The Extended Kalman Filter (EKF)
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The linear Kalman filter assumes straight-line physics. A rover that turns, a drone that rotates, a radar that measures angles: all of these are nonlinear. The extended Kalman filter handles them by linearising the models around the current estimate at every step.
This course takes you through the history (it was born for Apollo), the Jacobian maths and a full Python simulation of a rover localising itself against landmarks with a range-and-bearing sensor, the same structure used in LiDAR and camera-based localisation.
What you will be able to do
- Explain why the linear Kalman filter breaks on turning robots
- Derive Jacobians for unicycle motion and range–bearing sensors
- Implement EKF localisation with known landmarks
- Diagnose divergence and fix angle-wrapping bugs
Before you start: Course 1 (Kalman filter), partial derivatives and basic trigonometry.
Lessons
- The big idea: linearise, then filter▶ VideoFree preview
- How it was invented and its first uses▶ VideoLocked
- Where it is used today▶ VideoLocked
- The equations▶ VideoLocked
- Worked demo and tuning▶ VideoLocked
- Build your own, step by step▶ VideoLocked
- Python simulation labLocked
- Practice problems and quizLocked