Page 425 - Introduction to AI Robotics

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1.0 1.0 11 Localization and Map Making
don’t know U don’t know U
don’t know don’t know = Occupied = don’t know
Occupied
don’t know
don’t know U don’t know U
Bel’ t Occupied don’t know Bel’ t 0.54
1 1
= Occupied = don’t know
Occupied U Occupied U
occupied = Occupied = Occupied
Occupied
don’t know
0.0 0.0
occupied don’t know occupied don’t know
0.0 0.56 1.0 0.0 0.69 1.0
Bel t Bel t
1 2
a. b.
don’t know U don’t know U
Empty don’t know
1.0
don’t know = Empty = don’t know
0.86

Occupied U Occupied U
Bel’ t
2 Empty don’t know
= φ = Occupied
occupied

0.0
empty don’t know
0.0 0.50 1.0
Bel t
3
c.
Figure 11.16 Applying Dempster’s rule after three updates for the example.

The first step in applying Dempster’s rule is determine the focal elements
l
C k in the combined belief B tha et result from the set intersection of the focal
1 and B j from t n . Although this can be done analyti-
elements A i from t n
cally, it is easier to sketch the unit square out, as shown in Fig. 11.16a.
The total belief has only two focal elements, Occupied and dontknow .There
is no belief mass for ;. The computation of the belief mass is:

(1 :0)(0 :54)
ccupied
m(O ) = = :54 0
1:0 0:0