International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 5
Number 2
June 2011
205
1 INTRODUCTION
SDME (Speed and Distance Measurement Equip-
ment) which presents two axes velocities OG (Over
the Ground) to ship master and/or pilot, such as
Doppler SONAR, etc. is manufactured as the best
application of safety docking to dolphin or berth for
VLCC, etc.
Recently it is also developing to assist maneuver-
ing in approach to a dolphin/berth using high accu-
racy DGPS or RTK-GPS which requires communi-
cation to base-station, and now the new technology
on GPS, called VI-GPS (Velocity Information GPS)
and presents very high accuracy velocities stand-
alone or without communication to base-station, is
coming to onboard application (Tatsumi, et al.,
2009), (Yoo, et al., 2009), and Okuda, et al. (2008)
presented the trade-off between accuracy and re-
sponse in application of docking velocity that means
the performance of Velocity Information is affected
not only by the accuracy but also by the relationship
between the time lag of SDME and her math or time
constant of maneuverability.
Meanwhile, recently it is often taken to dock not
only to a dolphin/berth but also to a navigating ves-
sel called STS (Ship To Ship) operation (Yoo, et al.,
2009). In case of STS operation, it is taken on open-
sea or deep-sea, so the external forces such as cur-
rent, wave and wind affect ship maneuvering, and
onboard sensing external forces are essential to
make a good solution not only for safety but also for
efficiency. So, it is the trade-off between safety and
economical issues. Although it is very important is-
sues to efficiently apply the SDME, but onboard
sensing current and/or wave effect is very difficult
because of the low responsibility and/or poor per-
formance of STW (Speed Through the Water) (Arai,
et al. 1983). So, Arai, et al. (2009), (2010) developed
the algorithm to sense the current and wave effect
without two axes SDME TW (Through the Water).
In this paper, at first VI-GPS, at second the devel-
oped algorithm to sense external forces such as wave
and current are introduced, at third the onboard ex-
periments, results and evaluations are presented and
discussed, finally it is concluded that proposed algo-
rithm and availability of onboard wave sensing with
VI-GPS will be essential to ship operation not only
docking or STS operation but also ocean going, etc.
Onboard Wave Sensing with Velocity
Information GPS
Y. Arai
Marine Technical College, Japan
E. Pedersen
Norwegian University of Science and Technology, Norway
N. Kouguchi
Kobe University, Japan
K. Yamada
ex Hitachi Zosen Corporation, Japan
ABSTRACT: Even though it is essential that the wave information promotes greater safety also efficiency to
navigate and/or operate a ship not only ocean going but also docking/landing, it is very difficult to sense a
wave information such as wave heights and periods or wave lengths in real time at the present time. On the
other hand, the Velocity Information (VI) GPS is developed as the stand-alone 3D velocities measurement
equipment of which accuracies are precise (less than 1 cm/s) and the coverage is all over the world. It is able
to drive the wave information from the time history of not only wave amplitudes but also wave velocities. The
algorithm to sense the wave information such as not only significant wave height but also plural wave heights
and period intervals of encounter was presented by the authors in IAIN2009 and ANC2010. In this paper, the
introduction and the performance of wave sensing with VI-GPS and some results of onboard experiments are
described and discussed.
206
2 VELOCITY INFORMATION GPS
2.1 Outline of VI-GPS
VI-GPS consists of front-end GPS receiver to meas-
ure carrier phases at every epoch and processing unit
which has the differential system of carrier phases
and phased and/or coded GPS positioning system.
VI-GPS positioning system is same as conven-
tional system, so it is able to position fix within the
accuracy of several meters. In the conventional GPS
the measurement of carrier frequency with Doppler
shift drives the velocities or SOG (Speed Over the
Ground) and COG (Course Over the Ground), but
VI-GPS measures carrier phase at every epoch
(m) and calculates the time difference of carrier
phases between serial epochs
is following
(Tatsumi, et al. 2008):
=
= +
(
)
+
(1)
where, is the geometric distance between a sat-
ellite and a receiver (m); c is the light speed in vacu-
um (m/s); dt and dT are the receiver and satellite
clock error (s);
is the measurement noise and er-
rors which are not able to be modelled; and the sym-
bol is the time difference operator.
Time differential observation drives cancelling
propagation errors and little clock errors in the re-
ceiver and satellite, so VI-GPS is a stand-alone sys-
tem which presents high accuracies of velocities
without referential stations around the world.
