MOB LEC8 Recursive and Kalman Filter

Prerequisite knowledge

states of mobile robot, motion model, position orientation and velocity,

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More challenge see: GPS

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Kalman Filter

Predict, measure, combining

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Prediction and correction

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Linear Kalman Filter

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Recursive Least Squares + Process Model

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Extended Kalman Filter

Linear approximation, first-order term, still linear.

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Linearized motion model, Linearized measurement model.

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Jacobian matrix

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Limitation of Kalman Filter

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Summary

• 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.

Supplementary Readings

1. How a Kalman filter works, in pictures
2. Extended Kalman Filter: Why do we need an Extended Version?
3. PR, Section 3.1, 3.2, 3.3. (Optional)
4. A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking (Optional)
5. 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.

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Use approximate grid-based filters and particle filters for non-Gaussian cases.

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Origin: Dr. Chris Lu (Homepage) Translate + Edit: YangSier (Homepage)