states of mobile robot, motion model, position orientation and velocity,
More challenge see: GPS
Predict, measure, combining
Prediction and correction
Recursive Least Squares + Process Model
Linear approximation, first-order term, still linear.
Linearized motion model, Linearized measurement model.
- The Kalman Filter is very similar to RLS but includes a motion model that tells us how the state evolves over time.
- The Kalman Filter updates a state estimate through two stages: i. prediction and ii. correction.
- The EKF uses linearization to adapt the Kalman filter to nonlinear systems.
- Linearization relies on computing Jacobian matrices, which contain all the first-order partial derivatives of a function.
- The EKF uses analytical local linearization and, as a result, is sensitive to linearization errors.
- How a Kalman filter works, in pictures
- Extended Kalman Filter: Why do we need an Extended Version?
- PR, Section 3.1, 3.2, 3.3. (Optional)
- A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking (Optional)
- What is the difference between a particle filter and a Kalman filter?
Use approximate nonlinear Bayesian filters include EKF, approximate grid-based methods and particle filters for non linear cases.
Use approximate grid-based filters and particle filters for non-Gaussian cases.