cs685-particle-filters - Probabilistic Robotics Bayes...

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1 Probabilistic Robotics Bayes Filter Implementations Discrete filters, Particle filters 2 Piecewise Constant Representation of belief 3 Discrete Bayes Filter Algorithm 1. Algorithm Discrete_Bayes_filter ( Bel(x),d ): 2. η = 0 3. If d is a perceptual data item z then 4. For all x do 5. 6. 7. For all x do 8. 9. Else if d is an action data item u then 10. For all x do 11. 12. Return Bel’(x) 4 Piecewise Constant Representation
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2 5 Implementation (1) To update the belief upon sensory input and to carry out the normalization one has to iterate over all cells of the grid. Especially when the belief is peaked (which is generally the case during position tracking), one wants to avoid updating irrelevant aspects of the state space. One approach is not to update entire sub-spaces of the state space. This, however, requires to monitor whether the robot is de-localized or not. To achieve this, one can consider the likelihood of the observations given the active components of the state space. 6 Implementation (2) To efficiently update the belief upon robot motions, one typically assumes a bounded Gaussian model for the motion uncertainty. This reduces the update cost from O(n 2 ) to O(n) , where n is the number of states. The update can also be realized by shifting the data in the grid
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cs685-particle-filters - Probabilistic Robotics Bayes...

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