Maritime University of Szczecin
Akademia Morska w Szczecinie
2010, 20(92) pp. 140–145 2010, 20(92) s. 140–145
Navigation based on characteristic points from radar images
Prowadzenie nawigacji na podstawie punktów
charakterystycznych z obrazów radarowych
Mariusz Wąż
Polish Naval Academy, Institute of Navigation and Hydrography Akademia Marynarki Wojennej, Instytut Nawigacji i Hydrografii Morskiej 81-103 Gdynia, ul Śmidowicza 69, e-mail: m.waz@amw.gdynia.pl
Key words: navigation, radar, radar images Abstract
A radar image of a coastal zone is a source of information, which enables setting out a vessel’s positions precisely. A feature of radar navigational systems, if compared to the satellite ones, is connecting a pointed out fix to elements of seashore and dangers to navigation, surrounding a vessel. It’s an essential condition of navigating safely a vessel within the specified water area. Radar display elements, identified as characteristic points, should be included in the interactive navigational structure. Such a structure is a basis for accurate sailing a vessel on a water area. The whole process can be automatized. Automation may refer to a stage of setting out characteristic points in the navigation water area and also to a stage of marking out a position under observation.
Słowa kluczowe: nawigacja, radar, obrazy radarowe Abstrakt
Obraz radarowy strefy przybrzeżnej jest źródłem wielu informacji umożliwiających precyzyjne wyznaczanie pozycji jednostki. Cechą odróżniającą radarowe systemy nawigacyjne od systemów satelitarnych jest to, że wyznaczona pozycja jest połączona z elementami wybrzeża i otaczającymi jednostkę niebezpieczeństwami nawigacyjnymi. Jest to podstawowy warunek bezpiecznego prowadzenia jednostki na wyznaczonym akwe-nie. Elementy obrazu radarowego zidentyfikowane jako punkty charakterystyczne powinny wchodzić w skład interaktywnej struktury nawigacyjnej. Struktura ta będzie podstawą precyzyjnego prowadzenia jednostki po akwenie. Cały ten proces może być zautomatyzowany. Automatyzacja dotyczy zarówno etapu wyznaczania punktów charakterystycznych w akwenie pływania, jak również etapu wyznaczania pozycji obserwowanej.
Introduction
Within a coastal zone, a vessel’s fix should be set out in relation to elements, describing a layout of navigation distresses’ positions in the water area. For any watercraft, dangers are constituted by sea shore, shallow waters, also detached dangers (wrecks, sea bottom objects etc.), harbour structure members and others. A common practice is finding out a vessel’s fix, using satellite systems (GPS). It is applied – both in open sea and in a coastal zone, even within a port area and narrow passages and others. At present, the satellite systems enable navigators to obtain really exact position of vessels.
The position is continuous, currently updated. However, there may occur gross errors and sporadic fix fading. It effects from unfavourable configuration of satellites, improper operation of the systems etc. Approaching a location of any distress as a shore, port heads, beacon or quay, the navigator must not make any mistake. The costal navigation methods are linked with the dangers through observation thereof. An error of a fix coordinates measured towards the dangers is dependent only on navigational parameter survey accuracy. On approaching thereof, the fix survey accuracy grows, as a navigational parameter is set up more precisely. This is the most fundamental
condition of navigation carried out nearby a sea shore. To work up a vessel’s position in a coastal zone, a network of navigational on-shore or nearby the shore marks is used. A navigator should know such marks’ positions and each of the marks should be appropriately identified. Sometimes, characte-ristic coast elements are applied for positioning; in such a case they have to be identified and presented in a nautical chart. The whole process of setting out a vessel position is to be automatized. Therefore navigational radar, which allows observation of a coastal zone, is to be used. Thus, observation, recording and analyzing radar displays, also data processing are to be subject to automation. This paper presents the method of setting out and extracting characteristic points of radar displays. A part of the points coincide with those marked on the chart and stand for buoyage (navigational marking) of water area. Still not all of them have to be represented by their identified projections. The remaining points, characteristic for radar obser-vation, may stand for supplementing of the water area navigational marking structure.
