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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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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 subspaces of the
state space.
•
This, however, requires to monitor whether the robot is
delocalized 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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 Fall '08
 Luke,S

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