Aerospace and Electronic Systems Magazine August 2017 - 28

Inertial Navigation and Simultaneous Localization and Mapping

Figure 5.

Detailed views of tightly coupled SLAM and GPS during the first round. Top left: after taking off, the system initially fuses the pseudoranges from
seven satellite vehicles. The line of sight of each of the SVs is shown in magenta. The ground features are shown in red. The rectangular box on the
ground is the local region boundary with local map uncertainties (in blue). Map uncertainties outside the region are shown in red (top right) and (bottom
left) present incremental map building, simultaneously correcting IMU errors. The number of SVs drops to three. The bottom-right panel shows the
vehicle revisiting the initial place (loop closure) and the reduced map and vehicle uncertainties.

thus has a chance to estimate accumulated errors during the loops.
The large uncertainties that appeared from 130 s are related to the
registration of new features along the second racehorse track.
Figures 7 to 9 show 12 Monte-Carlo simulation results for the
navigation errors and IMU bias estimations. The north and east position errors with 2σ uncertainties are shown in Figure 7, in which
the errors are computed as the difference of the estimated and true
positions. Because the number of satellites drops to three around
50 s, the position error starts growing until 60 s, when the vehicle
closes the loop and thus improves map accuracy. When the vehicle
exits the first circuit and registers new features from the second
circuit, the position error increases again (the number of satellite
vehicles is one during this interval) until the loop closure occurs at
170 s. However, those uncertainties from the two tracks approach a
similar lower bound, which is determined by the sensing uncertainties. From these, the complementary benefits of tight integration of
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GNSS and inertial navigation with SLAM can be observed. SLAM
can effectively aid the low-cost inertial navigation system under a
lower number of visible GPS satellites (one satellite vehicle in this
demonstration).
Figure 8 provides 12 Monte-Carlo simulation results for roll
and yaw angle errors, showing consistent convergence but with
less sensitivity to the loop closures. Figure 9 (a) depicts the estimated bias from the accelerometer x-axis, showing the reliable
convergence to the true biases (2.0 × 10−2 m/s2). The estimated gyroscope x-axis bias also converges to the truth (100°/h).
One of the benefits of tightly coupled fusion is the capability
of estimating the GPS receiver clock bias and drift. Figure 10 illustrates the convergence of the estimated receiver bias and drift
to 0.1 m and 10−6 m/s, respectively, thus enabling a precise timing
output even when there is only one visible GPS satellite. Although
the clock bias and drift converge to the true value, the filter covari-

IEEE A&E SYSTEMS MAGAZINE

AUGUST 2017

Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine August 2017