Radar marking
In a coastal zone, navigation is carried out ba-sing on visual or technical observation of elements characteristic for this particular zone. None of navigators would fix positions applying radio navigation satellite systems while sailing along a fairway or approaching ports, also carrying out manoeuvring inside ports. Anyhow, while sailing nearby a beacon, standing by leading marks or passing by a cardinal buoy, the navigator is obliged to take measurement of navigational parameters and fixing positions by observation.
The wholeness of the above mentioned tional radar marking is a component of the naviga-tional structure, used for fixing positions with the coastal methods. Due to a variety of hydrometeoro-logical conditions, a position by observation should be fixed on the basis of radar observation. Using radar equipment offers one more advantage, which is a potentiality of automation of the whole process of fixing position. Automation should be unders-tood widely – beginning from the processes of ob-servation, recording and measuring navigational parameters, through identification of markings ob-served and ending at calculation of geographical latitude and longitude of the proper ship’s position by observation.
Interactivity of the structure is obtainable through current complementing it with marks, which are not represented in the nautical chart but which are characterized with strong, individual and
continuous radar echo. Such an object’s position can be constantly or temporary marked in the chart and the object can be accepted for observation in the navigating process.
Characteristic points from radar images
Extraction of the characteristic points from radar image is to be understood as distinguishing from among all the image points these points, which may be used to fix positions under observation, applying the coastal methods.
A source of the characteristic points in radar display can be a coastline, radar echoes of a land piece and singular, detached radar echoes occurring at sea.
A process of extracting the characteristic points from the image should be performed by many stages (Fig. 1). The coastline characteristic points can be determined from the invariant representa-tion. In examination of the radar image raster projection, we can assign a series of characteristic points located onshore and offshore. Additionally, it is possible to identify from among all isolated radar echoes the immovable echoes, taking advantage of automatic tracking echoes capability and digital transmission of navigational data – NMEA, used in radar technique. All the stages may proceed at the same time, as each of them applies different digital representation of the radar image.
Fig. 1. Diagram presenting the process of extracting the characteristic points from the radar display
Rys. 1. Schemat procesu ekstrakcji punktów charakterystycz-nych z obrazu radarowego
Extraction of characteristic points from the radar image contour invariant
Accurate presentation of the algorithm of extrac-ting the characteristic points from the radar image requires clear definition of the invariant. In such a representation, the image has been described in many works by [1, 2, 3]. In the literature it has been characterized applying the so-called “outline” invariant, which displays an image of a coastline, recorded in the polar system. Every pixel of the
Extracting characteristic points from radar image
characteristic points from radar image
bitmap of radar image radar image “contour” invariant tracking objects, NMEA transmission
coastline is represented by polar coordinates, i.e. a bearing and a relative distance, measured from a position of radar antenna.
If the digital radar image is considered, it has been presented in the following form:
nm N n N m M
Oc , 2: 0, , 0, (1)
where: Oc is a set of points P
ic(n,m) such, that
i = 0,1..,N*M–1 and for the assumptions that the
quantities which size up the image N and M assume odd values, thus for each image the central point
Po(n o,mo) is determinable, therefore: 2 1 , 2 1 N m M no o (2)
the “outline” invariant can be defined as function
ginw assuming the values [4]:
c o NR D P k c inv P P NR D A k g k c c min dla
360 ,.., 1 , 0 n k (3) where: Dc(NRk) – set of visible points (pixels) of the display, laying on a specific bearing (NR), it means the radar echoes in the defined bearing;
c oP
P – distance between the indicated pixel and the display’s centre (central point), distance between the radar echo and the antenna;
n – grade of the applied radar image invariant
resolution;
A – certain assumed distance exceeding the
range of observation.
