[ADD] orientation tracking project

docs/index.md

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 <center>
-# __Projects__ 🛠 
+# __Projects__ 🛠
+<table>
+<tr>
+ <td>
+ <center>
+ <h1>Robust Orientation Tracking for Panoramic Stitching: Projected Gradient Descent vs. Extended Kalman Filters</h1>
+ <img src="images/pgd_dataset3.gif" width="300" height"100">
+ <img src="images/ekf4_dataset3.gif" width="300" height"100">
+ <img src="images/ekf7_dataset3.gif" width="300" height"100">
+ <img src="images/vicon_dataset3.gif" width="300" height"100">
+ </center>
+ <br/>
+ <b>Abstract</b><br/>
+ The quest for precise 3D orientation tracking of
+ rotating bodies underpins advancements in robotics, augmented
+ reality, and navigational systems, necessitating methodologies
+ that balance accuracy with computational feasibility. This paper
+ introduces a projected gradient descent (PGD) methodology,
+ innovatively applied to orientation estimation through sensor
+ fusion from a 6-DOF inertial measurement unit (IMU). We
+ undertake a comparative analysis of PGD against established
+ Extended Kalman Filter (EKF) methods—specifically, 4-state and
+ 7-state variants—anchored by ground truth data from a VICON
+ motion capture system.
+ Our investigation reveals PGD’s superior accuracy and robustness over EKF approaches across a spectrum of datasets
+ characterized by noise, discontinuities, and dynamic changes.
+ Despite PGD’s reliance on future data, which poses a challenge
+ for real-time application, its performance advantage is notable,
+ especially in complex environments. The 7-state EKF, while
+ outperforming PGD in scenarios with frequent discontinuities,
+ exhibits limitations in smoothness, highlighting a trade-off between responsiveness and continuity. The practical utility of
+ these orientation estimation methods is further demonstrated
+ through the application of panoramic image stitching, where
+ PGD’s enhanced performance is evident, although EKF models
+ provide comparable outcomes under less variable conditions.
+ This study underscores PGD’s potential as a robust alternative
+ for 3D orientation tracking, offering insights into its com-
+ parative performance against traditional EKFs. By delineating
+ the strengths and limitations of PGD and EKF methodologies,
+ this work contributes to the broader discourse on advancing
+ sensor-based orientation estimation, encouraging future efforts
+to optimize PGD for real-time applications.
+ </td>
+</tr>
+</table>
 <table>
  <tr>
  <td> <img src="Projects/AutonomousRCCar/images/corneringros.gif" width="400" height"400">