International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 3

Number 1

March 2009

Application of 3-D Velocity Measurement of

Vessel by VI-GPS for STS Lightering

Y. Yoo & E. Pedersen

Norwegian University of Science and Technology, Trondheim, Norway

K. Tatsumi

Hiroshima National College of Maritime Technology, Hiroshima, Japan

N. Kouguchi

Kobe University, Kobe, Japan

Y. Arai

Marine Technical College, Ashiya, Japan

1 INTRODUCTION

Applications of ship-to-ship operations for cargo

transfer are expected to be increasing. Currently,

about 25 percentages of all oil imported to the US

comes through lightering operations. An ongoing re-

search program on Ship-To-Ship (STS) operations

with focus on STS lightering has a major objective

to develop a guidance and decision-support system

for the key operative personnel. The initial approach

phase can be regarded as a collision avoidance ma-

neuver which aim is to obtain the required safety

distance, while the final approach is maneuvering

towards the other ship and operation alongside until

the ships have been moored together after which

cargo transfer can commence. STS operations are

individually different because of variations in the

environmental conditions and the maneuvering char-

acteristics of ships.

The final approach phase is particularly critical in

order to avoid steel to steel contact. The officer in

charge of an STS lightering, the Mooring Master,

has currently no equipment at his disposal for de-

termining the relative speeds and distances with suf-

ficient accuracies and the decision of adequate ma-

neuvering orders is thus mainly based on visual ob-

observations (Pedersen et al. 2008).

The velocity of a movable body can be easily de-

termined by using the GPS receiver generated Dop-

pler measurement or the carrier-phase derived Dop-

pler measurement as long as the satellite velocity is

precisely known. The kinematic GPS (K-GPS) is

well known to provide accurate positions. Although

K-GPS assures high precision measurement in a cm

order of magnitude, it is required that the reference

station on land is within 20 km of the moveable

body (Hou et al. 2005).

ABSTRACT: A lightering operation is a type of Ship-To-Ship (STS) operation where two ships are together

in open waters and transfer the cargo e.g. crude oil, LNG. High skills and experience are required by the hu-

man operators as no relevant equipment for determining the relative speeds and distances with sufficient accu-

racies has been implemented. The officer in charge of an STS lightering takes the decision on adequate ma-

neuvering orders based on predominantly visual observations during the final approach. Landing on all

fenders simultaneously is an objective in order to minimize ship-fender contact forces, but this is rather diffi-

cult to achieve in practice even in calm sea due to the effect of hydrodynamic interaction when the ships are

closing in. Furthermore, currents that are present in the lightering zone add to the operational complexity. A

field measurement experiment has been carried out with a Velocity Information GPS (VI-GPS) system in-

stalled onboard a ferry approaching port for berthing which is similar to an STS lightering. The paper propos-

es to apply VI-GPS as input sensor to a decision-support and guidance system aiming to provide accurate ve-

locity information to the officer in charge of an STS operation. It is argued that DOP of VI-GPS is related to

the velocity error.

A method for precise velocity measurement using

Velocity Information GPS (VI-GPS) is described for

STS lightering ship. The Doppler measurement gen-

erated by GPS receiver is a measure of instantaneous

velocity that is measured over a very short time in-

terval, whereas the carrier-phase derived Doppler

measurement is a measure of mean velocity between

observation epochs. The velocity integration with re-

spect to time is the displacement during a period be-

tween the two epochs (Hou et al. 2005).

In this paper, an experiment has been conducted

onboard a ship entering port for berthing where the

velocity information by VI-GPS was used for meas-

uring precise 3-D velocity (longitudinal, transverse

and vertical). The results has been compared with

those of K-GPS and evaluated with respect to DOP

(Dilution Of Precision) of VI-GPS (Hoffmann-

Wellenhof et al. 2004).

2 CONCEPT OF SHIP-TO-SHIP OPERATION

A Ship-To-Ship (STS) transfer operation is an op-

eration where cargo (e.g. crude oil or petroleum

products) is transferred between seagoing ships

moored alongside each other. Such operations may

take place when one ship is at anchor or when both

are underway. In general, the operational phases in-

cludes the approach maneuver, berthing, mooring,

hose connecting, safe procedures for cargo transfer,

hose disconnection, unmooring and departure ma-

neuver (ICS & OCIMF, 2005).

