Page 398 - Introduction to AI Robotics

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11.3 Bayesian
approach presented here. In a Bayesian approach, the sensor model gener-
ates conditional probabilities of the form P (sjH). These are then converted
to P (Hjs) using Bayes’ rule. Two probabilities, either from two different sen-
sors sensing at the same time or from two different times, can be fused using
Bayes’ rule.

11.3.1 Conditional probabilities
PROBABILITY To review, a probability function scores evidence on a scale of 0 to 1 as to
FUNCTION whether a particular event H (H stands for “hypothesis”) has occurred given
an experiment. In the case of updating an occupancy grid with sonar read-
ings, the experiment is sending the acoustic wave out and measuring the
time of flight, and the outcome is the range reading reporting whether the
region being sensed is Occupied or Empty.
Sonars can observe only one event: whether an element g r[i][ i dis Occu-
]
j
pied or Empty. This can be written H = fH :Hg or H = fOccupied;Empty g.
;
The probability that H has really occurred is represented by P (H):
0 P (H) 1

An important property of probabilities is that the probability that H didn’t
happen, P (:H), is known if P (H) is known. This is expressed by:

1 P (H) P (:H) =

As a result, if P (H) is known, P (:H) can be easily computed.
UNCONDITIONAL Probabilities of the form P (H) or P (:H) are called unconditional probabil-
PROBABILITIES ities. An example of an unconditional probability is a robot programmed to
explore an area on Mars where 75% of the area is covered with rocks (obsta-
cles). The robot knows in advance (or a priori) that the next region it scans
has P (H = Occupied ) :75 . = 0
Unconditional probabilities are not particularly interesting because they
only provide a priori information. That information does not take into ac-
count any sensor readings, S. Itis more usefultoa robottohave a func-
]
j
tion that computes the probability that a region g r[i][ i dis either Occupied
or Empty given a particular sensor reading s. Probabilities of this type are
CONDITIONAL called conditional probabilities. P (Hjs) is the probability that H has really oc-
PROBABILITIES curred given a particular sensor reading s (the “j” denotes “given”). Uncon-
ditional probabilities also have the property that P (Hjs) P (:Hjs) +0. = 1
: