Aerospace and Electronic Systems Magazine August 2017 - 26
Inertial Navigation and Simultaneous Localization and Mapping
Figure 4.
The evolutions of the 172 feature uncertainties (only 1σ values on the north axis are shown for clarity),
along with the number of satellite vehicles, which drops from seven to three and one (right axis). As each
feature is added to the filter on the fly, its initial covariance monotonically decreases because of subsequent filter updates. The large uncertainties until 60 s and between 130 and 170 s are related to the new
features added, or georeferenced, from each trajectory cycle. However, those uncertainties drop rapidly at
the loop-closure events, which happen at 60 and 170 s.
COMPRESSED IMPLEMENTATION
As described in the previous section and Figure 3, the state estimates and the covariance matrix are partitioned into local and
global parts to reduce the computational complexity of SLAM
[15]. The state vector and the covariance matrix are represented as
xˆ L xˆ v
ˆ
xG = mˆ L
mˆ G
PL
P
GL
Pxx Pxm
PLG
Pmx Pmm
=
PGG
P
GL
(9)
PLG
PGG
0
,
I NG
(11)
with NG being the dimension of the global map. Similarly, for the
newly registered features, the global initialization Jacobian GG is
constructed from the local compressed Jacobian GL:
G L , k
G G ,k =
0
0
.
I NG
(12)
Because this work adopts the unscented filtering framework, all
Jacobians are induced from the sampled sigma points rather than
direct linearization, thus reducing the effects of the nonlinearity in
the system.
(10)
SIMULATION RESULTS
where xL includes the vehicle state xυ and the local landmarks mL,
while other landmarks are stacked as mG.
The key aspect of the compressed implementation is in accumulating, or compressing, the cross-correlation terms: Pxm between
the vehicle and the local map and PLG between the local and the
global maps. This is achieved by preserving the local Jacobian
FL,k and three auxiliary variables (for more details, refer to [15]).
Whenever the cross-correlation term PLG is required, a global Jacobian is formed as
26
FL , k
FG , k =
0
To validate the tightly coupled SLAM performance on a full 6DOF
platform scenario, the high-fidelity simulator GPSoft is used to
generate the flight trajectory, along with raw measurement data.
SIMULATION ENVIRONMENT
The simulation parameters are listed in Table 1 for IMU, GPS,
range, bearing, and elevation sensors. The IMU has an accelerometer bias of 2 mg and gyroscope bias of 100°/h, which are the typi-
IEEE A&E SYSTEMS MAGAZINE
AUGUST 2017
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