pitch_yaw(self):
+        fs = 100.0
+        alg = sf.ConingScullingAlg(fs)
+
+        f = np.array([0.0, 0.0, 0.0])  # m/s^2
+        w = np.array([np.radians(30.0), -np.radians(45.0), np.radians(60.0)])  # rad/s
+
+        for i in range(int(fs * 1.0)):  # 1 second
+            alg.update(f, w)
+
+        dtheta_out, dvel_out = alg.flush()
+
+        dtheta_expect = np.array(
+            [np.radians(30.0), -np.radians(45.0), np.radians(60.0)]
+        )
+        np.testing.assert_allclose(dtheta_out, dtheta_expect, atol=1e-8)
+        np.testing.assert_allclose(dvel_out, np.zeros(3))
+
     def test_surge_sway_heave(self):
         fs = 100.0
         alg = sf.ConingScullingAlg(fs)

From b02b514c3b87e2ac5905e75c2d58a37a712047cd Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 18 Dec 2025 13:53:56 +0100
Subject: [PATCH 41/42] test dtheta

---
 tests/test_coning_sculling.py | 32 ++++++++++++++++++++++++++++++++
 1 file changed, 32 insertions(+)

diff --git a/tests/test_coning_sculling.py b/tests/test_coning_sculling.py
index f7551156..cf43f3f8 100644
--- a/tests/test_coning_sculling.py
+++ b/tests/test_coning_sculling.py
@@ -283,3 +283,35 @@ def test_surge_sway_heave(self):
         dvel_expect = np.array([1.0, -2.0, 3.0])
         np.testing.assert_allclose(dvel_out, dvel_expect)
         np.testing.assert_allclose(dtheta_out, np.zeros(3))
+
+    def test_dvel(self):
+        fs = 100.0
+        alg = sf.ConingScullingAlg(fs)
+
+        f = np.array([1.0, 2.0, 3.0])  # m/s^2
+        w = np.array([0.0, 0.0, 0.0])  # rad/s
+
+        for i in range(int(fs * 1.0)):  # 1 second
+            alg.update(f, w)
+
+        dvel_out = alg.dvel()
+
+        dvel_expect = np.array([1.0, 2.0, 3.0])
+        np.testing.assert_allclose(dvel_out, dvel_expect)
+
+    def test_dtheta(self):
+        fs = 100.0
+        alg = sf.ConingScullingAlg(fs)
+
+        f = np.array([0.0, 0.0, 0.0])  # m/s^2
+        w = np.array([np.radians(30.0), -np.radians(45.0), np.radians(60.0)])  # rad/s
+
+        for i in range(int(fs * 1.0)):  # 1 second
+            alg.update(f, w)
+
+        dtheta_out = alg.dtheta()
+
+        dtheta_expect = np.array(
+            [np.radians(30.0), -np.radians(45.0), np.radians(60.0)]
+        )
+        np.testing.assert_allclose(dtheta_out, dtheta_expect)

From 455c6a5ff820bf6c25cb5bd81634a2bdfbe45f86 Mon Sep 17 00:00:00 2001
From: "Vegard R. Solum" <vegard.solum@4subsea.com>
Date: Thu, 18 Dec 2025 13:58:01 +0100
Subject: [PATCH 42/42] test flush

---
 tests/test_coning_sculling.py | 18 ++++++++++++++++++
 1 file changed, 18 insertions(+)

diff --git a/tests/test_coning_sculling.py b/tests/test_coning_sculling.py
index cf43f3f8..44899ea7 100644
--- a/tests/test_coning_sculling.py
+++ b/tests/test_coning_sculling.py
@@ -315,3 +315,21 @@ def test_dtheta(self):
             [np.radians(30.0), -np.radians(45.0), np.radians(60.0)]
         )
         np.testing.assert_allclose(dtheta_out, dtheta_expect)
+
+    def test_flush(self):
+        fs = 100.0
+        alg = sf.ConingScullingAlg(fs)
+
+        f = np.array([1.0, 2.0, 3.0])  # m/s^2
+        w = np.array([np.radians(30.0), -np.radians(45.0), np.radians(60.0)])  # rad/s
+
+        for i in range(int(fs * 1.0)):  # 1 second
+            alg.update(f, w)
+
+        dtheta_expect = alg.dtheta()
+        dvel_expect = alg.dvel()
+        dtheta_out, dvel_out = alg.flush()
+        np.testing.assert_allclose(dtheta_out, dtheta_expect)
+        np.testing.assert_allclose(dvel_out, dvel_expect)
+        assert np.allclose(alg.dtheta(), np.zeros(3))
+        assert np.allclose(alg.dvel(), np.zeros(3))