The Unscented Kalman Filter (UKF)
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The EKF needs Jacobians and can be badly wrong when models curve sharply. The unscented Kalman filter replaces derivatives with a small set of carefully chosen sample points, the sigma points, which are pushed through the real nonlinear model. It is usually more accurate than the EKF at similar cost and much easier to apply to complicated models.
You will learn the idea, the history, the exact equations and how to pick the tuning parameters, then build a UKF that tracks a pendulum and race it against an EKF.
What you will be able to do
- Explain the unscented transform and why it beats linearisation
- Generate sigma points and weights with the scaled (α, β, κ) scheme
- Implement a UKF from scratch with Cholesky decomposition
- Compare EKF and UKF accuracy on a strongly nonlinear system
Before you start: Courses 1 and 2, matrix square roots (Cholesky) will be explained.
Lessons
- The big idea: push points, not slopesFree preview
- How it was invented and its first usesLocked
- Where it is used todayLocked
- The equationsLocked
- Worked demo and tuningLocked
- Build your own, step by stepLocked
- Python simulation labLocked
- Practice problems and quizLocked