When analyzing the performance of the relative location-based GPS availability algorithm,
the relative location trajectories must first be examined to determine where GPS is expected
to be available. Figure6.3shows the ALT (Figure6.3(a)) and S L (Figure6.3(b)) trajecto- ries for each altitude. The pairs of dotted vertical lines in each figure represent the entrance
and exit of the intersections with the large white space between the pairs of line repre-
senting for the urban canyon. At h= 125 meters the ALT categorization stays above all buildings providing persistent GPS availability. At h= 75 meters the ALT categorization varies from below the tops of all buildings along the first block to above all buildings in the
second block, to above the tops of some buildings along the third and fourth blocks. This
variation results in sporadic GPS measurements initially, with more regular measurements
available as the UAS moves through the environment. When the UAS is at h= 50 meters the ALT categorization begins below the tops of all buildings until just prior to the third block
were it moves to below the tops of some buildings due to the adjacent open space along
the third block. Once the UAS crosses into the fourth block, ALT is again below the tops
of all buildings. At this altitude, GPS measurements will be much less frequent, but still
not completely eliminated. This thorough sampling of ALT categories over runs spanning
three separate altitudes ensures navigation accuracy through all possible ALT transitions
will be reported. Since the same lateral profile is flown for all three altitudes, each of the
0 200 400 600 0 0.5 1 1.5 2 2.5 3
Longitudinal Position (meters)
ALT (−) h = 50 meters h = 75 meters h = 125 meters (a) ALT 0 200 400 600 0 0.5 1 1.5 2 2.5 3
Longitudinal Position (meters)
SL (−)
(b) SL
Figure 6.3: Relative location categorization for straight and level trajectories through urban environment.
Figure 6.4 is a representative plot, using data from Monte Carlo Trial #500, to view trends in GPS measurement generation as a function of altitude and and surrounding urban
canyon characteristics. It shows that the most GPS measurements occur at h= 125 meters since GPS is available to take a measurement every second, while this number decreases
as the UAS altitude decreases due to loss of satellite line of sight. For this specific run
only 8 of a possible 19 measurements are available at an altitude of 75 meters with 5 of the
measurements coming in the second canyon where the UAS is above all buildings. At 50
meters, only 6 of 19 measurements available with multiple measurements only occurring
in the third canyon. These values demonstrate the possible ineffectiveness of GPS as a
reliable navigation sensor when the UAS is below the tops of buildings.
Figures 6.5 and 6.6 show the horizontal position and altitude/airspeed RMSE trajec- tories at h= 75 meters comparing the GPS constant availability method with the relative location-based algorithm. Each shows the trajectory at h= 125 meters for comparison. For the longitudinal position shown in Figure6.5(a) the two techniques yield similar results, reaching a steady error of roughly 0.8 meters, because the measurements provided by the
0 200 400 600 0 20 40 60 80 100 120
Longitudinal Position (meters)
Altitude (meters)
Figure 6.4: GPS measurement locations at each altitude using the varying GPS availability technique.
constant availability method were not sufficiently accurate upon exiting the second canyon
to outperform the varying availability trajectory that generally had fewer measurements
available. This was due to the UAS ALT category switching from above the tops of all
buildings to above the tops of some buildings with its larger measurement noise values af-
ter that point. Neither method performed as well as the h= 125 meter trajectory as it had more accurate measurements available at each sampling point along the canyons, reaching
a steady error of approximately 0.7 meters.
The lateral position trajectories shown in Figure6.5(b)show the similar sawtooth trend to those in the previous chapter as the UAS attempted to center itself within the canyon.
