International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 1

Number1

March 2007

Combined Maneuvering Analysis, AIS and Full-

Mission Simulation

K.G. Aarsæther & T. Moan

Norwegian University of Science and Technology, Trondheim, Norway

ABSTRACT: This paper deals with a method for identifying the main parameters of a maneuver using both

real-time full mission simulators and positioning data obtained from the Automatic Identification System of

the same area. The effort required for experiments in real time maneuvering is naturally larger than the effort

required to collect already available data. Analysis of both data sources is presented. We show how the

curvature of the ships track can be related to the wheel-over point and further used to estimate the main

parameters of a course-changing maneuver. The southern approach to the Risavika harbor in the southwest of

Norway is used as a demonstration. The approach angle and turning circle diameter was accurately identified

in both AIS and simulator data, but significant navigational markings was only quantifiable in simulator data.

1 INTRODUCTION

To investigate the effect on navigation decisions and

external effects on ship maneuvering it is convenient

to test these scenarios in a simulator with controlled

conditions and good opportunities for data

collection. If such simulations are to represent the

real world it is important that the processes that are

simulated are similar to their real world counterparts.

In traditional fully automated maneuvering simula-

tions (Hutchinson, 2003, Merrick, 2003), a regular

control-theoretic guidance and autopilot combination

is often used to represent the maneuvering decisions

on the bridge of the ship. This control theoretic

construct is not well suited to represent the decisions

on the bridge, as it does not follow the same guiding

rules as a human would. The first step to replace this

control theoretic construct is to identify the proper

maneuvering processes and then to quantify their

main parameters. These main parameters can later be

used as input to a numerical navigator for fully

automatic maneuvering simulation. Quantification of

the main features and parameters can be made from

expert opinion and simulator studies with human

operators. Simulator studies are a costly and time

consuming process, but offers the best accuracy and

provides control of the environment in which the

maneuver is executed. Simulator studies can also be

augmented by real world data whenever possible,

with simulator studies providing the entry point into

analysis of coarser real world data.

Risavika

Harbor

Traffic

Entering/Leaving

Traffic

Entering/Leaving

Fig. 1. Risavika With Main Traffic Concentration

Data from the Automatic Identification System

(AIS) has a potential to reveal the preferred naviga-

tional patterns and maneuver parameters in use in a

specific area. The AIS system is implemented by all

IMO member states as per requirement of SOLAS.

The system represents an opportunity to study the

traffic and navigational patterns in costal areas. Data

available from AIS introduced in recent years has

not been used for this purpose.

In this paper we will show how the main

parameters of maneuvering can be quantified by use

of simulator trials and AIS data. We will focus on

the area around the Risavika harbor in the southwest

of Norway. An overview of the area and the main

traffic routes is seen in Figure 1. The routes of traffic

shown are extracted from AIS data from the area.

1.1 Representation of maneuvering

Maneuvering of a ship in transit can be represented

as a combination of course keeping and course

changing maneuvers stringed together to form a

complete plan for the voyage. This representation is

described in (Lüzhöft, 2006) where it is presented as

the standard planning procedure for pilots and

shipmaster operating in the costal areas around

Stockholm in Sweden. The voyage plan is in the

form of straight sections with the heading for both

passage directions noted with turning diameters for

each turn. In addition the significant landmarks and

navigation aids used to determine when and where to

transit between these maneuvers are noted. The

maneuvers of the vessel is joined together at points

where the wheel of the vessel is either used to

initiate a turn (wheel-over-point) or the point where

action is taken to exit the circular turn path (pull-out-

point). The approach to Risavika harbor is modeled

as a section with constant course followed by a Rate-

of-turn maneuver to change the vessels course to a

more beneficial course for entry into the harbor.

1.1.1 Course keeping

Course keeping is the simplest of maneuvers and

is the task of keeping the vessel on a straight course.

The only variability one expects is the individual

error tolerances in deviation from desired course or

the variability in entry of autopilot targets. The main

parameter of this maneuver is the desired course.