2.2 Accuracies of Ship’s Velocities
The essential maneuvering information is catego-
rized and shown in Figure 1. In this figure, Heading,
ROT (Rate Of Turning) and Wind Speed and Direc-
tion are measured by the conventional instruments,
and controllable parameters of ship maneuvering are
rudder motion (RUD) and/or propeller revolution
(RPM), etc. Ship’s speed SOG and course OG are
measured by two axes SDME OG such as Doppler
SONAR, etc.
Figure 1. Maneuvering Information
To maneuver for safety and economically espe-
cially in docking, longitudinal and lateral velocities
at a Setting Point P
S
, and the disturbances such as
wind, current and/or wave information are essential.
The relationship between velocities at Setting Point
= (
,
) and Surge/Sway at the Center of Ship
O are following (Arai, et al. 2010):
=
= +
(2)
where,
and
are longitudinal and lateral
velocities at Setting Point of the sensor P
S
; =
(, ) u and v are surge and sway (m/s); and r is
ROT (rad/s).
In case of using VI-GPS, it is able to measure
SOG/COG, so the relationship between SOG/COG
at Sensor Position
= (
,
) is following:
=
cos
(
)
+
=
sin
(
)
(3)
where,
=
(
,
)
is the vector of two
axes velocities OG at center of ship O.
Considering the error propagation from sensor er-
ror, the deviations of surge and sway (d
, d
)
are resolved and following with total differential
equation:
d
= d
+
(
d+
)
+
d(1
+ )
d
= d
(
d+
)
d(1
+ )
(4)
where, deviation of longitudinal/lateral velocity by
VI-GPS is (d
= d
cos+ d
sin) and
(d
= d
cosd
sin);
and
are
the velocities of N-S and E-W direction components
by GPS; and is time difference between VI-GPS
and Compass.
The variances of surge and sway are driven by
Equation 4 and following, if every parameter is in-
dependent statistically:
=
+
+
=
+
+
(5)
where, the variances of VI-GPS, Heading and ROT
are
,
and
.
According to Equation 4 and 5, the countermeas-
ure to decrease the deviations and variances of surge
and sway are described as follows:
1 To install GPS antenna at same point as setting
point where ship master requires to docking.
207
2 In case of STS operation longitudinal velocity is
not so slow, so it affects the accuracy of lateral ve-
locity with the performance of compass.
3 Synchronizing between sampling time of VI-GPS
and heading/ROT information is essential to keep
high accuracy in ship’s turning.
4 In case of sensing wave effect, to install GPS an-
tenna at the ship’s center.
SOG or STW (Speed Through the Water) accord-
ing to logical consideration such as sensor position
and setting point as discussed Equation 2 to 5, but
also it is essential to consider fitting error of sensor,
effect of wake in STW, etc. (Arai, et al., 1983).
2.3 Performance of VI-GPS
Two axes velocities are precisely measured by VI-
GPS, but in the stage of converting to surge and
sway from COG and SOG (Equation 3) there are
some troubles which caused by mismatching of tim-
ing between onboard communication systems in
Compass and VI-GPS. This problem should be sur-
veyed using correlation function or another method,
and the time difference or synchronization should be
within minimum effects. So, in case of high ROT
such as under turning, the effect of mismatching
would increase and it would be difficult to maintain
high accuracy.
The performance of VI-GPS is following and nu-
merical performance is shown in Table 1:
1 VI-GPS works stand-alone and presents high accu-
racy velocities or SOG and COG.
2 VI-GPS has a good response to measure as shown
in Table 1, but total system response should be
limited because of on-board Navigational Infor-
mation system’s data interval.
3 Accuracy of VI-GPS is excellent, and onboard
measuring two axes velocities essential with head-
ing information is available.
4 RAIM (Radio Autonomous Integrity Monitoring)
function is much important to gain the reliability of
ship maneuvering.
Table 1. Performance of VI-GPS
___________________________________________________
The accuracy of Velocity less than 1cm/s
Sampling Time 5 Hz (0.2 s)
Responsiveness less than 1 s
Stand alone Yes
Coverage All over the world
___________________________________________________
3 ALGOLITHM FOR ONBORD WAVE
SENSING
3.1 Effect of the External Forces
The external forces which affect ship operation are
wind, current and wave. The effect of wind is easily
able to be sensed in real time and to be counter-
measured for safety navigation, but it is very diffi-
cult to sense the effects of current and/or wave in re-
al time. The effects of current and wave =
(
,
)
are included in the difference between surge/sway
OG
=
(
,
)
which are easily measured in
high accuracy using two axes SDME OG such as
Doppler SONAR and VI-GPS, and surge/sway TW
=
(
,
)
which are not so easy able to be
measured.