However, there was a linear increase in error at h= 75 meters using both GPS availability algorithms as the available measurements became less accurate in the third canyon. How-
ever, halfway though the third canyon, the constant availability trajectory error dropped
while the varying availability trajectory error continued to climb, signifying the lack of
available measurements for this algorithm. As both error trajectories continued to increase
UAS continued to receive more accurate measurements. 0 200 400 600 0 0.2 0.4 0.6 0.8 1 1.2
Longitudinal Position (meters)
x N
RMS Error (meters)
h = 125 meters/GPS Avail Constant h = 75 meters/GPS Avail Constant h = 75 meters/GPS Avail Varies
(a) Longitudinal 0 200 400 600 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Longitudinal Position (meters)
x E
RMS Error (meters)
(b) Lateral
Figure 6.5: Horizontal position RMSE trajectories at h= 75 meters for both GPS availabil- ity methods with h= 125 meters baseline shown.
The altitude trajectories shown in Figure 6.6(a) show no real difference in accuracy performance between the two GPS availability algorithms at different altitudes since the
ADS provided an accurate high sampling rate measurement regardless of GPS availability
or accuracy. A steady-state error of 0.2 meters in altitude is sufficient to navigate in the
urban environment, assuming all sensors are working properly. The airspeed trajectories in
Figure6.6(b)show a steep decrease in error regardless of the GPS availability method since the ADS also measures airspeed. However, the h= 125 meter trajectory does not decrease as fast as the h= 75 meter trajectories since it is not able to take advantage of optical flow airspeed when above all buildings. However, by the second canyon, a sufficient number
of measurements have been received for all three trajectories to approach the same steady-
state error value below 0.1 meters/second.
Figures 6.7 and 6.8 show the horizontal position and altitude/airspeed RMSE trajec- tories at h= 50 meters comparing the GPS constant availability method with the relative location-based algorithm. Each shows the trajectory at h= 125 meters for comparison.
0 200 400 600 0 0.2 0.4 0.6 0.8 1 1.2
Longitudinal Position (meters)
h RMS Error (meters)
h = 125 meters/GPS Avail Constant h = 75 meters/GPS Avail Constant h = 75 meters/GPS Avail Varies
(a) Altitude 0 200 400 600 0 0.1 0.2 0.3 0.4 0.5
Longitudinal Position (meters)
V T
RMS Error
(meters/second)
(b) Airspeed
Figure 6.6: Altitude and airspeed RMSE trajectories at h= 75 meters for both GPS avail- ability methods with h= 125 meters baseline shown.
The longitudinal error trajectory in Figure6.7(a)shows that the error worsens when GPS is unavailable and gets slightly better with variable GPS availability at h= 50 meters. The dif- ference is based solely on the number of location measurements received. In the constant
availability case, the only measurements received are those from the LTE sensors which
are scarce and 4 seconds delayed when received. In the varying availability case, even if
a small number of GPS measurements are received, they still augment LTE to provide a
more accurate estimate. For the lateral position in Figure 6.7(b), both error trajectories at h= 50 meters increase with the constant availability increasing roughly linearly from 1 meter to 2 meters and the varying availability increasing from 1 meter to 1.75 meters until
the third canyon and then leveling off as more position measurements are received. For the
varying availability case, the error will grow in areas where measurements are scarce and
level off in areas where measurements become available with more regularity. These error
increases highlight the difficulty in controlling the lateral position of the UAS when so few
measurements are available to increase the accuracy of the estimate.
0 200 400 600 0 0.2 0.4 0.6 0.8 1 1.2
Longitudinal Position (meters)
x N
RMS Error (meters)
h = 125 meters/GPS Avail Constant h = 50 meters/GPS Avail Constant h = 50 meters/GPS Avail Varies
(a) Longitudinal 0 200 400 600 0 0.5 1 1.5 2
Longitudinal Position (meters)
x E
RMS Error (meters)
(b) Lateral
Figure 6.7: Horizontal position RMSE trajectories at h= 50 meters for both GPS availabil- ity methods with h= 125 meters baseline shown.
show similar results to those at h= 75 meters since the state accuracy is mostly depen- dent on the accuracy of the ADS altitude and airspeed measurements. As previously seen,
the availability of V IS ION − OF × 2 airspeed measurements allows the error to initially
decrease more quickly in the first canyon at h= 50 meters than at h = 125 meters.