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11.2 Sonar Sensor Model 11 Localization and Map Making
All methods of updating uncertainty require a sensor model. Models of sen-
sor uncertainty can be generated in a number of ways. Empirical methods for
generating a sensor model focus on testing the sensor and collecting data as
to the correctness of the result. The frequency of a correct reading leads to
a belief in an observation; the set of beliefs from all possible observations
form the model. Analytical methods generate the sensor model directly from
an understanding of the physical properties of the device. Subjective methods
rely on a designer’s experience, which are often an unconscious expression
of empirical testing.
One robotic sensor which has been heavily studied is the Polaroid ultra-
sonic transducer, or sonar. This chapter will use Polaroid sonars as an exam-
ple; however, the principles of scoring and fusing belief apply to any sensor.
Most roboticists have converged on a model of sonar uncertainty which looks
like Fig. 11.2, originally presented in Ch. 6.
SONAR MODAL The basic model of a single sonar beam has a field of view specified by ,the
PARAMETERS half angle representing the width of the cone, and R, the maximum range it
can detect. This field of view can be projected onto a regular grid. The grid
OCCUPANCY GRID will be called an occupancy grid, because each element l (for eLement) in the
ELEMENT L grid will hold a value representing whether the location in space is occupied
or empty. As shown in Fig. 11.2, the field of view can be divided into three
regions:

Region I: where the affected elements are probably occupied (drawn as a
“hill”),

Region II: where the affected elements are probably empty (drawn as a “val-
ley”), and

Region III: where the condition of the affected elements is unknown (drawn
as a flat surface).

Given a range reading, Region II is more likely to be really empty than Re-
gion I is to be really occupied. Regardless of empty or occupied, the readings
are more likely to be correct along the acoustic axis than towards the edges.
Recall that this is in part because an obstacle which was only along one edge
would be likely to reflect the beam specularly or generate other range errors.
While the sensor model in Fig 11.2 reflects a general consensus, there is
much disagreement over how to convert the model into a numerical value