Current is steady for short term, so the current
components (speed and/or direction) will be easily
able to be sensed using LPF (Low Pass Filter) or
moving average method. After sensing current, the
wave effect component will be sensed to subtract
from current component.
The advanced algorithm shown as Figure 4 which
has been developed to improve the demerit of for-
mer algorithm which is able to sense the wave direc-
tion not all around but the limit measurement only
for 90 deg. and the average wave length. So we de-
veloped the advanced algorithm which is able to
sense the direction, length and height of plural
waves using the Fast Fourier Transform. The dis-
turbance forces except DC or very low frequency
components which mean current are following:
=
(
)
sin (
+
)
=
(
)
sin (
+
)
=
(
) (6)
where, angular frequency of encounter is
(rad/s) ; angular frequency of wave is
(rad/s); pe-
riod of encounter is
= 2/
(s); wave length of
encounter
= 2/
(m); wave direction
(deg.); wave amplitude of longitudinal/ lateral com-
ponents are
,
(m); response function of
longitudinal/lateral ship motion are
/
(
)
and
i means i-th wave components.
Surge/sway are affected by ship’s motion, and it is
possible to solve the response functions or models of
longitudinal and lateral motions of ship using differ-
ential equations. It will be assumed that these re-
sponse models are primary response, so response
functions are defined as follows:
/
(
)
= 1/
1 + (
/
/2)
(7)
208
where,
/
is time constant of each response
model.
The values U = (u, v) are observed during proper
time, then the wave components which mean spec-
trum amplitudes
/
(
) and phases
(
)
are resolved by FFT. So, it is able to drive the wave
information from these data and follows:
(
)
=
(
)
+
(
)
(
)
= Atan2[sign
(
)
, sign
(
)
](8)
where,
(
)
and B(
) are speed and direction of
water particles by wave at each frequency; and
sign
/
means sign of
/
(
)
according to
B(
).
The examples of FFT results are following:
Figure 2. The time series of wave effect or U are sampled at
every 1 s during 1 min. Plural waves are found and roughly
reading shows that the average period is less than 10 s
Figure 3. Sample Result of FFT (128 points). The unit of am-
plitude spectrum is shown as “m/s*s^2”, it means amplitude of
velocity at every
Hz
. The unit of amplitude spectrum should
be “(m/s)/
Hz
. The result clearly shows that five waves exist
and their periods. The longest one is 7.5 s and the shortest one
is 1.5 s
3.2 Algorithm of Onboard Wave Sensing
The flow chart of proposed algorithm is shown in
Figure 4, and consists of 5 parts as follows.
1 MMG: this part calculates to gain the two axes ve-
locities TW U
TW
which are longitudinal velocity u
w
(here we call as Surge TW) and lateral velocity v
w
(Sway TW) without effect of current and wave or
only calculated from propeller thrust (ENG), rud-
der motion (RUD) and wind effect (Arai, et al.,
1990).
2 CONVERT: Measured COG and SOG S
OG
are
converted using heading ? ? and sensor position to
gain the two axes velocities OG U
OG
which are
longitudinal velocity OG u
OG
(Surge OG) and lat-
eral velocity v
OG
(Sway OG).
3 SUB: To gain the current including wave effect,
the subtraction from U
OG
to U
TW
and is executed.
U = U
OG
－U
TW :
U consists of the velocity com-
ponents of external forces which are affected
ship’s math, and is named as disturbances. After
subtraction, the coordinate system of U is convert-
ed from the ship coordinates to the terrestrial ones.
4 SPLITTER: It is done to split from U to current
Uc and wave effect Uw using the Low Pass Filter
(LPF) and the High Pass Filter (HPF). Output from
LPF consists of the current component Uc and cut-
off frequency of LPF should be set as lower as
possible and usually be set as 1/30 or 1/60 Hz
which is lower than wave frequency.
5 FFT: FFT gains the frequency component of wave
effect Uw. From the results of FFT, the amplitude
and direction of wave effect Uw with respect to
each frequency or period of wave are possible to
be sensed according to Equation 6.
3.3 Accuracies of Wave Information
The wave amplitude at each frequency is drawn
from the wave velocities Equation 6~8 and shown as
Equation 9.
