IEEE Robotics & Automation Magazine - September 2019 - 47

For the network predicting the sway velocity, the variables
are 2, 3, 4, and 7. The input patterns are thereby reduced to
66% (surge velocity) and 44% (sway velocity) of the original
input length. The data set used for training contains 10 4
samples spaced by 1 s. Over the course of about 2.5 h of simulation time, 12 randomly chosen weather conditions were
run. Wave heights and wind velocities were chosen within
the ranges given in Table 4.
A comparison of the performance in terms of estimated
position, relative to the sampled true position, is shown in

Figure 7, which displays the mean error with and without MI
over a 1-min DR period for all weather conditions in the test
set within which the vessel was able to keep the desired position. The deselected weather conditions are highlighted in
case study 2. As noted in the "Vessel and Environment
Description" section, each individual weather condition lasts
for 14 min; 1 min toward the end of each weather condition
was applied for the DR tests. Using the complete input vector
for both the surge velocity and sway velocity estimators
results in an increase in position error. Figures 8 and 9 show

Learning Rate

6
4

North (m)

2

-6
-8

-6

-4

-2
0
East (m)

2

4

6

Figure 6. A visual representation of the vessel position for a part
of case study 2. The noiseless position measurement (red line) is
included only to provide a reference to the raw dGNSS position
output (blue line).

Average
Position Error (m)

With MI
6

0 m/s
4 m/s
11 m/s

4
2
0

0

10

20

30
Time (s)
(a)

40

50

60

Block Number

-4

0

2

2.5

3

2
0

0

10

20

30
Time (s)
(b)

40

50

60

Figure 7. The mean DR error of the LSTM method for all wind
directions at wind velocities of 0, 4, and 11 m/s. (a) A subset of
the elements in the complete input vector was extracted using
MI and used as input to the LSTM model. (b) All entries in the
complete input vector were used as input to the LSTM model.

Block Number

Average
Position Error (m)

0 m/s
4 m/s
11 m/s

4

200

4.5

5
×10-3

MI
No MI

150
100
50
0

2

2.5

3

3.5
MSE
(b)

4

4.5

5
×10-3

Sway Velocity

0.1

MI
No MI

0.05
0

2

2.5

3

Without MI
6
4

3.5
MSE
(a)

Figure 8. The results of running the LSTM hyperparameter
optimization function on the two parameters, (a) learning
rate and (b) block number, for the surge velocity
estimation model.

Learning Rate

Measured
Noiseless
Start Position

MI
No MI

0.05

0
-2

Surge Velocity

0.1

3.5
MSE
(a)

4

200

4.5

5
×10-3

MI
No MI

150
100
50
0

2

2.5

3

3.5
MSE
(b)

4

4.5

5
×10-3

Figure 9. The results of running the LSTM hyperparameter
optimization function on the two parameters, (a) learning
rate and (b) block number, for the sway velocity
estimation model.

SEPTEMBER 2019

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IEEE ROBOTICS & AUTOMATION MAGAZINE

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47
IEEE Robotics & Automation Magazine - September 2019

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - September 2019
