2D EKF using GPS and IMU Sensor Fusion

This project implements a probabilistic 2D localization system using an Extended Kalman Filter to fuse noisy control inputs with landmark measurements. The goal was to maintain accurate robot pose estimates while explicitly modeling uncertainty in both motion and sensing.

The EKF was structured with separate prediction and update stages, where non-linear motion and measurement models were linearized using Jacobian matrices. Early iterations of the filter suffered from divergence due to inconsistent linearization, which I identified by comparing analytical Jacobians against numerical gradients. Correcting these formulations and tuning noise covariances significantly improved filter stability.

The final system produced smooth, low-error trajectories and maintained well-behaved covariance estimates over time. By dynamically adjusting the Kalman Gain based on uncertainty, the estimator remained robust under noisy conditions, demonstrating reliable localization performance suitable for real-time robotic applications.