Page 103 - Autonomous Mobile Robots

86 Autonomous Mobile Robots

sections and absorption coefficients are approximately the same in
all directions with respect to that feature.
• The measured returned power should be independent of range (due to
the built-in range compensation filter). This filter must first be
removed or post-filtered to remove its effect, to produce range
dependent power returns from all objects [15].
• The beam-width of the RADAR wave does not increase considerably
with range.

A target is assumed to affect the incident electromagnetic radiation in three
possible ways:

1. A portion of the incident energy ϒ R ,0 ≤ ϒ R ≤ 1, is reflected and
scattered
2. A portion of the incident energy ϒ a ,0 ≤ ϒ a ≤ 1, is absorbed by the
target
3. A portion of the incident energy 1−(ϒ R +ϒ a ) is further transmitted
through the target

ϒ R is thus referred to as the “normalized” RCS section. Figure 2.27 shows
a MMW RADAR in an environment with i-features down-range at a particu-
lar bearing. The following terms are used in formulating the predicted power
observation:

• P INCi = Power incident on the ith feature
• P REFi = Power reflected from the ith feature
• P TRANi = Power transmitted through the ith feature
• P INCi1 = Power incident on the first feature which is reflected from
the ith feature
• P REFi1 = Power reflected back toward the ith feature from the first
feature. This component will not reach the RADAR receiver directly
and is not considered in this formulation
• P TRANi1 = Power transmitted through the first feature which is the
reflection from the ith feature

The power incident at the first feature is given by

P t GA I
P INC1 = (2.27)
2
4πR 1
where P t is the power transmitted by the RADAR, G is the antenna gain, and
R 1 is the distance between RADAR and the first feature and A I is the area
be the normalized
of the object illuminated by the RADAR wave. Let ϒ R 1

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c002” — 2006/3/31 — 17:29 — page 86 — #46