Aerospace and Electronic Systems Magazine August 2017 - 29

Kim et al.

Figure 6.

Detailed views of tightly coupled SLAM and GPS during successive loops. The number of SVs drops to one for the rest of the flight. The plots show
that the uncertainties of the vehicle and map further decrease monotonically because of successive reobservations and loop closures. The bottom-right
panel shows the top-down view of the map or trajectory.

ance parameters seem too conservative considering relative to the
actual errors. This implies that further refinement of error models
may be warranted.

COMPUTATIONAL COMPLEXITY
The computational complexity of the filter is determined by the
UKF sampling strategy and the size of the feature map (N). The
complexity of the full-sampling UKF increases rapidly as O(N3).
Because the partial sampling strategy is adopted in this work, the
UKF attains a O(N2) complexity, which is comparable to that of
the EKF. Figure 11 (a) compares the UKF update times of an uncompressed version (in dash-dotted red lines) and a compressed
version (in solid blue lines). The map size N of the uncompressed
UKF increases as the vehicle explores the area, as does the filter
update time. However, the compressed version maintains a constant local map size of N = NL ≤ 12 during the simulation, making it
suitable for real-time implementation. Figure 11 (b) compares the
AUGUST 2017

cumulative runtime, which includes the inertial navigation, prediction, and update, for the uncompressed and compressed versions of
EKF and UKF. The total flight time is 245 s, and the total running
time of the UKF is 219 s, which is the slowest but slightly faster
than that of the EKF at 204 s. The total cumulative time of the
compressed UKF (26 s) is comparable to that of the compressed
EKF (20 s), but considering the total flight time, both compressed
filters seem to be efficient enough to run in real time.

CONCLUSIONS
In this article, we presented a computationally efficient and tightly
coupled integration of GNSS and inertial navigation with SLAM,
aiming for continuous 6DOF navigation solutions in cluttered environments. The unscented SLAM filter was developed to be suitable for IMU-based navigation and then extended to a compressed
form by dividing the map into a small, manageable local map and a
global map. The locally collected information was compressed and

IEEE A&E SYSTEMS MAGAZINE

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