feat: Implement time-weighted triangulation for enhanced 3D point reconstruction

- Added two new functions: `triangulate_one_point_from_multiple_views_linear_time_weighted` and `triangulate_points_from_multiple_views_linear_time_weighted` to perform triangulation with time-based weighting, improving accuracy in 3D point estimation.
- Introduced a method to group detections by camera while preserving the latest detection, enhancing tracking state management.
- Updated the `update_tracking` function to incorporate time-weighted triangulation, allowing for more robust updates to tracking states based on new detections.
- Refactored the `TrackingState` to utilize a mapping of historical detections by camera, improving data organization and access.

app/tracking/__init__.py

@@ -13,9 +13,9 @@ from typing import (
     TypeAlias,
     TypedDict,
     TypeVar,
+    Union,
     cast,
     overload,
-    Union,
 )
 
 import jax.numpy as jnp
@@ -23,9 +23,11 @@ from beartype import beartype
 from beartype.typing import Mapping, Sequence
 from jax import Array
 from jaxtyping import Array, Float, Int, jaxtyped
-from pyrsistent import PVector, v
+from pyrsistent import PVector, v, PRecord, PMap
 
-from app.camera import Detection
+from app.camera import Detection, CameraID
+
+TrackingID: TypeAlias = int
 
 
 class TrackingPrediction(TypedDict):
@@ -440,7 +442,7 @@ class TrackingState:
     The last active timestamp of the tracking
     """
 
-    historical_detections: PVector[Detection]
+    historical_detections_by_camera: PMap[CameraID, Detection]
     """
     Historical detections of the tracking.
 
@@ -449,13 +451,13 @@ class TrackingState:
 
 
 class Tracking:
-    id: int
+    id: TrackingID
     state: TrackingState
     velocity_filter: GenericVelocityFilter
 
     def __init__(
         self,
-        id: int,
+        id: TrackingID,
         state: TrackingState,
         velocity_filter: Optional[GenericVelocityFilter] = None,
     ):
@@ -512,6 +514,15 @@ class Tracking:
         # pylint: disable-next=unsubscriptable-object
         return self.velocity_filter.predict(timestamp)["keypoints"]
 
+    def update(self, new_3d_pose: Float[Array, "J 3"], timestamp: datetime) -> None:
+        """
+        update the tracking with a new 3D pose
+
+        Note:
+            equivalent to call `velocity_filter.update(new_3d_pose, timestamp)`
+        """
+        self.velocity_filter.update(new_3d_pose, timestamp)
+
     @property
     def velocity(self) -> Float[Array, "J 3"]:
         """
@@ -537,7 +548,7 @@ class AffinityResult:
     indices_T: Int[Array, "T"]  # pylint: disable=invalid-name
     indices_D: Int[Array, "D"]  # pylint: disable=invalid-name
 
-    def tracking_detections(
+    def tracking_association(
         self,
     ) -> Generator[tuple[float, Tracking, Detection], None, None]:
         """