1.1.2 The rate-of-turn maneuver

The rate of turn maneuver is marine

craftsmanship and is based on simple rules of thumb

calculations of an object speed and the curvature of

the path it follows. An object will travel on a circle

of diameter D if the ratio of the speed and rate of

turn is constant; the constant determined by the

circle diameter is a defining parameter of the

maneuver. The rate-of-turn of the vessel is reported

as degrees per minute on the bridge of the vessel.

The time in minutes for a vessel with speed V m/s to

complete a turn of 360° on a radius of r m is

t =

2 ⋅

⋅ r

(1)

To get the rate of turn in ° per second needed to

stay on the circle of radius r we divide 360° with

time from Equation (1).

ROT=

360°

2 ⋅ r ⋅

⋅ 60

3°⋅V

r ⋅

≈

(2)

The final simplification is to transfer the

expression into an easy to remember rule of thumb.

This simple rule is the foundation for the rate-of-turn

maneuver where the master of the vessel actively

will use the controls to keep the relationship between

the vessel speed and rate-of-turn constant. The

constant determines the radius of the turning circle.

The turning circle radius is then the defining

characteristic of the rate-of-turn maneuver. In a

nautical setting the rule is applied with knots as

speed and nautical miles as measure for the radius.

With a given turning radius of 0.5 nautical miles,

this relationship between rate of turn and speed in

knots easily gives the required rate-of-turn for this

maneuver.

ROT =

0.5

= 2 ⋅V

(3)

1.2 Quantification of parameters

From the AIS data and simulator trials the following

maneuvering characteristics were identified in the

northbound approach to Risavika:

− Approach course angle

− Number of turning maneuvers used

− Wheel-over-point position

− Pull-out-point position

− Mean and max turning circle radius for each

turning maneuver

The Rate-of-turn maneuver used in the simulator

study has characteristics, which we also can

calculate from the data available from AIS. This will

be done in turn to show the accuracy of these

calculations. The radius of the turning circle used in

the maneuver is identifiable from the rate-of-turn vs.

speed ratio maintained by the vessel during the

maneuver.

The curvature of the track line can be used to

extract the number of turning maneuvers used on a

section of the passage.

From the charts of the area and the simulator

environment we have the location of the significant

navigational lights in the area. The positions of these

lights are used together with the wheel-over and

pull-out points to try to determine the most probable

navigational light used. The position of the

navigational lights in the simulator area was used

both in the simulator trials and in the analysis of the

AIS data.

2 SIMULATOR TRIALS

Full mission simulator data was recorded from

training exercises at the Ship Maneuvering

Simulator Centre (SMSC) in Trondheim, Norway.

Simulator trials were used to determine a benchmark

maneuver and used with the greater fidelity of the

synthetic environment to analyze the time series of

available variables. Simulations where carried out

with human operators on the bridge simulators

piloting the vessel into Risavika harbor. The

simulator centre has three full mission simulators in

operation and by introducing an automatic logging

application on the simulator network the communi-

cation from each simulator was intercepted. The start

of logging was triggered by the start of the exercise

for the Risavika maneuver. Data was written to disk

and made both the simulated vessel state as well as

the control inputs for rudder and engines available as

time series for offline analysis. Data was sampled at

1 sec intervals to limit file size.

2.1 Trial maneuver

The trial maneuver selected for study was a

maneuver to enter the harbor in Risavika from the

south starting at a course of 0° N. The starting

position for the ship has no obstructions on the

initial heading, and will with the initial speed in a

relatively short amount of time be in a position to

initiate the turning maneuver into the harbor. The

turning maneuver into the harbor is predefined. The

bridge crews were instructed to change the ship’s

course using a rate of turn maneuver with a radius of

0.5 nautical miles until they were on a course

suitable for the final approach. By inspecting the

rudder time series in the simulator trials the wheel-

over-point for the transition between the first course

keeping section and the rate-of-turn maneuver was

identified. This point for each dataset allowed

calculation of the heading at the time of maneuver

transition, and the angle between the vessels and all

the visible navigation lights in the simulated area.

