Database Reference
In-Depth Information
automatically using a density analysis. In this context, a beginning position of
a trajectory is a position that is inside a zone
Z
and whose next position of the
trajectory is outside this zone. An ending position of a trajectory is a position
that is inside a zone
Z
and whose previous position of the trajectory is outside
this zone. Therefore, the sequence
S
of position of a given ship can then be split
into a subset of trajectories
={
T
0
,...,T
N
}
such as
⊆
S
.
Once the positions are assigned to trajectories, a filtering process selects the
key positions of a given trajectory. A position is considered as a key position
when either the speed or the direction changes significantly. The other positions
can be removed.
The algorithm initially introduced by Douglas and Peuker in 1973 is relevant
as it performs well on typical straight trajectories of vessels. The principles
of the original algorithm are as follows. The start and end points of a given
polyline are connected by a straight line segment. Perpendicular offsets for all
intervening end points of segments are then calculated from this segment, and
the point with the highest offset is identified. If the offset of this point is less than
the tolerance distance, then the straight line segment is considered adequate for
representing the line in a simplified form. Otherwise, this point is selected, and
the line is subdivided at this point of maximum offset. The selection procedure
is then recursively applied to the two parts of the polyline until the tolerance
criteria is satisfied. Selected points are finally chained to produce a simplified
line.
This simplification algorithm for trajectory filtering could be adapted in order
to be more efficient. Conversely to Meratnia and By (2004), who used Euclidean
Distance between points at a same time, the Haversine distance can be used.
This distance is the shortest distance (
d
s
) between two points measured along a
path on the surface of a sphere. The perpendicular distance is therefore derived
as a spatio-temporal distance
d
ST
andisasfollows:
d
ST
(
T
i
,T
j
,t
)
=
d
s
(
p
i
(
t
)
−
p
j
(
t
))
The spatio-temporal distances between position
p
i
of the trajectory
T
j
,and
position
p
i
of the interpolated trajectory
T
j
taken at a same time (relative
time from the departure) are computed. Let us note that these spatio-temporal
distances are influenced by the speed and the direction of the mobile object.
A tolerance distance should be defined appropriately. According to the GPS
position accuracy, a tolerance of 10 meters is acceptable.
In order to exemplify this filtering process, three vessel trajectories have
been selected for illustration purposes. The first trajectory concerns a passenger
boat called
Bindy
, whose trajectory is smooth and speed is regular. The second
trajectory is the one of a port pilot ship in the harbor of La Rochelle. This
trajectory is very sinuous, and several loops appeared. The third trajectory is
composed of long straight polylines made by the cargo ship
AB Valencia
.