In the case of maneuvering alongside with two

ships at forward speed, the ship acting as the Ship-

To-Be-Lightered maintains steering speed (approx-

imately 5 knots) and keeps a steady course heading.

It is normal that the maneuvering ship, also referred

to as the Service Ship, approaches and berths with

the port side to the starboard side of the STBL.

The other case of maneuvering is that the STBL

is at anchor, which is quite common in STS opera-

tions. For such operations, the STBL anchors in a

pre-determined position using the anchor on the op-

posite side to where the maneuvering ship will ap-

proach. A berthing operation should only be carried

out after the ship at anchor is lying on a steady head-

ing with reference to prevailing environmental con-

ditions.

Figure 1 shows the final stage with both ships

maneuvering alongside with forward speed in calm

seas.

Figure 1. The two ships have come alongside and commenced

mooring operation while still underway at slow forward speed.

The ships will be brought dead in the water and the STBL is to

anchor if the operation takes place in a lightering zone with

shallow waters.

3 VELOCITY INFORMATION BY GPS

The observation equation for the GPS carrier phase

measurements is the following (Hou, 2005):

++−+−⋅+=Φ

ελρ

tropion

ddN)dTdt(c

(1)

where

is the carrier-phase observation;

is the

geometric distance between a satellite and a receiver;

is the light speed in vacuum;

are the re-

ceiver and satellite clock error;

ion

trop

are the

ionospheric and the troposheric delay;

is the re-

ceiver noise and multipath error.

3.1 Velocity Information GPS (VI-GPS)

The velocity information GPS uses the epoch single

difference technique and the first order central dif-

ference approximation of the carrier-phase rate.

Time differential observations are obtained by

subtracting the observations at the previous epoch,

k-1 from those at the present epoch, k. It is assumed

that variations of propagation errors in the iono-

sphere and troposphere are small and negligible

when the interval of observations is short. The time

differential observation is expressed in the following

equation and temporal differences remove the phase

ambiguities:

+−⋅+=Φ

εδδδρδ

)dTdt(c

(2)

Here, the symbol

means the time differential

operator, and

is the phase observation in tem-

poral difference between two epochs. In discrete ex-

pression of Equation 2, the phase difference between

two sequential epochs is measured as following

equation:

∆⋅

Φ−Φ

≈Φ

∆−∆+

(3)

where superscript j represents the satellite; k and

t∆

are the observation epoch and time interval of the

observation, respectively. Figure 2 shows the time

differential carrier phase measurement by VI-GPS.

satellite j

at time t

receiver k

at time t

satellite j

at time t

receiver k

at time t

coordinate origin

)

∆Φ

+∆−∆⋅+∆=∆Φ

dTdt

)(c

)

b(t

)

∆

Rs(t

)

Rs(t

)

-t

∆

t )

)( dTdt

δδ

−

Figure 2. Time differential carrier phase measurement by Ve-

locity Information GPS.

The observation equation can be written as the

following:

L = f (X) + V

(4)

],,[

ΦΦ=

δδ

L

dTdtcdTdtc )](,),([

δδδρδδδρ

−⋅+−⋅+= X

where

is the vector of observations; f(*) is the

vector of known function mapping

;

is the

vector of unknown parameters;

is the vector of re-

siduals; subscript

is satellite number; and

is vec-

tor transposition.

The equation must be linearized with respect to

unknowns before performing the least-squares ad-

justment. Linearization of Equation 4 is made by re-

placing the nonlinear functions with their Taylor se-

ries approximations at the point an initial value of

the solution vector,

and taking only the first or-

der terms.

XL +

∂

=− d

)(f

(5)

W = AX + V

(6)

where

is the misclosure vector,

L − f (X

)

; A is

the design matrix of partial derivatives evaluated us-

ing

; and the vector of residuals.

Assuming that the matrix A at the present epoch k

is identical to the one at the previous epoch k-l, the

least-squares solution of Equation 6 is the displace-

ment between the two epochs. The misclosure vector

that is obtained from Equation 2 is distinguished

from the observation equation for positioning ob-

tained Equation 1.

VXAW +⋅=

δδ

(7)

When the weight of measurement is not equal, the

equation must be weighted with an observation

weight matrix P. If the technique with double differ-

ence observation is used, the mathematical correla-

tion has to be taken into account, using the matrix P.

