AdvancedTopic 101 of 101Signals, Control & Comms
Extended Kalman filter
Applies Kalman estimation to nonlinear systems by local linearisation.
In depth
The EKF extends the Kalman filter to nonlinear systems by linearising the state and measurement functions around the current estimate using Jacobians at every step. It is widely used in navigation and SLAM but can diverge when nonlinearities are strong; UKF and particle filters are alternatives.
Key points
- Prediction and update with Jacobians
- Covariance propagation
- Linearisation error
ExampleEKF fuses IMU, GPS and magnetometer to estimate drone attitude and position.
What is Extended Kalman filter?
Applies Kalman estimation to nonlinear systems by local linearisation.
Why is it important to understand extended Kalman filter?
The extended Kalman filter brings state estimation to nonlinear systems, which covers navigation and tracking in real vehicles and robots.
How does the extended Kalman filter work?
It linearises the nonlinear model and measurement equations around the current estimate, then applies the standard Kalman update.
What is the main weakness of the EKF?
Linearisation can be inaccurate for strong nonlinearity, which can make the estimate diverge if the model is poor.
How is Extended Kalman filter used in practice?
Typical applications include estimating the attitude of a drone from gyroscope and accelerometer data, tracking the position of a vehicle with GPS and wheel speed sensors and estimating the state of charge of a battery with a nonlinear model.
What should I learn before Extended Kalman filter?
Study "Compressed sensing" first (topic 100 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Extended Kalman filter?
Prediction and update with Jacobians. Covariance propagation. Linearisation error.
Can you give an example of Extended Kalman filter?
EKF fuses IMU, GPS and magnetometer to estimate drone attitude and position.
What comes after Extended Kalman filter?
This is the final topic in Signals, Control & Comms.
How difficult is Extended Kalman filter?
It is classed as Advanced in Signals, Control & Comms (topic 101 of 101). It is an advanced topic. It assumes you are comfortable with the intermediate topics in Signals, Control & Comms.