diff --git a/bytetracker/byte_tracker.py b/bytetracker/byte_tracker.py
index 5e0f8f0..f9c0d3c 100644
--- a/bytetracker/byte_tracker.py
+++ b/bytetracker/byte_tracker.py
@@ -5,8 +5,17 @@
 from bytetracker.kalman_filter import KalmanFilter
 
 
-def xywh2xyxy(x):
-    # Convert nx4 boxes from [x, y, w, h] to [x1, y1, x2, y2] where xy1=top-left, xy2=bottom-right
+def xywh2xyxy(x: np.ndarray):
+    """
+    Converts bounding boxes from [x, y, w, h] format to [x1, y1, x2, y2] format
+
+    Parameters
+    ----------
+    x: Array at [x, y, w, h] format
+    Returns
+    -------
+    y: Array [x1, y1, x2, y2] format
+    """
     y = np.copy(x)
     y[:, 0] = x[:, 0] - x[:, 2] / 2  # top left x
     y[:, 1] = x[:, 1] - x[:, 3] / 2  # top left y
@@ -15,8 +24,18 @@ def xywh2xyxy(x):
     return y
 
 
-def xyxy2xywh(x):
-    # Convert nx4 boxes from [x1, y1, x2, y2] to [x, y, w, h] where xy1=top-left, xy2=bottom-right
+def xyxy2xywh(x: np.ndarray):
+    """
+    Converts bounding boxes from [x1, y1, x2, y2] format to [x, y, w, h] format
+
+    Parameters
+    ----------
+    x: Array at [x1, y1, x2, y2] format
+
+    Returns
+    -------
+    y: Array at [x, y, w, h] format
+    """
     y = np.copy(x)
     y[:, 0] = (x[:, 0] + x[:, 2]) / 2  # x center
     y[:, 1] = (x[:, 1] + x[:, 3]) / 2  # y center
@@ -39,13 +58,25 @@ def __init__(self, tlwh, score, cls):
         self.cls = cls
 
     def predict(self):
+        """
+        updates the mean and covariance using a Kalman filter prediction, with a condition
+        based on the state of the track.
+        """
         mean_state = self.mean.copy()
         if self.state != TrackState.Tracked:
             mean_state[7] = 0
         self.mean, self.covariance = self.kalman_filter.predict(mean_state, self.covariance)
 
     @staticmethod
-    def multi_predict(stracks):
+    def multi_predict(stracks: list["STrack"]):
+        """
+        takes a list of tracks, updates their mean and covariance values, and
+        performs a Kalman filter prediction step.
+
+        Parameters
+        ----------
+        stracks (list): list of STrack objects
+        """
         if len(stracks) > 0:
             multi_mean = np.asarray([st.mean.copy() for st in stracks])
             multi_covariance = np.asarray([st.covariance for st in stracks])
@@ -59,8 +90,16 @@ def multi_predict(stracks):
                 stracks[i].mean = mean
                 stracks[i].covariance = cov
 
-    def activate(self, kalman_filter, frame_id):
-        """Start a new tracklet"""
+    def activate(self, kalman_filter: KalmanFilter, frame_id: int):
+        """
+        initializes a new tracklet with a Kalman filter and assigns a track ID and
+        state based on the frame ID.
+
+        Parameters
+        ----------
+        kalman_filter: Kalman filter object
+        frame_id (int): The `frame_id` parameter in the `activate` method.
+        """
         self.kalman_filter = kalman_filter
         self.track_id = self.next_id()
         self.mean, self.covariance = self.kalman_filter.initiate(self.tlwh_to_xyah(self._tlwh))
@@ -72,7 +111,19 @@ def activate(self, kalman_filter, frame_id):
         self.frame_id = frame_id
         self.start_frame = frame_id
 
-    def re_activate(self, new_track, frame_id, new_id=False):
+    def re_activate(self, new_track: "STrack", frame_id: int, new_id: bool = False):
+        """
+        Updates a track using Kalman filtering
+
+        Parameters
+        ----------
+        new_track : STrack
+            The new track object to update.
+        frame_id : int
+            The frame ID.
+        new_id : bool
+            Whether to assign a new ID to the track, by default False.
+        """
         self.mean, self.covariance = self.kalman_filter.update(
             self.mean, self.covariance, self.tlwh_to_xyah(new_track.tlwh)
         )
@@ -84,13 +135,16 @@ def re_activate(self, new_track, frame_id, new_id=False):
         self.score = new_track.score
         self.cls = new_track.cls
 
