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1 INTRODUCTION

ECDIS systems can integrate various types of

navigation information and display them on an

System Electronic Navigation Chart (SENC),

providing a platform for real-time navigational

decisions. In MSC Resolution 232(82), an amendment

regarding ECDIS performance standards released in

2006, it is emphasized that an ECDIS system must

provide an automatic Dead Reckoning

(DR)/Estimated Position (EP) facility for DR

navigation in the event of GPS failure, and to

crosscheck received positions by other means, such as

visual bearings (Radar, Line of Position [LOP],

celestial fix). Thus, celestial positioning has already

been listed as one of the assisted-positioning options

[1]. Generally, however, only positioning by plotting

LOP using the traditional Intercept Method (IM) is

provided while celestial positioning methods are not

yet implemented. GIS is an important base module for

visual display and processing of navigational

information in an ECDIS system, and eliminates some

of the restraints in previous positioning techniques

conducted on paper maps. Therefore, the positioning

approach proposed in this study was developed using

the ECDIS framework. The method was implemented

within a GIS module, and relies on fundamental

theories of celestial navigation (obtaining a fix by

plotting celestial circle of position - COP). Electronic

chart work is performed using the spatial data

processing and analysis capabilities found in GIS,

achieving outcomes that would be impossible with

paper chart work. The proposed method is simple,

fast, and accurate, and can avoid the cumbersome

work and inaccuracy of the traditional Intercept

Method (IM) or the complicated, and often obscured,

computation involved in numerical methods [2, 3, 4,

5, 6, 7]. The method can also provide a reference for

the development of next-generation electronic

Using GIS to Obtain Celestial Fix under the Framework

of an

ECDIS System

C. Tsou

National Kaohsiung University of Science and Technology

, Cijin District, Kaohsiung City, Taiwan

ABSTRACT: This study proposes a simple method for obtaining a celestial fix, developed within a Geographic

Information System (GIS) under the framework of an ECDIS system. The underlying principle is dependent on

the most fundamental theory in celestial navigation; the circle of position (COP) of the celestial bodies is plotted

to find the fix. Through the spatial data processing, analysis, and visualization capabilities available in GIS, a

celestial fix may be obtained directly from plotting. This eliminates the limitations associated with finding the

fix manually using a paper map, but also avoids the cumbersome work and inaccuracy of the traditional

Intercept Method (IM) or the complicated, and often obscured, computation involved in numerical methods.

The proposed method is simple and accurate, and it applies to problems involving two or more celestial bodies

and high-altitude observations. It provides a reference for the development of a celestial positioning module in

an ECDIS system, and could also be integrated into an educational program on electronic celestial navigation.

http://www.transnav.eu

the

International Journal

on Marine Navigation

and Safety

of Sea Transportation

Volume 14

Number 3

September 2020

DOI: 10.12716/1001.14.03.

676

celestial navigation modules that improve the visual-

fixing functions in ECDIS systems.

2 POSITIONING BY PLOTTING COP

The principle of the COP fix is quite simple, and can

be carried out provided one can plot the COP directly

onto a paper chart. According to the relationship

between celestial and Earth coordinates, in which

they are each other’s projections, an observer’s COP is

the projection of the circle of zenith distance onto the

surface of the Earth. The center of the COP is the

Geographic Position (GP) of the celestial body. The

point of intersection closest to the estimated vessel

position is the observed vessel position (Figure 1).

Figure 1. The principle of COP positioning[4]

3 LIMITATIONS OF TRADITIONAL COP

POSITIONING

Although the principle of obtaining the position fix by

plotting COP is simple, it is difficult to use in practice

due to the following reasons:

1 The radius of COP is too large when plotted on a

typical paper chart.

2 As the measured latitude becomes further from the

equator, there is more distortion of the circle at

higher latitudes (Figure 2).

3 If a globe were used for direct positioning, the

diameter of the globe would need to be very large

to achieve the required accuracy. This is clearly

impractical.

In view of these limitations, the graphical

positioning method using COP can only be applied to

high-altitude observations for celestial bodies with an

altitude greater than 87°. However, such cases are

rare in practice, and therefore this case has very

limited value.

