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)

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