Aerospace and Electronic Systems Magazine August 2017 - 27

Kim et al.
Table 1.

The Simulation Parameters Used for IMU, GNSS, and the Range, Bearing, and Elevation Sensors
Sensor

IMU

GPS

Type

Unit

Specification

Sampling rate

Hz

100

Accel bias

mg

2

Gyro bias

°/h

100

Accel bias stability

g, 1

0.02

Gyro bias stability

°/h, 1

100

Accel bias correlation
time

s

300

Gyro bias correlation time

s

300

Frame rate

Hz

1

Receiver clock bias

m

0.1

Receiver clock drift

m/s

10−6

Pseudorange noise

m, 1

2

m/s, 1

1

Earth model

-

WGS-84

Frame rate

Hz

5

FOV angle

°

30

Range noise

m

1

Bearing noise

°

1

Elevation noise

°

1.5

Pseudorange rate noise

RBE

RBE, range, bearing, and elevation.

cal performance of a low-cost, automotive-grade IMU. The GPS
sensor utilizes the WGS-84 Earth model and has a pseudorange
noise of 2 m (1σ) and a pseudorange rate noise of 1 m/s (1σ). The
receiver clock bias and drift are simulated to have values of 0.1 m
and 10−6 m/s, respectively. The range, bearing, and elevation sensor
has a 5-Hz output rate with a down-looking field of view (FOV) of
30°. The flight trajectory generated is shown in Figure 5. It consists
of two racehorse tracks after taking off, and each track has two
loops at an altitude of 50 m. The flight time is 245 s, and the average flight speed is 20 m/s. MATLAB was used to implement the
SLAM filter on a computer with an Intel i7 processor at 3.4 GHz
and 8 GB of random access memory (RAM). For the data association between the feature observations and the map, the joint compatibility branch and bound (JCBB) method is implemented [33],
in which a set of feature measurements are matched to multiple
hypotheses of map features to improve the robustness of matching.

TIGHTLY COUPLED SLAM RESULTS
Figures 5 and 6 illustrate the three-dimensional trajectory and the
evolution of the states in the tightly coupled SLAM and GPS system. Figure 5 depicts the results during the first racehorse loop,
initially fusing the pseudoranges from seven satellite vehicles (in
AUGUST 2017

magenta lines upward) and the ground feature measurements (in
red). The rectangular box underneath the vehicle is the dynamic
local region boundary with local map uncertainties shown in blue,
while the global feature uncertainties are shown in red outside of
the box. The number of satellite vehicles (SVs) drops to three while
maintaining the navigation performance, and the first loop-closure
event, revisiting the initial place, successfully reduces the map and
vehicle uncertainties. Figure 6 shows the successive loops with a
single SV measurement. The plots show that the uncertainties of
the vehicle and map further decrease monotonically because of
the successive loop closures. The bottom-right plot shows the topdown view of the final trajectory, showing the estimated features
on the ground with uncertainty ellipsoids (10σ is used for clarity).
Recall that Figure 4 showed the evolutions of the feature uncertainties in the northward direction (172 registered out of 400 total
features, and only the north axis is shown for clarity), along with
the number of satellite vehicles dropping from seven to three at 50
s and one at 100 s (the right axis of the plot). Because new features
are added to the filter during the flight, their initial covariances
monotonically decrease due to subsequent observations. Around
60 s, the map uncertainties decrease below 0.5 m, as well as around
170 s, which is the effect of the loop closure in each track-that is,
the vehicle reobserves the previously registered map features and

IEEE A&E SYSTEMS MAGAZINE

27



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