The normal matrix N, the vector U and the least-

squares solution are derived from the application of

the least-squares principle (

VPV

ˆˆ

→ min.) to Equa-

tion 7 as follows:

N = A

(8)

U = A

(9)



X N U=

−1

(10)

Observation at a one second interval gives a solu-

tion for unit displacement, i.e. velocity. Using the

position from absolute positioning with a single GPS

receiver as a prior position, the least-squares solu-

tion provides the correction to the a priori position.

3.2 Kinematic GPS (K-GPS)

The kinematic GPS uses the double differences

technique and the carrier phase observation equation

is the following (Tatsumi, 2008):

∆∇Φ = ∆∇

+ ∆∇d

+ ∆∇

N − ∆∇d

ion

+ ∆∇d

trop

∆∇Φ

(11)

where

∆∇

is the double difference operator. The

double differences technique needs two receivers.

The reference station is set as a fixed point on land,

while the rover station is set on the movable body.

When the distance between the two stations are

within 20 km, the orbital and atmospheric errors,

∆∇d

ion

and

∆∇d

trop

are illuminated. Equation

11 then becomes as follows:

Φ∇∆

+∇∆+∇∆=Φ∇∆

ελρ

(12)

It is well known that over four double differences

carrier phase observations from four satellites can

decide precise kinematic GPS 3-D position of the

rover station,

rover

. The velocity of the movable

body is calculated from the time differential opera-

tion of this precise rover 3-D position as follows:

rover

∆⋅

−

=∆≈

∆−∆+

(13)

4 SIMULATED STS OPERATION

A simulated STS operation was carried out with a

ferry on 17

of September, 2007 when it was enter-

ing the Sibusi port of Kagoshima prefecture that is

located in southwest of Japan. Figure 3 shows the

experimental area overview. The ferry was equipped

with two GPS receivers that were located on stern

and bow, respectively.

Figure 3. Experimental area overview of Sibusi port.

Table 1. General specification of the ferry, data details and ex-

perimental conditions.

___________________________________________________

Gross tonnage 12,418 [tons]

Service speed 23.0 [knots]

Length overall 186.0 [m]

Width 25.5 [m]

Sampling frequency 5 [Hz]

No. of data samples 8000

No. of GPS satellites 7

(satellites no.) (no. 5, 9, 12, 14, 18, 22, 30)

___________________________________________________

The first part (800 sec) of the approach was simi-

lar to a STS maneuver with the STBL at anchor. It

should be noted that during the time range around

800-1300 seconds the ferry turned backward to the

berth, which is a maneuvering that is not taking

place in any STS operation. The reference station

was about 3 km apart from the berth while the max-

imum distance from the ferry (rover station) was 7

km. (It is well known that K-GPS accuracy has cm

order if the reference station is within 20 km from

the rover station.)

bow antenna

stern antenna

Figure 4. The ferry and positions of GPS receivers.

Table 1 shows the general specification of the fer-

ry, data details and experimental conditions. The ex-

perimental period was about 27 minutes from

standby for entering port until stop engine order with

5 Hz data sampling frequency. The number of data

samples was 8000 recorded by PDA (Personal Digi-

tal Assistance), and each GPS receiver processed the

same GPS signals transmitted by 7 GPS satellites.

Figure 4 shows the ferry and the two GPS receivers

set on the bow and stern side.

K-GPS data was calculated from the reference

station data to rover station while VI-GPS data was

calculated from rover station alone. In this paper, the

velocity by K-GPS is defined as a standard velocity,

and then the velocity error subtracts K-GPS velocity

results from VI-GPS results.

4.1 Experimental results

Figures 5-7 show the results of longitudinal, trans-

verse and vertical velocity components of bow, re-

spectively.

0 200 400 600 800 1000

1200

1400

1600

-4

-2

time (s)

longitudinal velocity (m/s)

Longitudinal velocity component of bow

VI-GPS longitudinal velocity

K-GPS longitudinal velocity

longitudinal velocity error

Figure 5. Longitudinal velocity component of bow.

0 200 400 600 800 1000 1200 1400 1600

-3

-2

-1

time (s)

transverse velocity (m/s)

Transverse velocity component of bow

VI-GPS transverse velocity

K-GPS transverse velocity

transverse velocity error

Figure 6. Transverse velocity component of bow.