-    def update(self, new_track, frame_id):
+    def update(self, new_track: "STrack", frame_id: int):
         """
-        Update a matched track
-        :type new_track: STrack
-        :type frame_id: int
-        :type update_feature: bool
-        :return:
+        Update a matched track.
+
+        Parameters
+        ----------
+        new_track : STrack
+            The new track object to update.
+        frame_id : int
+            The frame ID.
         """
         self.frame_id = frame_id
         self.cls = new_track.cls
@@ -120,7 +174,8 @@ def tlwh(self):
     @property
     # @jit(nopython=True)
     def tlbr(self):
-        """Convert bounding box to format `(min x, min y, max x, max y)`, i.e.,
+        """
+        Convert bounding box to format `(min x, min y, max x, max y)`, i.e.,
         `(top left, bottom right)`.
         """
         ret = self.tlwh.copy()
@@ -130,7 +185,8 @@ def tlbr(self):
     @staticmethod
     # @jit(nopython=True)
     def tlwh_to_xyah(tlwh):
-        """Convert bounding box to format `(center x, center y, aspect ratio,
+        """
+        Convert bounding box to format `(center x, center y, aspect ratio,
         height)`, where the aspect ratio is `width / height`.
         """
         ret = np.asarray(tlwh).copy()
@@ -167,7 +223,23 @@ def reset(self):
         self.kalman_filter = KalmanFilter()
         BaseTrack._count = 0
 
-    def update(self, dets, frame_id):
+    def update(self, dets: np.ndarray, frame_id: int):
+        """
+        Performs object tracking by associating detections with existing tracks and updating their states accordingly.
+
+        Parameters
+        ----------
+        dets : np.ndarray
+            Detection boxes of objects in the format (n x 6), where each row contains (x1, y1, x2, y2, score, class).
+        frame_id : int
+            The ID of the current frame in the video.
+
+        Returns
+        -------
+        np.ndarray
+            An array of outputs containing bounding box coordinates, track ID, class label, and
+            score for each tracked object.
+        """
         self.frame_id = frame_id
         activated_starcks = []
         refind_stracks = []
@@ -318,7 +390,23 @@ def update(self, dets, frame_id):
         return outputs
 
 
-def joint_stracks(tlista, tlistb):
+def joint_stracks(tlista: list["STrack"], tlistb: list["STrack"]):
+    """
+    Merges two lists of objects based on a specific attribute while
+    ensuring no duplicates are added.
+
+    Parameters
+    ----------
+    tlista : List[STrack]
+        list of STrack objects.
+    tlistb : List[STrack]
+        list of STrack objects.
+
+    Returns
+    -------
+    List[STrack]
+        A list containing all unique elements from both input lists.
+    """
     exists = {}
     res = []
     for t in tlista:
@@ -332,7 +420,22 @@ def joint_stracks(tlista, tlistb):
     return res
 
 
-def sub_stracks(tlista, tlistb):
+def sub_stracks(tlista: list["STrack"], tlistb: list["STrack"]):
+    """
+    Returns a list of STrack objects that are present in tlista but not in tlistb.
+
+    Parameters
+    ----------
+    tlista : List[STrack]
+        list of STrack objects.
+    tlistb : List[STrack]
+        list of STrack objects.
+
+    Returns
+    -------
+    List[STrack]
+        A list containing STrack objects present in tlista but not in tlistb.
+    """
     stracks = {}
     for t in tlista:
         stracks[t.track_id] = t
@@ -343,7 +446,22 @@ def sub_stracks(tlista, tlistb):
     return list(stracks.values())
 
 
-def remove_duplicate_stracks(stracksa, stracksb):
+def remove_duplicate_stracks(stracksa: list["STrack"], stracksb: list["STrack"]):
+    """
+    Removes duplicate STrack objects from the input lists based on their frame IDs.
+
+    Parameters
+    ----------
+    stracksa : List[STrack]
+        list of STrack objects.
+    stracksb : List[STrack]
+        list of STrack objects.
+
+    Returns
+    -------
+    Tuple[List[STrack], List[STrack]]
+        Two lists containing unique STrack objects after removing duplicates.
+    """
     pdist = matching.iou_distance(stracksa, stracksb)
     pairs = np.where(pdist < 0.15)
     dupa, dupb = list(), list()
diff --git a/bytetracker/kalman_filter.py b/bytetracker/kalman_filter.py
index 2259754..06f920f 100644
--- a/bytetracker/kalman_filter.py
+++ b/bytetracker/kalman_filter.py
@@ -68,7 +68,7 @@ def initiate(self, measurement):
         covariance = np.diag(np.square(std))
         return mean, covariance
 
-    def predict(self, mean, covariance):
+    def predict(self, mean: np.ndarray, covariance: np.ndarray):
         """Run Kalman filter prediction step.
 