(
)
=
(
)
(
)
(9)
So, it is able to drive the accuracy of wave ampli-
tude which is following.
d =
(
)
(
)
(10)
=
(
)
+ (
)
(11)
= 2
(12)
where,
,
and
are root mean square of
variances of wave amplitude, measured velocity and
frequency;
is sampling frequency (Hz); and N is
sampling number of FFT.
209
Figure 4. Flow Chart on Algorithm of Onboard Wave Sensing
According to Equation 11, the variance of sensed
wave height consists of two parts. The former is af-
fected by the ship’s mass or the response of ship’s
motion, and the latter is proportional one as sam-
pling parameters.
Using FFT, the every span of sequential frequen-
cies is same. In case of short period, the number of
wave in the width of periods increases. So, it is ex-
pected that the accuracy of wave information will
increase according to averaging in the width of peri-
ods, and these are following:
=
(
(
)
(13)
where, = 1/
(s); is period interval (s);
and INT means integer of ( ).
1 In case of onboard experiment, accuracy of wave
height is within approximately 10 cm until period
is under 15 s and it is available to observe the
wave information.
2 Using VI-GPS, it is not necessary to make a data-
link to base station such as RTK-GPS.
3 In case of large ship such as VLCC, the accuracy
is not so good (1.5 m) because of her ship’s re-
sponse.
Figure 5. Expected variances of Wave Height. (V1: 150GT
T/S, V2:500GT T/S, V3:VLCC) and (A means “f
S
= 5 Hz,
N=1024”, B means “f
S
=1 Hz, N=256”)
4 EVALUATION
4.1 Onboard Experiment
To evaluate the performance of the advanced sys-
tem, the onboard data are used in the former paper
(Yoo, et al., 2009) which used “T/S Shioji-maru” be-
long to Tokyo University of Marine Science and
Technology was executed. Her principals are shown
in Table 1, and the installation of VI-GPS antenna
used in this experiment is shown in Figure 6.
Table 2. Principals of T/S Shioji-maru.
___________________________________________________
Gross Tonnage 425 tons
Lpp 46.00 m
Breadth 10.00 m
Depth 6.10 m
Draught 3.00 m
Displacement 785 DWT
___________________________________________________
Mean wind direction 165 deg
Mean wind speed 5.3 knots
Data length 1200 s
Sampling freq. 1 Hz
___________________________________________________
Figure 6. Arrangement on the Flying Bridge of T/S Shioji-
maru. (VI-GPS ANT is shown in the white circle)
4.2 Results of Onboard Experiments
To survey the availability of the application of the
system using the maneuvering data or onboard wave
sensing, experimentation was executed.
STW Information includes some fluctuation, so it
was confirmed that conventional Speed Log is not
210
applicable to do with high precise and higher re-
sponse. It is easily supposed that according to a poor
performance of Speed Log it was affected by the
wake and/or propeller effects in case of worth instal-
lation.
The advanced system modified to add the FFT ac-
cording to sensing the wave effect. In this experi-
ment original data sampling time is 1 s, so the per-
formance of wave information should be affected by
sampling time. So performance of sensing wave
and/or current at experimented and ideal are shown
in Table 3.
Table 3. Performance of FFT
___________________________________________________
Items Experiment Ideal
Performance Performance
___________________________________________________
Sampling Frequency 1 Hz 5 Hz
Sampling Duration 256 s 204.8 s
Sampling points 256 1024
Frequency Range 1/256 ~ 0.5 Hz 1/102.4 ~ 2.5 Hz
Period Range 2 ~ 256 s 0.4 ~ 102.4 s
___________________________________________________
The results of wave effect information are shown
in Figure 7. Sampling Points of FFT used as shown
in the left column of Table 3 was 256, so the resolu-
tion of frequency is higher in short period. Figure 7
were recalculated and reformed the period width is
approximately 1 s. In shorter period or higher fre-
quency range will be averaged and gain the accura-
cy, so the results are shown under the maximum pe-
riod 17 s.
Figure 7. Current and Wave Information on board Experiment
The sea area of the executed experiments was off
Tateyama at the East side of Tokyo Bay entrance,
the course of T/S Shioji-maru was approximately
040 deg including changing course to 030 deg at 900
s. The observed wave information during the exper-
iments was “light breeze”, but no recorded of the
wave direction.
The solutions of wave effect are shown in Fig-
ure 8. The left graphs show wave level of which the
unit is meter same as wave height, and lower ones
show wave direction which is relative motion to ship
not true motion. The parameter of the horizontal axis
of all of graphs is the period of encounter.