Figure 2. The projected curve of a COP, with the same

diameter, at various latitudes

4 REVISITING GRAPHICAL POSITIONING USING

COP

Digital storage and processing in ECDIS systems has

removed some limitations associated with paper

charts. When displaying vector data, for example, the

entire world or any part thereof may be displayed at

any scale provided adequate computer memory is

available. Maps covering different regions match

perfectly at the boundaries, and may therefore be

viewed as a single contiguous map with no limit on

map size. Moreover, on an ECDIS system, within

which GIS plays a key role, geodetic datum, and

projection can be changed to plot projected curve of

COP easily. For COP positioning, a general chart with

a small scale or an electronic plotting sheet covering

the whole world is enough. Upon completion, the

results can be overlaid on a chart with a larger scale

for display without compromising the accuracy.

5 CELESTIAL NAVIGATION FIX BASED ON GIS.

GIS has been widely applied in a variety of fields.

For example, Traffic Geographic Information Systems

(GIS-T) are an extension of GIS technology into the

realm of transportation, integrating GIS with various

kinds of traffic information analysis and processing

techniques. Marine Geographic Information Systems

(MGIS) are an important application of GIS in the

management of the marine environment and ocean

resource data. Both systems have their own areas of

expertise and technologies. Provided it can be

integrated into Marine Traffic GIS (MTGIS), the new

system can be applied in marine traffic and ocean

surveying. ECDIS can be viewed as such an example.

6 THE INTEGRATION OF GIS WITH THE

NAVIGATION INFORMATION SYSTEM

Figure 3 demonstrates the framework of a Navigation

Information System (NIS). The ECDIS system, as the

core of the NIS, manages spatial data (GIS) and

attribute data (Management Information System –

MIS), and provides a platform for integration of

navigation data and decision-making. Most common

features, such as navigation route planning (e.g.,

checking safety contours and critical area) and

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position monitoring (e.g., XTE alerts, waypoint alerts,

and anchor watch) are derived from the geo-

processing capabilities in MTGIS. It is also shown in

Figure 4 that only a very small portion of GIS

functionality is used in ECDIS at present. To develop

more intelligent NIS in the future, the capabilities of

MTGIS must be expanded.

Figure 3. The relationship between GIS and ECDIS in the

NIS framework [9]

7 IMPLEMENTATION OF GIS IN CELESTIAL

POSITIONING

GIS software ArcGIS 10.5 released by ESRI is

employed in this study; this software package

includes complete GIS functionality and has been

widely applied in geographical information related

research. There is no extra data required other than

the general astronomical observation data. The GIS

functions used are also basic functions that may be

found in any normal GIS software package.

7.1 Input Data

To plot COP of a celestial body in the ECDIS system,

the required input data are a map, the Greenwich

Hour Angle (GHA) and Declination (Dec), and the

observed altitude (Ho) of the body. A general chart

with a small scale or an electronic plotting sheet

covering the whole world may be used. The results

may subsequently be overlaid onto any electronic

navigation chart. Dec corresponds to the latitude of

the GP of the celestial body. GHA must be converted

to represent the longitude of GP. Ho is used to

calculate the radius of COP with the unit of nautical

miles. DR position is used to determine the vessel

position.

7.2 Main Functions in GIS and Operating Procedure

To make the execution automatic, the ModelBuilder

module in ArcGIS was used. The procedure is shown

in Figure 4. The main GIS functions involved in the

process are:

1 Defining the Geodetic Datum: The default geodetic

datum in ECDIS is WGS84, which assumes that the

earth is an ellipsoid with a semi-major axis of

6378137 meters and semi-minor axis of 6356752.3

meters. Both the celestial sphere and the Earth are

considered as perfect spheres in celestial

navigation. The coordinates between the two are

each other’s projections. In astronomical

positioning, COP plotted with respect to the

geodetic datum (WGS84) in an ECDIS system is

slightly different to the COP plotted by assuming

the earth as a perfect sphere. Therefore, the former

datum cannot be directly applied in celestial

positioning. To adjust the geodetic datum, the

average radius of earth (6371000 meters) is taken

as the geodetic datum of Earth as a perfect sphere.