The suggested method of extraction of the cha-racteristic points from radar image consists in ana-lysis of the second derivative of the function ginv(k). However, to make the analysis possible, it is neces-sary to have an analytic form of this function. Yet the “outline” invariant has to fulfill the condition of continuity and differentiability within 0,n360 interval. Determination of the analytic form of the function is very difficult. We are capable only to determine a certain estimator of this function
) (k
ginv . As its estimator in the method suggested in [4] the following function has been accepted:
2( ) 1 0 1 ) ( 2 0 , , , N M k k M N k k inv inv x x k g x g (4)
2 2 2 , k x k x e (5)Operation of the algorithm consists in determi-nation of the function:
, 2 2 dx g d x z inv (6)for the determined in the points
k = 0,1,...,2(N+M) – 4 and next finding such k for
which:
k zk
g
k A z k z k z k z inv 1 1 (7)where is a parameter of the algorithm allowing to classify the whole potential set of the characteristic points to a group of the “clear-cut” (clearly visible) points, it means these for which z(k) > and a group of poorly distinguishable, for which
z(k) ≤ . The other parameter of the algorithm is coefficient , allowing to eliminate from ginw(x,)
minor corrugations, which may generate unnecessa-rily a large number of the characteristic points. Thus, with the parameter , the poorly clear-cut points are removed from the list of the characteris-tic points, whereas the coefficient avoids genera-tion thereof. Finally, each point which satisfies (7) is considered to be characteristic point.
The figure below (Fig. 2) presents selection of the optimal estimator of the outline invariant function. The first graph illustrates a situation where the estimator had been selected in a way that the algorithm generates an excessive number of the characteristic points. The following graph shows invariant and its optimally selected estimator.
Fig. 2. Optimal selection of the “outline” invariant function’s estimator
Rys. 2. Optymalny dobór estymatora funkcji inwariantu „kon-turowego”
The characteristic points determined with the optimally selected function of the outline invariant are marked (Fig. 3).
0 50 100 150 200 250 300 1 70 139 208 277 346 415 484 553 622 691 760 829 898 967 1036 1105 1174 1243 1312 1381 1450 1519 1588 1657 1726 1795 1864 1933 k gin w (k ) k ginw (k )
Fig. 3. The determined characteristic points of the estimated outline invariant’s functions
Rys. 3. Wyznaczone punkty charakterystyczne estymowanych funkcji inwariantu konturowego
Extraction of characteristic points from the radar raster image (bitmap)
Every point of the radar image introduced as a discrete value presents a succeeding coordinate, which informs on occurrence either of radar echo or lacking thereof. The radar image can be recorded as a vector circumscribed on a set of real numbers:
R k O (8) where:
N K R W K W W k , , , 0 180 , 0 , 90 , 0 : , , o o Oin the navigational coordinates system ,
are geographic coordinates of specific image pixels;
W – level of amplification of the image pixel;
the image is identified as radar echo; and
N K R W y x K W M y N x W y x k , , , 0 , 0 , , 0 : , , O (9)in the Cartesian coordinates system for N and M which determine the radar image dimensions.
If every point of the radar image is represented by a volume of its amplification Wi,j then extraction of the characteristic points consists in finding such points, amplification of which is exceeding a cer-tain assumed threshold volume and where their neighborhood is characterized with lower or equal volume W. Thus we search for such Wi,j which ful-fill the dependence:
prog j i j i j i j i j i j i j i j i j i j i j i j i j i j i j i j i W W M j N i f W W W W W W W W W W W W W W W W ,..., 1 ,..., 1 or 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , , 1 , , , 1 , , 1 , (10)
In case there occurs a large number of the neighboring points of the same volume W, the cha-racteristic point is represented by the pixel located nearest to the central point Po. If the situation is different and a sequence (series) of the neighboring points (assigned to the neighboring bearings), lay-ing at the same distance from the screen centre is of the same amplification volume W, then the charac-teristic point is represented by the pixel laying on the bearing – central for the whole range of the neighboring pixels bearings (Fig. 4).
Fig. 4. Extraction of the characteristic points from the bitmap Rys. 4. Ekstrakcja punktów charakterystycznych z bitmapy
An excess or insufficiency of the characteristic points determined in the radar display can be controlled with the volume Wprog. It is necessary to remember about optimal selection of this volume.
Extraction of characteristic points with a use of digital transmission of navigational data (NMEA)
Now radars are capable to track objects, to cal-culate polar coordinates of the tracked objects, their speeds, courses and approach elements. The above data in a form of digital transmission – NMEA – are transferred to other navigational aids. Taking advantage of this quality it is possible to obtain
information about detached and immovable objects, surrounding the own, proper ship. The objects can make characteristic points of the coastal water area. Thus the algorithm of the characteristic points’ extraction enables finding from among all the points assumed for tracking these of zero or close to zero speed. It has been presented in the figure 5.