200

400

600

800

1000

1200

1400

1600

-3

-2

-1

time (s)

vertical velocity (m/s)

Vertical velocity component of bow

VI-GPS vertic al velocity

K-GPS vertical veloc ity

vertical velocity error

Figure 7. Vertical velocity component of bow.

Figure 5 shows the longitudinal velocity compo-

nents by VI-GPS with black dot line, K-GPS with

blue line and longitudinal velocity error with red line

subtracted the longitudinal velocity component by

K-GPS from VI-GPS result. The velocity is decreas-

ing from around 11 m/s to zero during the recorded

logging time. The velocity is oscillating the first 400

seconds which is due to low frequency waves

(swell) outside the breakwater. As is shown, the two

results by VI-GPS and K-GPS show a good corre-

spondence. Figure 6 shows the transverse velocity

components of bow. VI-GPS and K-GPS results also

show a good correspondence, and similar to the lon-

gitudinal velocity results. Figure 7 shows the vertical

velocity component and the velocity error also has a

small difference.

200

400

600

800

1000

1200

1400

1600

-4

-2

time (s)

longitudinal velocity (m/s)

Longitudinal velocity component of stern

VI-GPS longitudinal velocity

K-GPS longitudinal velocity

longitudinal velocity error

Figure 8. Longitudinal velocity component of stern.

200

400

600

800

1000

1200

1400

1600

-3

-2

-1

time (s)

transverse velocity (m/s)

Transverse velocity component of stern

VI-GPS transverse velocity

K-GPS transverse velocity

transverse velocity error

Figure 9. Transverse velocity component of stern.

0 200 400 600 800 1000 1200 1400 1600

-3

-2

-1

time (s)

vertical velocity (m/s)

Vertical velocity component of stern

VI-GPS ver tic al veloc ity

K-GPS ver tic al veloc ity

vertical velocity error

Figure 10. Vertical velocity component of stern.

Figures 8-10 show the results of longitudinal,

transverse and vertical velocity components of stern,

respectively. Figure 8 shows the longitudinal veloci-

ty components by VI-GPS with black dot line, K-

GPS with blue line and velocity error with red line

subtracted K-GPS results from VI-GPS results. The

results are oscillating during the first 400 seconds

due to the swell. Two results by VI-GPS and K-GPS

show a good correspondence, similar to the bow re-

sults, and its velocity error also shows smaller dif-

ference compared to the longitudinal velocity error.

Figure 9 shows the transverse velocity component of

stern. As same with the results of bow, it shows a

good correspondence with VI-GPS and K-GPS re-

sults. Figure 10 shows the result of vertical velocity

component of stern. The results show a good corre-

spondence between VI-GPS and K-GPS results, and

the vertical velocity error subtracted K-GPS results

from VI-GPS results shows small difference.

Table 2 is the results of longitudinal, transverse

and vertical velocity errors subtracted K-GPS results

from VI-GPS results. From the results, the velocity

errors of bow side show slightly higher standard de-

viation values than stern side velocity errors. Among

the velocity errors at bow, the vertical velocity error

shows the largest standard deviation value with 0.72

cm/s. The vertical velocity error at stern also shows

large value with 0.70 cm/s standard deviation.

Table 2. Longitudinal, transverse and vertical velocity errors of

bow and stern sides.

___________________________________________________

Longitudinal Transverse Vertical

Bow V-error V-error V-error

___________________________________________________

Mean (cm/s) -0.03 -0.13 -0.06

Std (cm/s) 0.24 0.22 0.72

Stern

___________________________________________________

Mean (cm/s) -0.04 -0.13 -0.07

Std (cm/s) 0.22 0.21 0.70

___________________________________________________

4.2 Considerations

From the results showing bow velocity errors the

standard deviations of longitudinal, transverse and

vertical velocity errors have been analyzed. In order

to identify the relation between velocity errors and

DOP (Dilution Of Precision), DOP changes of VI-

GPS was also examined as well as the relation with

bow velocity errors.

200 400

600

800 1000

1200

1400 1600

3.4

3.8

4.2

4.6

time (s)

DOP of bow

VI-GPS DOP of bow

Figure 11. VI-GPS DOP of stern side.