All subsequent distance calculation is based on

this datum.

2 Buffer: In this study, it is proposed that the buffer

function may be used to construct the COP of the

celestial body. The circle is centered at its GP, and

radius is the co-altitude (90°–Ho). In the GIS

environment, different distance units can be used

as radius of the buffer ring, and previously

arduous tasks (such as plotting COP on Mercator

paper chart in high latitude regions or for large

areas) may be easily achieved. In the construction

of COP, radius of the buffer ring must be set as the

co-altitude in nautical miles.

3 Intersections: Locate the intersection of spatial

entities; the intersections of the resultant COPs are

the possible vessel positions.

4 Spatial Query: As there may be more than one

point of intersection between COP, DR position is

needed for further determination. In this study, the

spatial query function is used to search for the

point of intersection near the DR position and to

determine vessel position. The query operator is

set to ‘within a distance’. The radius for the search

is user-defined; however, 60 NM is generally

sufficient. In a two-body fix, a single point is

obtained from this operation, and this point is the

celestial fix of the vessel; in case of a multi-body

fix, a further processing step is required .

5 Mean Center: In a multi-body fix, a group of

intersection points in the proximity of the DR

vessel position is obtained via a spatial query from

multiple COP intersections. The mean center

function calculates the center of this group; this is

the most probable position (refer to Figure 5). This

operation is equivalent to finding vessel position

from the cocked hat region between the points of

intersection.

Figure 4. The procedure used to obtain a multi-body

celestial fix in GIS

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Figure 5. Determination of the Mean Centre.

8 RESULT VALIDATION.

Two-body fix, multi-body fix, and high-altitude

observation data was used to validate the proposed

graphical approach using COP in GIS, by comparing

results with those from three previously published

methods for obtaining a celestial navigation fix. The

three methods used for comparison are traditional IM,

programed IM by Dewit [8], and the computational

method proposed by Metcalf and Metcalf [10].

8.1 TWO-BODY FIX

The data in this case study is taken from Hsu et al.

(2005). It can be seen from Table 1 that the observed

altitude of Alkaid is as high as 77°34.9’, which exceeds

the upper limit of 70° in the intercept method. Hsu et

al. (2005) found that at high altitude, LOP drawn

using the intercept method shifted due to curvature

error, resulting in an inaccurate estimate of vessel

position. Comparison in Table 2 indicates that GIS

COP is not affected by the altitude or latitude of

observation, and the obtained results are the same as

those from other computational methods except for

tradition IM.

Table 1. Extract of relevant information from Hsu et al.

(2005) for two-body

_______________________________________________

Body Capella Alkaid

_______________________________________________

ZT 20-03-58 20-02-56

Ho 15° 19.3' 77° 34.9'

GHA 131° 24.8' 003° 14.2'

Dec 45° 58.4' N 49° 25.7' N

_______________________________________________

Table 2. Two-body fix position

_______________________________________________

DR : L = 41° N, λ = 017° W

_______________________________________________

Method L λ

_______________________________________________

IM 41° 38.6' N 017° 08.1' W

Dewit 41° 39.1' N 017° 07.3' W

Metcalf 41° 39.1' N 017° 07.3' W

GIS COP 41° 39.1' N 017° 07.3' W

_______________________________________________

Figure 6. Results of the two-body fix

8.2 MULTI-BODY FIX

There are four celestial bodies used for calculation in

this case study. In addition to the increased number of

celestial bodies, correction on the running fix is also

applied. Except for IM, where graphical errors may

have resulted in some discrepancies, the vessel

position estimate from the proposed method is close

to the estimate obtained using computational

methods.

