IEEE Robotics & Automation Magazine - March 2014 - 59

building under consideration as well as its width. These data
are obtained from aerial images of Google Earth. Then, a
frontal view of the building is needed to estimate its height. To
address the complexity of determining this unknown, a
Canny detector algorithm [8] has been programmed. This
algorithm processes the frontal view of the facade of the
building, which is obtained with the Street Viewer tool of
Google Earth, to provide a scale model. The relation between
the parameters of both the real object and its model is then
used to determine the real height of the building.
Since a complete frontal view of the facade is not always
available in Google Earth, a second complementary approach
called story-based method is foreseen and can be applied when
needed. The principle of this latter method is the application
of the prior algorithm only to the parts of the buildings which
are visible in the Google Earth image, normally the ground
floor and the first few stories. Then, a straightforward computation is used to extrapolate results for the entire building,
with the common assumption that upper stories have the
same height as those at the lower part of the building. More
details of this can be found in [9].
EEmap-Based Method
With the purpose of classifying signals from satellites according to their visibility, an appropriate NLOS detection algorithm has been developed. The principle is to combine the
information stored in the EEmap described before and the
data from GPS, particularly the satellite positions, to determine whether nearby buildings are blocking a given satellite
signal. It is important to know that an initial estimate of the
receiver position, more precisely of the position of the
antenna, is required to define the relative geometry between
the rover and the surrounding buildings. In the frame of this
study, this position is interpolated from the reference trajectory (see the "Test Equipment" section).
Both elevation and azimuth angles are delivered by the
receiver for each satellite. Then, the coordinates of the corners
of the facade of the building and the estimated height stored
in the EEmap are used to compute its elevation and azimuth
angles. Finally, the geometrical interval of blockage of the
obstacle is obtained. This concept is depicted in Figure 1.
Let i and j denote the identifiers of a satellite and a building, respectively. If the elevation and azimuth angles of satellite i (E si and A si, respectively) are inside the region of nonvisibility of building j, satellite i is determined to be in an
NLOS situation.
The elevation (E si ) angle for satellite i is calculated
cos (E si) =

sin (c)

1

re 2
re
2
;1 + ` j - 2 $ ` j $ cos (c)E
rsi
rsi

(1)

with
cos (c) = cos (L e) $ cos (L si) $ cos (l si - l e) + sin (L e) $ sin (L si),
(2)

Bj

Si

Ebnj
Esi

Vehicle
Abnj
Asi

Abj

North

Figure 1. The EEmap concept for an NLOS detection.

Local Horizontal

Esi

Subsatellite Point

rsi

c
Earth
Station

re

Center
of Earth

Figure 2. The geometry of elevation angle.

where:
rsi = radius of satellite i
re = radius of the earth
c = angle with respect to the earth's center between the subsatellite point and the edge of coverage (see Figure 2)
L si = latitude of satellite i
l si = longitude of satellite i
L e = latitude of the reference position
l e = longitude of the reference position.
To find the azimuth angle for each satellite, an intermediate angle a must be used. The intermediate angle allows the
correct quadrant to be determined since the azimuthal direction can lie anywhere between 0° (true north) and clockwise
through 360° (back to true north again). The intermediate
angle is found from
a

= arctan =

tan |(l si - l e)|
G.
sin (L e)

(3)

Then, the azimuth angle for each satellite A si can be
obtained as follows:
MARCH 2014

*

IEEE ROBOTICS & AUTOMATION MAGAZINE

*

59



Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - March 2014

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https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2021
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