Figure 11 shows how the VI-GPS DOP changes

at the bow side. DOP is increasing according to time

progression from 3.4 to 4.8. Figure 12 shows the re-

lation between bow velocity errors and DOP chang-

es of VI-GPS divided into every 100 seconds. In the

figure, blue ∆, red • and black + symbols show the

standard deviation of longitudinal, transverse and

vertical velocity errors with respect to DOP changes,

respectively. According to the increase of DOP, the

standard deviation of longitudinal and vertical veloc-

ity errors are increasing, but the transverse velocity

error does not show a particular increase according

to DOP changes compared to other velocity errors.

As shown in Figure 12, VI-GPS can be used with a

good accuracy within 1 cm/s standard deviation if

DOP could be obtained under 4.8.

0 0.2 0.4 0.6

0.8 1 1.2

3.4

3.8

4.2

4.6

standard deviation (cm/s)

DOP of bow

Relation between bow velocity error and DOP of VI-GPS

longitudinal V-error

transverse V-error

vertical V-error

Fig 12. Relation between bow velocity error and DOP of VI-GPS.

Table 3. Standard deviation of longitudinal, transverse and ver-

tical velocity errors with respect to DOP changes of bow.

___________________________________________________

Data no. DOP Longitudinal Transverse Vertical

(sec) std (cm/s) std (cm/s) std (cm/s)

___________________________________________________

1-200 3.4-3.5 0.14 0.18 0.54

101-200 3.5 0.17 0.17 0.54

201-300 3.5-3.6 0.19 0.15 0.56

301-400 3.6-3.7 0.23 0.16 0.58

401-500 3.7-3.8 0.22 0.16 0.64

501-600 3.8-4.0 0.24 0.16 0.63

601-700 4.0-4.1 0.21 0.14 0.60

701-800 4.1-4.2 0.17 0.17 0.59

801-900 4.2-4.3 0.16 0.21 0.70

901-1000 4.3-4.4 0.25 0.18 0.72

1001-1100 4.4-4.6 0.22 0.16 0.68

1101-1200 4.6-4.7 0.27 0.18 0.74

1201-1300 4.7 0.24 0.17 0.76

1301-1400 4.7-4.8 0.27 0.16 0.75

1401-1500 4.8 0.28 0.22 0.78

1501-1600 4.8 0.31 0.17 0.83

___________________________________________________

In the final approaches of STS lightering opera-

tion, the longitudinal and transverse velocity infor-

mation is very important for the mooring master.

Therefore, more precise relation between DOP and

longitudinal, transverse velocity errors has been

shown in Table 3 with vertical velocity error as well.

Table 3 shows the standard deviations of longitudi-

nal, transverse and vertical velocity errors with re-

spect to DOP changes of VI-GPS at bow. The veloc-

ity error shows a small standard deviation within 1

cm/s when DOP is under 4.8. The vertical velocity

error has increased gradually according to DOP in-

crease from 0.54 to 0.83 cm/s. Even though, it shows

high values of 0.83 cm/s with maximum velocity er-

ror compared to other velocity errors, it is consid-

ered that VI-GPS has an enough accuracy under 1

cm/s. Furthermore, because the longitudinal and

transverse velocities are mainly used as important

information in the final approaches of STS lightering

operation, the vertical velocity error can be negligi-

ble.

5 CONCLUSIONS

STS operations represent a challenge to the officer

in charge because currently there is no equipment

implemented that can provide the relative speeds and

distances with sufficient accuracies. Decision of ad-

equate maneuvering orders is then based on visual

observations. VI-GPS has been applied to measure

precise 3-D velocity (longitudinal, transverse and

vertical) for STS operations. The advantage is that

precise accuracy is not limited to distances within 20

km as the case of K-GPS.

An experiment representing a simulated STS op-

eration was done in Sibusi port of western Japan

during entering the port. The results of VI-GPS ve-

locity showed a good correspondence with K-GPS

velocity results, i.e. within 1 cm/s.

From the result of relation between bow velocity

errors and DOP of VI-GPS, 3-D velocity by VI-GPS

has precise accuracy within 1 cm/s level compared

to K-GPS if DOP of VI-GPS can be obtained under

4.8. The longitudinal and transverse velocity of bow

side showed standard deviation of 0.24 and 0.22

cm/s, respectively. It is considered that VI-GPS has

sufficient accuracy to serve as sensor input for

providing relative velocities in a decision-making

and guidance system tailored for STS operations.

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