         Parameters
@@ -109,7 +109,7 @@ def predict(self, mean, covariance):
 
         return mean, covariance
 
-    def project(self, mean, covariance):
+    def project(self, mean: np.ndarray, covariance: np.ndarray):
         """Project state distribution to measurement space.
 
         Parameters
@@ -138,7 +138,7 @@ def project(self, mean, covariance):
         covariance = np.linalg.multi_dot((self._update_mat, covariance, self._update_mat.T))
         return mean, covariance + innovation_cov
 
-    def multi_predict(self, mean, covariance):
+    def multi_predict(self, mean: np.ndarray, covariance: np.ndarray):
         """Run Kalman filter prediction step (Vectorized version).
         Parameters
         ----------
@@ -179,7 +179,7 @@ def multi_predict(self, mean, covariance):
 
         return mean, covariance
 
-    def update(self, mean, covariance, measurement):
+    def update(self, mean: np.ndarray, covariance: np.ndarray, measurement: np.ndarray):
         """Run Kalman filter correction step.
 
         Parameters
diff --git a/bytetracker/matching.py b/bytetracker/matching.py
index 2e198d0..753fbc9 100644
--- a/bytetracker/matching.py
+++ b/bytetracker/matching.py
@@ -2,7 +2,21 @@
 import numpy as np
 
 
-def linear_assignment(cost_matrix, thresh):
+def linear_assignment(cost_matrix: np.ndarray, thresh: float):
+    """
+    Assigns detections to existing tracks based on a cost matrix using linear assignment.
+
+    Parameters
+    ----------
+    cost_matrix : np.ndarray
+        The cost matrix representing the association cost between detections and tracks.
+    thresh : float
+        The threshold for cost matching.
+
+    Returns
+    -------
+    Tuple containing matches, unmatched detections, and unmatched tracks.
+    """
     if cost_matrix.size == 0:
         return (
             np.empty((0, 2), dtype=int),
@@ -22,11 +36,19 @@ def linear_assignment(cost_matrix, thresh):
 
 def ious(atlbrs, btlbrs):
     """
-    Compute cost based on IoU
-    :type atlbrs: list[tlbr] | np.ndarray
-    :type atlbrs: list[tlbr] | np.ndarray
+    Compute cost over Union (IoU) between bounding box pairs
+
+    Parameters
+    ----------
+    atlbrs : Union[list, np.ndarray]
+        The bounding boxes of the first set in (min x, min y, max x, max y) format.
+    btlbrs : Union[list, np.ndarray]
+        The bounding boxes of the second set in (min x, min y, max x, max y) format.
 
-    :rtype ious np.ndarray
+    Returns
+    -------
+    np.ndarray
+        An array containing IoU values for each pair of bounding boxes.
     """
     ious = np.zeros((len(atlbrs), len(btlbrs)), dtype=np.float32)
     if ious.size == 0:
@@ -63,7 +85,22 @@ def iou_distance(atracks, btracks):
     return cost_matrix
 
 
-def fuse_score(cost_matrix, detections):
+def fuse_score(cost_matrix: np.ndarray, detections: np.ndarray):
+    """
+    Fuse detection scores with similarity scores from a cost matrix.
+
+    Parameters
+    ----------
+    cost_matrix : np.ndarray
+        The cost matrix representing the dissimilarity between tracks and detections.
+    detections : np.ndarray
+        The array of detections, each containing a score.
+
+    Returns
+    -------
+    np.ndarray
+        The fused cost matrix, incorporating both similarity scores and detection scores.
+    """
     if cost_matrix.size == 0:
         return cost_matrix
     iou_sim = 1 - cost_matrix
@@ -74,7 +111,7 @@ def fuse_score(cost_matrix, detections):
     return fuse_cost
 
 
-def bbox_ious(boxes, query_boxes):
+def bbox_ious(boxes: np.ndarray, query_boxes: np.ndarray):
     """
     Parameters
     ----------