Figure 8. Solution of Wave Information
Figure 9 shows the time history of wave spectrum
for approximately 1,000 s, so it presents the trend of
wave information.
Figure 9. Time History of Wave Height
Summarize of the results of wave information is
following:
1 In early time the wave of which period is 6 s and
relative direction is -90 deg (true direction is 320
deg).
2 After (1) the true direction of the wave (T=7 s) is
080 ~ 130 deg.
3 The wave (T=6 s) and wave (T=7 s) fade out after
approx. 600 s.
4 The wave (T=15 s) appears at 2nd duration (128 ~
383 s) and 4th, the maximum level is 0.8 m and
true direction is 030 ~ 045 deg.
The performance of onboard sensing wave infor-
mation such as level and direction in these experi-
ments is not able to be close investigated, but the
possibility of onboard sensing wave information
211
even during sailing because the trend of wave in-
formation sensed by this algorithm is reasonable
which is wind condition (wind speed: 5 knots, direc-
tion: 165deg.), sea state is light breeze, and accord-
ing to her sailing area the possibility of shadow ef-
fect of Peninsula Bousou.
5 CONCLUSION
The availability of Onboard Wave Sensing using VI-
GPS is discussed and advanced algorithm is pro-
posed to sense the wave effect.
According to the onboard experiments which
show good results and possibility to sense wave ef-
fect on board, the possibility to achieve the meas-
urement and application with a good solution of
onboard sensing wave direction with the advanced
algorithm and the performance of SDME required
not only high accuracy but also high response and
reliability are shown in this paper.
Onboard Wave Sensing system is also advantage
to monitor the ocean wave using free-mooring buoy
with VI-GPS.
Proceeding to develop this system, few points
which should be resolved are following:
1 It is very difficult that absolute onboard evalua-
tion would be done, but many cases should be
surveyed, and gain the reliability of this system.
2 It is essential to review the response function of
ship’s motion because of reliability of wave in-
formation.
3 To apply the good performance of VI-GPS, one
of which is a good response, so using a Gyro-
compass, it takes care to exactly match timing.
REFERENCES
Arai Y., Pedersen E., Kouguchi N. & Yamada K. 2010. The
Availability of VI-GPS for Ship-Operation, In Proceedings
of ANC 2010 in Inchon, KOREA, pp.88-95, November
2010.
Arai Y., Okuda S., Hori A. & Yamada K. 2009. Strategic Ap-
plication of Two Axes Velocities Information for Ship Ma-
neuvering, In Proceedings of IAIN Congress 2009 in
Stockholm.
Arai, Y., Okamoto Y., Asaki K., Kouguchi N., & Yonezawa Y.
1990. A Method of Evaluating Simulation on the Ship’s
Maneuvering, In Review of the Marine Technical College,
No.33, pp.17-34., March 1990.
Arai, Y., Yonezawa, Y., Kouguchi, N., Hashimoto, S., Yama-
da, T., Ueda, H. & Nagao, S. 1983. The Measurement of
Ship’s Path Using the Computer Plotting System with Dop-
pler Sonar. In Journal of Japan Institute of Navigation,
Vol.68, pp.25-36.
Okuda, S., Arai, Y., Hori A. & Yamada, K. 2008. Simulation
Study on the Reliability of Ship’s Velocity for Docking
Maneuvering. In Proceedings of 8th Asian Conference on
Marine Simulator and Simulation Research, pp.217—221.
Tatsumi, K., Kouguchi, N., Yoo, Y., Kubota, T. & Arai, Y.
2009. Precise 3-D Vessel Velocity Measurement for Dock-
ing and Anchoring. In Proceedings of International Off-
shore and Polar Engineering Conference (ISOPE) in Van-
couver.
Tatsumi, K., Fujii, H., Kubota, T., Okuda, S., Arai, Y., Kougu-
chi, N., & Yamada. K. 2006. Performance Requirement of
Ship’s Speed in Docking/Anchoring Maneuvering. In Pro-
ceedings of International Association Institute of Naviga-
tion IAIN 06, Jeju South Korea, pp.67-73.
Yoo, Y., Pedersen, E., Tatsumi, K., Kouguchi, N. and Arai, Y.
2009. Application of 3-D Velocity Measurement of Vessel
by VI-GPS for STS Lightering. In International Naviga-
tional Symposium on Marine Navigation and Safety of Sea
Transportation (TRANS-NAV) in Gdynia.
