Kalman filter 
itching radar 
e electronic 
etected by a 
| matched to 
same tech- 
, and elec- 
ours and the 
position and 
ops. For the 
lip’s position 
rding to the 
Also actual 
a gyroscope 
Kalman filter 
y integrated 
ocess. The 
linates Sp(—) 
sensor and 
icquisition of 
, the time for 
^s the ship is 
| obtained by 
e time when 
ip's heading 
rpose of the 
corrections 
(1) 
rcial vessels 
indings. The 
idth of 0.5 to 
bout 15 to 20 
omplete turn 
Jar pulses of 
are repeated 
"hus the raw 
dial beams. 
na are digi- 
1ain memory 
image, a re- 
formed. The 
made up as 
ith 256 radial 
'osen as 3 Or 
g distance of 
to the radar 
nber of 4096 
On the digitized, binary radar image some prepro- 
cessing steps are performed. The radar image is 
segmented into radar objects representing a contin- 
uous echo area. Also characteristic values like the 
area of the object and its extremal coordinates are 
determined. 
Relevant echos for the matching process are 
gained from the radar data by selecting appropri- 
ate radar objects and extracting the front contour of 
these radar objects. Aggregating contour points lo- 
cated closely together, the echo points are deducted. 
Thus a further data reduction is achieved, resulting 
in about 200 echo points within one radar image. 
Figure 3 shows the measurement of one echo point 
before matching. The echo coordinates r; and ¢; are 
given in a polar coordinate system assigned to the 
ship's body, the index i is used to distinguish the echo 
points within one radar image. As shown in figure 
3 the nearest point on the contour of the electronic 
chart with its coordinates k,, and k,, is computed. 
The distance vector d; is perpendicular to the chart 
contour. Based on the distance to the next chart 
contour a validation step is performed. If the distance 
exceeds a certain threshold, the assignment of echo 
and chart is assumed erroneous and the measure- 
ment is discarded. Erroneous assignments may arise 
from noise in the radar image or other vessels obvi- 
ously not contained in the electronic chart. After the 
validation step n measurements are assumed to be 
available for further processing. In the determination 
of the nearest chart point, the motion of the ship is 
taken into account by using an individual position 
and heading s,,, s, v; for each echo point. This is 
expressed by the following equation: 
Sy, Sp AS, 
Sn, Cs) Frey As: (2) 
Vi V) Avi 
The corrections As,,, As,, and Av; are gained by 
interpolating and extrapolating the position estimates 
of the last radar image and the initial position of the 
matching process. This is done using the exact mea- 
suring time of echo :. 
Based on figure 3 the following equation can be 
derived: 
—ri Sin(y; + Vi + A) Sri AS, 
Bust sits [4l | 
Kr, 
= | ky; | (3) 
As,, As, and Av are the desired corrections to 
the initial position and heading. By linearizing these 
equations with respect to the variable Av, taking 
into account equation (2) and neglecting higher or- 
der terms, equation (3) can be transformed to the 
67 
following form: 
As 
19 . T : 
Le y | Ae i= | s | (4) 
Ti Av hi 
M; As d; 
All n measurements result in the system of equa- 
tions: 
M; AS di 
éss T —] ^ TI: (5) 
M, l^" d,, 
mum e = 
M As d 
The accuracy of matching is affected by many fac- 
tors. Especially effects that impair the correspon- 
dence of radar image and electronic chart must be 
taken into account. Major impacts on the accuracy of 
matching are: 
1. The accuracy of the radar sensor. 
2. The nature of the specific radar objects and their 
influence on the reflection properties. The echo 
received for example from a concrete river bank 
is more reliable than one from a flat, sandy river 
bank. 
3. The dependency of the echo locus on the actual 
water level. 
4. The direction specific information of the distance 
vectors d;. They contain only information per- 
pendicular to the chart contour. 
5. Possible erroneous assignments of echos and 
electronic chart. Such assignments may be 
caused for example by ships located close to the 
chart contour. 
The measurement accuracy of the radar sensor is 
a-priori known. It is assumed that the errors in the 
coordinates r; and v; are independent and normally 
distributed with the variances c? and a2. In a lo- 
cal cartesian (¢;,n;)-coordinate system according to 
figure 3 the following equation for the measurement 
errors A£; and An; holds: 
ES 
Ani 
r?c2 0 
= | A | (6) 
0, 
The measurement errors belong to different mea- 
surements / andm in a (£;,n;)-coordinate system. The 
nature of the chart objects and their dependency on 
the water level can also be stored in the electronic 
chart. In the matching, the reliability of a echo : is