Aerospace and Electronic Systems - November 2018 - 5

spaces. Gandor in [22] challenged the problem of GNSS signal
masking in complex mountainous terrain. Zimmermann et al. [23]
presented straightforward approaches to improve the direct positioning accuracies for unmanned aerial vehicle (UAV)-based mapping and surveying applications under challenging GNSS measurement conditions. Starting from a 3D model of the surrounding
buildings and vegetation in the area of interest, a GNSS geometry
map is determined and integrated in the flight planning process, to
reduce GNSS challenging environments. In [24], the authors created a positioning error distribution by simulating the multipath
effect in a control volume. This error distribution, along with a 3D
building model, was used for a path planning which avoids buildings and regions with high multipath effects. In [25] a virtual image processing algorithm is used to detect and eliminate possible
faulty measurements and NLOS satellites, to improve GNSS navigation in urban canyons. Groves in [26] introduced the concept of
intelligent urban positioning, which combines multi-constellation
GNSS, multiple techniques for detecting NLOS signal propagation, and multiple techniques using three-dimensional mapping. In
[27] and [28], a number of advances in the shadow-matching algorithm were presented. Furthermore, a new scoring scheme was developed to account for signal diffraction and reflection. In [29] and
[30], an efficient smartphone-based shadow-matching positioning
system was designed.
Part of the previous work is focused on improving the GNSS
accuracy to enhance the local platform position estimation. The
remaining part is focused on mapping the GNSS accuracy over
a wider area for path planning purposes. The present work uses
both approaches. In particular, this article presents an efficient
algorithm to determine the occluded regions for each satellite,
starting from the knowledge of a mountain digital elevation
model [31], [32]. Based on this occlusion map, a time dependent
DEM is designed for obstacle avoidance. Defining for each satellite the invisible regions in a 3D control volume, the DOP value,
restricted to the visible satellites, can be calculated. A 3D map of
flight and no-fly zones is obtained according to the local value of
the DOP. Once the DOP map is available in the control volume,
the real DEM is updated, by considering a surface that interpolates the DOP values that exceed a given threshold. This new
time-dependent map is called the Digital Morphing Map (DMM).
The DMM can be used to optimize aircraft or helicopter trajectories when they are involved in particularly risky missions, such
as search and rescue operations in mountainous regions, flight
support during wildfires [33], [34] or UAVs applications in urban
NOVEMBER 2018

environments. A further advantage is the compatibility of this approach with all the previously described techniques for positioning error reduction. The integration of the proposed algorithm
with these techniques has the potential to improve the trajectory
planning and, at the same time, guarantee a higher position accuracy. By calculating the DOP map in the control volume, an
obstacle avoidance technique, based on a safety bubble (SBOA),
could be developed. The mathematical background of this technique is introduced in this article. The algorithm, with all the numerical and experimental results, is extensively presented in the
following sections.

METHODOLOGY
This section presents the procedure to calculate and update the
satellite positions, starting from the knowledge of the almanac
data. It also introduces a method for selecting the satellites that
are potentially visible to a user located at a specific place on Earth.
After this, the algorithm to calculate occlusion points is explained
in detail. In conclusion, the methodology to calculate the DMM is
presented.

VISIBLE GNSS CALCULATION
In order to calculate and update the satellite position, the orbital
parameters, listed in Table 1, are required. These values can be
downloaded from the CelesTrack website [35].
The almanac is used to simulate the entire constellation. In case
of a real application, where the more accurate ephemeris data, sent
by the satellites, are available, their use is mandatory. For simulation purposes, the use of a set of data with respect to the other
is irrelevant, preserving the solution consistency. The complete
procedure to estimate the satellite position in the Earth-Centered
Earth-Fixed (ECEF) reference frame, starting from the knowledge
of the almanac data, is extensively described in [36] and reported
for the sake of clarity in Table 2.
Once the position of every satellite is obtained in the ECEF
reference frame, the satellites that are visible from a point P on the
Earth surface can be calculated.
These satellites are those with an elevation angle above the
horizon in the range 5 deg and 25 deg [37]. These values are determined by the link budget and terrain orography. Once the elevation
angle is known, a visibility cone can be defined. The cone angular
aperture is θlim and is defined with respect to the vector direction n

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Aerospace and Electronic Systems - November 2018

Table of Contents for the Digital Edition of Aerospace and Electronic Systems - November 2018