example with AINS

Author: vegard-solum-4ss

docs/user_guide/quickstart.rst

@@ -256,17 +256,32 @@ The :class:`~smsfusion.FixedIntervalSmoother` implements fixed-interval smoothin
 for an :class:`~smsfusion.AidedINS` instance or one of its subclasses (:class:`~smsfusion.AHRS`
 or :class:`~smsfusion.VRU`). After a complete forward pass using the AINS algorithm,
 the smoother applies a backward pass using the Rauch-Tung-Striebel (RTS) algorithm [1]
-to refine the state (and covariance) estimates.
+to refine the state (and covariance) estimates:
 
+.. code-block:: python
+
+    import smsfusion as sf
+
+    smoother = sf.FixedIntervalSmoother(ains)
+
+    for f_i, w_i, p_i, h_i in zip(acc_imu, gyro_imu, pos_aid, head_aid):
+        smoother.update(
+            f_i,
+            w_i,
+            degrees=False,
+            pos=p_i,
+            pos_var=pos_noise_std**2 * np.ones(3),
+            head=h_i,
+            head_var=head_noise_std**2,
+            head_degrees=False,
+        )
 
+    pos_est = smoother.position()
+    vel_est = smoother.velocity()
+    euler_est = smoother.euler(degrees=False)
 
-Smoothing is a post-processing technique used to enhance the accuracy of Kalman
-filter state estimates by incorporating both past and future measurements to produce
-more accurate estimates. This is in contrast to the standard Kalman filter algorithm,
-which only uses past and current measurements to produce estimates at each time step.
 
-The :class:`~smsfusion.FixedIntervalSmoother` provides a fixed-interval smoothing
-layer for the :class:`~smsfusion.AidedINS` class and its subclasses (:class:`~smsfusion.AHRS`
-and :class:`~smsfusion.VRU`). After the initial forward pass with the AINS algorithm,
-the smoother performs a backward sweep with the Rauch-Tung-Striebel (RTS) algorithm [1]
-to refine the filter estimates.
+References
+----------
+[1] R. G. Brown and P. Y. C. Hwang, "Random signals and applied Kalman filtering
+    with MATLAB exercises", 4th ed. Wiley, pp. 208-212, 2012.