The same procedure was used to identify the pull-

put-point, completing information about the

maneuver.

2.2 Results

In total 44 maneuvers were recorded from SMSC

exercises with a variety or bridge crews. Some

exercises were discarded due to approach path. The

discarded exercises followed a radically different

path with fundamentally different features than the

typical maneuvers, 36 cases remained in the end.

Maneuver transition points and track curvature was

extracted form this data. The mean and max value of

the relationship between rate-of-turn and the speed

during the rate-of-turn maneuver is seen in Figure 2.

Figure 2 shows a median value of the mean rate-

of-turn/speed relationship of 1.75. This translates to

a turning circle radius of 0.571 nautical miles. If we

account for the introduction of 3/3.14 = 1 in the

rule-of-thumb simplification of the formula, the

theoretical turning circle has a radius ≈ 0.54 nautical

miles. The deviation then becomes only 0.03

nautical miles and is in good agreement with the

theoretical value. Both mean and max values shows

skewed data. The mean rate-of-turn/speed relation-

ship packed tight around the median. The results

showed very good agreement with the ideal turning

circle radius one should expect from the briefing.

Some of the deviations are from the exercises

following a slightly different path into the harbor.

Fig. 2. Distribution of rate-of-turn/speed from simulator trials

Fig. 3. Angle from vessel to navigational lights in simulator

trials at the wheel-over-point

The results from the calculation of the angle

between the wheel-over-point and the visible lights

in the simulator were plotted as a boxplot to

determine correlation. The results are seen in Figure

3, where the angle to the first landmark seems to be

very consistent across trials and at an angle of 90° it

is preferable since it is indifferent to cross track

deviations (the last landmark is in close proximity,

and shows a very similar distribution). If the first

landmark is taken as the significant maneuvering

landmark used, then we can find a statistical

description of the variability of the wheel-over-point

in relation to the angle to the landmark. We see a

skewed distribution around a median of about 90°

for the first landmark, with a few outlier cases, again

from a different approach path.

Another result from the simulator experiments

was the relation between the Wheel-over-point, Pull-

out-point and the local extreme values of the track

curvature. The wheel-over point was always located

near a local minimum while the pull-out point was

located near a local maximum. An example time

series is seen in Fig. 4 where the relevant points are

indicated. The nonzero curvature for zero rudder

angles shows the tendency of single-screw ships to

turn at zero rudder angles due to propeller inertia and

asymmetric flow around the stern

Fig. 4. Rudder angle and curvature in relation to wheel-over

and pull-out points

In the simulator studies the difference in time

between the Wheel-over-point and the local

minimum was computed and is shown in Fig 5. This

proximity can be used to make a qualified guess

about the location of these points based on rate-of-

turn and speed data. The local extreme value

behavior will be used later to find good candidates

for wheel-over and pull-out points in the AIS data

for the same area.

Fig. 5. Wheel-over-point deviation from local extreme value of

the track line curvature

3 AIS DATA ANALYSIS

The Norwegian Costal Administration provided AIS

data in form of position reports for April, May and

June 2006 for the presented area. The position

reports where then restricted to the immediate area

around Risavika before it was grouped according to

each ships unique MMSI number (IMO, 1974).

Requiring the track line to start to the south and end

in the harbor was used to restrict the AIS data

further. The data for each MMSI number was then

further sorted by time and grouped in space to form

datasets of track lines continuous in these

dimensions. This procedure was necessary due to the

presence of misconfigured AIS transponders making

identification solely based on MMSI number

difficult. The AIS data received contained time,

position, speed over ground, rate of turn and course

over ground. The sample rate of the AIS data

depends on the ships speed and state of the vessel

and will during transit and turning maneuvers for

moderate speed be in the area of 0.3 – 0.5 Hz (IMO,

1974).