At all the stages of extracting the characteristic points it is necessary to take into consideration selecting a suitable observation range (Fig. 6). The range should enable availability of necessary number of the characteristic points, located in the coastal water area. A situation where radar’s range fails covering a coastline and markings installed in water area is not admissible. One should also remember that too low number of available infor-mation may cause deterioration or loosing of the fixed position’s accuracy.
Fig. 5. Exemplary NMEA data sentences; the immovable echoes are marked
Rys. 5. Przykładowe sentencje danych NMEA; podkreślono echa nieruchome
Fig. 6. A number of the accessible characteristic points in the Gulf of Gdansk water area for observation range of 12 nautical miles
Rys. 6. Liczba dostępnych punktów charakterystycznych na akwenie Zatoki Gdańskiej dla zakresu obserwacji 12 mil mor-skich
Identification of the characteristic points
Several characteristic points identification me-thods have been described in the literature [4, 5, 6]. The methods are used to assign to the points deter-mined from the radar image their equivalents, pre-sented in the chart. This task is aimed at assigning accurate position (survey) to the radar image cha-racteristic points. In one of the methods there are used bearings trees and distances to the characteris-tic points, seen from different positions and their equivalents in the chart are searched [3]. There have been worked out also methods, which involve more advanced techniques [7]. One of the methods, worked out and tested by the authors and described in [6], has been presented below.
Let’s designate the successively ordered characteristic points of the chart as A1,A2,A3,...,An. The positions assigned to the points are
i
A , . Now let’s define close neighborhood of these points. Let it be determined with a radius of a value, so that:
2
min 1
Ai Ai
a (11)
A close neighborhood a should be yet characte-rized with the next condition:
z i i z z i i A A A A a a 2 min for 2 min for 1 1 (12)
where z is an error of the position reckoned at the moment of recording the radar image.
Let’s designate with Pj the successive characte-ristic points found in the radar image (P1,P2,P3,...,Pk) and let’s assign to them their posi-tions
j
P
, . Identification of a sign will consist in assigning positions of the chart’s characteristic points to the points of radar image, located in close neighborhood of these signs:
j i j P i j n i A P k j a A P ) , ( if ) , ( ) , ( 1... ... 1 (13)
Optimal selection of the values a is an essential operation of the above algorithm of identification. Accuracy of fixing position by observation apply-ing automatic system of radar navigation is influ-enced by correctly carried out estimation thereof.
The figure 7 presents the result of identification of the characteristic points, determined within the Gulf of Gdańsk water area.
Fig. 7. Identification of the radar image characteristic points Rys. 7. Identyfikacja punktów charakterystycznych obrazu radarowego
Conclusions
The identified characteristic points are to build a navigational structure necessary to fix ships posi-tions. A nature of the structure, constructed in such a way and enriched with successive characteristic points determined in radar images, is considered to be the Interactive Navigational Structure (IANS) described in details in [8, 9]. In this case inter-activity consists in a possibility of continuous navi-gator’s intervention in the structure. Newly appear-ing radar image displays will be a source of succes-sive characteristic points. A part of them will be identified as points of already known geographic coordinates accepted for navigation. The other part may be a supplementation of this structure at loca-tions where availability of marks / signs of the known coordinates is insufficient for fixing posi-tions. At this stage the marks should be mapped in the chart preserving a specified accuracy. This process should be carried out taking into considera-tion mutual dependencies between correctly identi-fied points and the other characteristic points.
This paper presents a comprehensively drawn up problem concerning automation of fixing ship posi-tions using radar observation. The objects observed with radar are a source of information, necessary
to define a proper position’s vector correctly. The characteristic points displayed in radar image can be identified, then they can enrich the navigational structure, used by navigators to carry on navigation safely. An advantage of this concept is an availability of information obtained with radar and a capability of supplementation of the structure with new elements extracted from radar image. One ought to remember that a distribution of error of the position observed, fixed in this way, depends on arrangement of geometric location of dangers to navigation, which are a coastline, buoys, beacons and others. It results from the fact of linking to a character of configuration and arrangement of structure elements through carrying out radar measurements. It significantly improves navigation safety.
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