Table 3. Multi-body fix

_______________________________________________

Course: 220° Speed: 18 kts

_______________________________________________

Body ZT (1993/9/13) Ho GHA Dec

_______________________________________________

Altair 18-00-00 37° 53.0' 325° 06.6' 08° 51.4' N

Fomalhaut 18-04-00 27° 54.0' 279° 24.2' 29° 39.1' S

Achernar 18-08-00 17° 46.5' 240° 21.7' 57° 15.8' S

Rasalhague 18-12-00 41° 35.5' 002° 04.8' 12° 34.1' N

_______________________________________________

Table 4. Milti-body fix position

_______________________________________________

DR : L =35° S, λ = 005° E

_______________________________________________

Method L λ

_______________________________________________

IM 35° 19.0' S 005° 26.5' E

Dewit 35° 18.6' S 005° 27.0' E

Metcalf 35° 18.6' S 005° 27.0' E

GIS COP 35° 18.5' S 005° 27.1' E

_______________________________________________

Figure 7. Results of the multi-body celestial fix

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Figure 8. Cocked hat region in a multi-body fix

8.3 HIGH ALTITUDE OBSERVATION FIX

In this case, three high-altitude observations were

conducted before and after the sun transit time. Due

to curvature of the line of position, IM is no longer

applicable, and it would be necessary to resort to

graphical methods for high altitude or computational

methods to find the vessel position. Results from the

current study resemble those obtained by

computational methods, and are evidently superior to

those obtained from the graphical method using COP.

Table 5. High altitude observation

_______________________________________________

Course: 290° Speed: 15 kts

_______________________________________________

Body ZT (1996/9/8) Ho GHA Dec

_______________________________________________

Sun 11-56-13 89° 19.4' 269° 38.9' 05° 34.6' N

Sun 11-58-19 89° 36.2' 270° 10.5' 05° 34.5' N

Sun 12-00-41 89° 19.2' 270° 46.0' 05° 34.5' N

_______________________________________________

Table 6. High altitude fix position

_______________________________________________

DR : L = 06° N, λ = 090° E

_______________________________________________

Method L λ

_______________________________________________

COP Plot 05° 59.0' N 089° 47.8' E

Dewit 05° 58.1' N 089° 47.6' W

Metcalf 05° 58.1' N 089° 47.6' W

GIS COP 05° 58.0' N 089° 47.6' W

_______________________________________________

Figure 9. Results of a high-altitude observation fix

9 RESULT DISCUSSION

While the results of this study are slightly different

from those of the other computational methods

described, they are evidently more accurate than

those obtained using the graphical method. The main

reason for the difference lies in the mean-center

function used in multi-body fix procedure, and the

resolution of the COP constructed using the buffer

function (refer to Figure 10). However, the resolution

of the COP produced in the buffer function is

sufficient for normal navigation purposes. Moreover,

the macro functions in the GIS software can link

related functions and make the process more

automatic. The execution time of the whole

positioning process is very short, satisfying the

requirement for real-time positioning.

Figure 10. Different vertex resolution at the intersection of

two COPs

10 CONCLUSIONS

Considering the applications of GIS in marine traffic,

current ECDIS only uses a small portion of GIS

capabilities. To give ECDIS more capability to support

decision-making during navigation, and hence

enhance navigational safety, the functionality of GIS

in ECDIS needs to be expanded. In this work, a direct

celestial fix technique using the COP fix principle

within a GIS system is proposed. The method applies

to two-body fix, multi-body fix, and high-altitude

observation problems; it is simple compared to other

numerical analysis methods, and avoids the

cumbersome calculation and plotting that is required

in more manual methods. Experience with the system

demonstrates that the complicated and cumbersome

calculation and plotting of traditional methods are

avoided, and the proposed method is easier to

perform than other numerical methods. Through

complete integration with an ECDIS system,

positioning results can be presented visually,

facilitating the promotion and application of celestial

navigation. Currently, ECDIS lacks comprehensive

support for celestial fix procedures, and new

functions in this area need to be implemented to offer

alternatives to the existing assisted-positioning

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system in ECDIS so that GPS position can be

crosschecked during ocean voyages. The proposed

framework provides a reference for future

development of celestial positioning modules in an

ECDIS system. The graphical positioning procedures

are simple, fast to perform, produce accurate results

and are also suitable for use in modern celestial

navigation education.

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