The AIS data does not contain information that

makes it possible to pinpoint the transitions between

the different maneuvers, such as the instantaneous

position of the rudder. We can however find features

from the maneuvering techniques used in the data in

form of the speed, rate-of-turn and position in the

AIS data with an accuracy of about 5 seconds as

presented in Fig. 4 and Fig. 5. The AIS data does not

contain rate-of-turn information for all vessels, but

calculation of the curvature of the track line of the

vessel will accurately identify the value of the

speed/rate-of-turn relationship. The ratio between

the vessels rate-of-turn and the speed relationship

corresponds to the curvature of the ship track.

Calculation of the curvature will work regardless of

the absence of rate-of-turn information in the signal.

The total number of AIS track lines was 429, which

was further subdivided into 308 single turn

maneuvers, 107 two turn maneuvers and 14

maneuvers with 3 or more turns which were

discarded due to accuracy of the procedure and

implied poor accuracy in the position reports.

3.1.1 Calculating curvature from position data

The curvature κ of the ships track can be

calculated from the position and time data. This can

done by filtering the position data to remove noise

and then use a numerical expression for the

curvature calculated by solving the equation for a

circle passing through the three consecutive points. κ

can also be directly from the time domain signals for

the position x=x(t) and y=y(t). The curvature of

these two signals in Cartesian coordinates with

the tangential angle of the signal.

dtds

dtd

φφ

(4)

2 2 22

( /) ( /) () ()

d dt d dt

dx dt dy dt x y

φφ

= =



(5)

The need for d

/dt can be eliminated by the

following identity

tan

dy /dt

dx /dt

(6)

sec

(tan

)

(7)

1 tan

d xy yx

dt x

−

   



(8)

Equation (8) substituted into Equation (5) gives

the final expression for the curvature

2 2 3/2

()

xy yx

−

   



(9)

This expression for κ relies on the derivative and

double derivative of the vessel track line positions.

Numerical calculation of these derivatives from

noisy position data is inherently error prone. Instead

of calculating the derivatives numerically, the

derivatives are evaluated by fitting polynomials to

the x(t) and y(t) signals. It is impossible to find a

general polynomial to describe the complete track

with sufficient accuracy for the entire ship track. To

calculate the curvature at a specific track sample, a

order polynomial is fitted at a section spanning

20 samples both forward and backward in time. This

provides both a theoretical form for the evaluation of

the derivatives and suppresses the noise in the

positioning data. The derivatives and double

derivatives can then easily be evaluated from the

corresponding formulas for polynomials. The

polynomial fit was computed using MATLAB’s

‘polyfit’ function using both centering and scaling to

improve the numerical properties of the fitting

procedure.

3.1.2 Detection of turning maneuvers

Detection of turning maneuvers was done by

discretizing the number range for the curvature into

regions of size 1e-4. The curvature signal was then

compared to this interval forming an array of 0 and 1

values. The array represents the image of the area

between the x-axis and the curvature signal. This

representation made it easy to determine where the

curvature crossed certain numerical values, and how

many crossings it did of a particular value. The

curvature level used to detect significant changes in

track curvature was 3e-4; the number of crossings

over this value was easily extracted from the line of

the kappa image array corresponding to this value.

The number of up-crossings over this value was an

initial estimate of the number of turns in the

maneuver. The area beneath each turn was compared

and if the area during one turn of a two-turn

maneuver was less than 10% of the area of the other

turn, the maneuver was reclassified as a one-turn

maneuver. After the turning maneuvers were

identified the Wheel-over and pull out point where

assigned to the local extreme values.

3.2 Results

The results from the AIS data processing showed a

deviation in the preferred route into the harbor for

the southern approaches compared to the simulator

experiments. The difference concerns the approach

angle towards the harbor, making the turn into the

harbor less severe in reality than in the simulator.

The AIS data further showed that the traffic entering

the harbor was divided into one and two turn

approaches. The one turn approach still followed the

same basic principle as the simulator experiments,

while the two turns approach used an additional

course-changing maneuver before the final turn into

the harbor. The two-turn approach followed a sepa-

rate pattern with a course change roughly the same

place as the one turn maneuver but with a final sharp

turns used to enter the harbor. Only data for a single

turn maneuver is used to calculate the approach

angle, curvature, wheel-over and pull out points.

