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of no more than 0.10 seconds which is enough time to close the yaw angle control
loop on-board of the UAV.
4.3 Performance Metrics
In this work, we apply two standard metrics to evaluate the performance of
the proposed multilevel data decomposition:
speedup
and
e
ciency
.Bothare
common metrics used by the research community to evaluate the performance
of parallel algorithms [17].
The speedup evaluates how much faster is a parallel algorithm than its sequen-
tial version. The
relative speedup
(SRS) is defined as the ratio of the execution
times of the sequential algorithm (
TS
1
) and the parallel version executed on
m
computing elements (threads or processors) (
TP
m
) (7). We also evaluate the
parallel capabilities/scalability of the proposed algorithm by comparing the exe-
cution times of the parallel algorithm executing on one (
TP
1
)and
m
computing
resources (
TP
m
), which we call
Parallel Relative Speedup
(PRS) (8). When ap-
plied to non-deterministic algorithms (i.e., due to non-deterministic situations in
the computing environment or non-deterministic bifurcations in the algorithm
itself), the speedup should compare the
mean
values of the sequential and paral-
lel execution times, obtained in a reasonable number of independent executions.
The ideal case for a parallel algorithm is to achieve linear speedup (
SPS
m
=
m
),
but the common situation is to achieve sublinear speedup (
SPS
m
<m
), due to
the times required to communicate and synchronize the parallel processes.
The eciency (9) is the normalized value of the speedup, regarding the num-
ber of computing elements used for execution. This metric allows comparing
algorithms executed in non-identical computing platforms. The linear speedup
corresponds to
e
m
= 1, and in usual situations
e
m
<
1.
SPS
m
=
TS
1
TP
m
PRS
m
=
TP
1
TP
m
e
m
=
SPS
m
m
(7)
(8)
(9)
4.4 Results and Discussion
To validate the parallel implementation, previous to the performance analysis,
the yaw angle estimation of the sequential application and various of the parallel
configurations were compared using the sFly and QA3 data sets, and the results
are reported in Fig 6 and Fig. 7, respectively.
Figure 6a shows that the different estimates are almost coincident and most
of the time are overlapped. In Fig. 7a is also possible to see the overlapping of
the parallel and sequential versions. Black lines show in both cases the actual
orientation. These results validate the parallel implementations and they lead to
use any parallel configuration as a reference baseline, provided that time is not
being measured like in Fig. 6b and Fig. 7b where the absolute error is shown.
