IEEE Robotics & Automation Magazine - September 2019 - 41

sample step and consist of variables related to the actuators of the vessel, wind conditions, and vessel heading.
The initial learning block performs offline training based
on the sampled targets and inputs. If a GNSS failure
occurs, no targets are available, which precludes any further supervised training. At this point, the input vector is
used to form one-step predictions of the vessel's longitudinal (surge) and lateral (sway) velocities. The proposed
method has the advantage of not being dependent on a
mathematical model of the vessel. Thus, it offers a more
generic way of representing the velocity/position of a vessel due to force input by thrusters and other relevant and
obtainable measurements.
In addition, automatic parameter adaptation can be performed based purely on sampled data. This may be relevant if,
for example, the load distribution on the hull changes during
operation. On the other hand, state estimators, such as the KF
and nonlinear observers, allow for proof of stability and a
more transparent input/output relationship. Figure 2 shows
how the KF approach to DR may be performed. For both Figures 1 and 2, the vertical red line marks the demarkation
between measured position signals and predicted position
signals. A comparison in terms of position estimation performance was made between the two methods to gauge the feasibility of the LSTM model for DR.
Related Work
The DR mode is a position reference fallback system for
marine surface vessels. Vessels operating beneath the ocean
surface may apply DR positioning techniques as the primary
system for determining position [12]. German et al. compared two methods of determining position for an autonomous underwater vehicle [13]. Internal sensors included a
three-axis magnetic compass, a Doppler velocity log, and a
depth sensor. The first method relied on an extended KF fusing global positioning system (GPS) data-transferred acoustically from an autonomous tender vessel-with the onboard
sampled data. The second used only the internal sensors,
which produced DR position solutions.
For DR of ocean surface vessels, Diamant and Jin used a
three-axis accelerometer to provide the DR heading and position of a vessel [14]. They used machine learning to classify
accelerometer data into bins of similar pitch angle and then
projected these onto the local north-east horizontal plane. The
projected accelerations were integrated to yield the estimated
position and heading. The authors used only a three-axis accelerometer as sensor input for DR to avoid using measurements
from a gyrocompass, which, according to them, may be
unavailable or contain too much noise to be of use in estimating the attitude of the vessel.
Rogne et al. investigated the DR capabilities of an INS aided
by dGNSS signals [9]. They applied two different low-cost
IMUs, providing accelerometer, compass, and angular velocity
measurements. Two different nonlinear observers were compared, using no information about the vessel model, on a test
set sampled on a vessel performing a DP operation in the

North Sea. The authors found that the top performer had a
position error of about 100 m after 10 min of dGNSS outage.
DR has been used in other domains as well, such as for automobiles and in aerospace applications. When comparing seagoing vessels with airplanes, it is clear that there is a large
difference in dynamic properties and the severity of wind
impact on the frame of the respective objects. This is especially
true for unmanned aerial vehicles (UAVs) due to their small
size. Mokhtarzadeh and Gebre-Egziabher performed a study of
cooperative navigation for UAVs [15]. Several UAVs connected
in a network shared navigational information during a 5-min
GPS outage to reduce the position error drift rate of a
DR-based navigation filter. The authors opted to
use an integration of airIn the event of a dGNSS
speed measurements
instead of the more tradiposition reference failure,
tional INS sensors to avoid
the double integration necthe state estimator,
essary to determine position from the acceleration
assuming the KF is used,
estimated by the INS. An
additional advantage to
can make estimates based
this approach is the separation of the DR operaonly on the vessel model.
tion from the attitude and
heading reference system.
Instead of using an airspeed sensor, Fusini et al. used a downward-looking camera and
a machine-vision system to provide the velocity of the UAV [16].
The acquired velocity was input to both a nonlinear observer and
an exogenous KF for performing DR, and a bounded error rate
was achieved during experimental real-system testing.
Land vehicles usually follow predefined tracks, often in
areas that are not conducive to robust GNSS signal reception. To produce continuous in-car navigation services,
DR/INS systems, digital maps, and mathematical models of

Wind Speed/
Direction

GNSS
Failure
Position
(Velocity)

t+1

Wind Coeffs
Predicted
Position
in Vessel
Frame

KF
Thruster
Coeffs
Thruster
Revolutions
per Minute

Rotation

Predicted
Position
in World
Frame

Figure 2. The approach for performing DR using the KF. coeffs:
coefficients.

SEPTEMBER 2019

IEEE ROBOTICS & AUTOMATION MAGAZINE

IEEE Robotics & Automation Magazine - September 2019

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