Fig. 6. Course angle at the wheel-over-point

The curvature of the track line was calculated as

described in Section 3.1.1 and is shown in Fig. 7.

The mean and max curvature is calculated using

values between the wheel-over and pull-out point

identified in the manner described in Section 3.1.2.

The results are similar to those of the simulator study

but with more variation and a larger discrepancy

between the mean and max curvature. The median of

the mean curvature is 0.00101 corresponding to

990m ≈ 0.535 nautical miles. This result fits nicely

with the numerical values for the turning circle

diameter estimated from the simulator trials. The

curvature distribution from AIS is less skewed and

follows a more normal distributed form. Outlier

cases are fewer as shown in Fig 7, but the maximum

curvature shows a far greater range.

Fig. 7. Curvature of AIS Track Lines During Turn

The wheel-over and pull-out point for the AIS

data was harder to quantify, and only a qualitative

conclusion could be drawn from the data. No clear

candidate as in the case of the simulator trial

emerged.

4 DISCUSSION

The approach angle, number of turns and turning

circle diameter was well estimated with a good

accuracy in comparison with the values found in the

simulator trials. The relatively small number of

simulator trials highlights a drawback: the limited

amount of time and resources to study a maneuver.

However a more intense simulation program can

mitigate this effect.

The position of the wheel-over and pull-out point

is harder to relate to the navigational lights in the

area. This may be because of the inherent error in

estimating these points from the curvature or due to

the numerical effects on the calculation due to the

proximity of the navigational lights to the track line,

exaggerating any errors in the angle estimate.

Another cause for the difficulty in identifying a

pattern in the wheel-over and pull-out points in the

AIS data is the possibility that its high dependence

of vessel dynamics makes it a poor candidate for

analysis across a wide selection of vessels. The

points where the track line curvature exceeded 1e-4

were more clustered around a specific point. This

effect is possible with a large selection of ships with

different dynamic responses all aiming for the same

turning circle starting at the same point, a pattern we

have seen in the AIS data. This effect can be further

investigated using static ship data available from the

ITU’s Maritime mobile Access and Retrieval System

database linked with ship statistics for dynamic

response.

The turning circle diameter used and the number

of turns used was more accurately identified in both

the simulation trials and the AIS data from the same

area. Ships entering Risavika use a turning circle

diameter of 0.5 nautical miles for one course change

approaches to the harbor. The main difference from

the simulator trials here is the approach angle which

was 15° in service compared to 0° in the simulator

studies. Ships using a 0° approach angle used

navigational light 1, “Laksholm” initiating the turn

at 90° angle. This pattern was also visible in AIS

where a very limited number of vessels used the 0°

approach.

5 CONCLUSION

It has been shown that analysis of the ship track line

can be used to estimate the parameters of standard

maneuvers. This can be useful either in conjunction

with simulator studies or by itself. The parameters of

the rate-of-turn maneuver extracted from the

combination of simulator and AIS data can be used

later as input to a numerical navigator to mimic the

behavior of the real navigator. AIS present itself as

an easily available source of information about the

desired maneuvering patterns in a specific area.

More importantly the parameters of the maneuvers

are quantifiable from this data. The navigational aids

used are best identified using full-mission simulation

or expert opinion.

REFERENCES

Hutchinson B.L, Gray D.L, Mathai T, “Manoeuvring Simula-

tions – An Application to Waterway Navigability”

Transactions - Society of Naval Architects and Marine

Engineers, Vol 111, 2003, p 485-515

International Maritime Organization, “The International

Convention for the Safety of life at Sea (SOLAS)”, London,

1974, as amended

Lüzhöft M.H, Nyce J.N, “Piloting By Heart And By Chart”.

The Journal of Navigation Vol 59, 2006, 221-237

Merrick J.R. W. van Dorp J.R., Blackford J.P, Shaw G.L.

Harrald J., Mazzuchi T.A. “A Traffic Density Analysis of

Proposed Ferry Service Expansion in San Francisco Bay

Using a Maritime Simulation Model”, Reliability Engineer-

ing and System Safety Vol 81, 2003, 119-132