International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 4
Number 4
December 2010
429
The basic idea behind this new navigation filter is
twofold:
1 A cluster of the observed position fixes contains
true kinematic information about the vehicle in
motion,
2 A motion model of the vehicle associated with
the error statistics of the position fixes should be
able to get, to a large extent, the information out
of the measurements for use.
We base the filter on an analogy. We consider the
statistical confidence region of every position fix as
“source” tending to “attract" the undetermined tra-
jectory to pass through this region. With these posi-
tion fixes and their error statistics, a virtual potential
field is constructed in which an imaginary mass par-
ticle moves. To make the filter flexible and respon-
sive to a changing navigation environment, we leave
some parameters free and let the filter determine
their values, using a sequence of observations and
the criterion of least squares of the observation er-
rors. We show that the trajectory of the imaginary
particle can well represent the real track of the vehi-
cle.
In our poster we presents basic idea this filter and
numerical method for calculate best position using
this filter also we show experiment (with
RTK/SPAN technology) that we do for verification
presented filter.
Filter function:
=
exp
(
r r
)
C
(
r r
)
(1)
=
y
x
r
position vector in actual time “t”
=
0
0
0
y
x
r
position vector in time “t
0
”
=
(
2
)
(
)
(2)
Where C is a matrix of covariance
=
=
(, )
(, )
(3)
The basis for estimation position is potential U
i
(
)
=
(
r r
)
C
(
r r
)
e
(
)
(4)
Next step is conversion U
i
when we know “n”
position before time “t”
=
=
(
r r
)
C
(
r r
)
e
(5)
() =
() =
(
)
+
(
)
e
(6)
where
=
y
x
r
=
i
i
i
y
x
r
0
0
0
(
)
=
(
)
;
(7)
Alternative for Kalman Filter – Two Dimension
Self-learning Filter with Memory
A. Fellner
Silesian University of Technology, Gliwice, Poland
K. Banaszek
Polish Air Navigation Services Agency, Warsaw, Poland
P. Trominski
GNSS-Consortium, Poland
ABSTRACT: We propose new solution for idea Prof. Vanicek and Prof. Inzinga. This filter relies basically
on the information contained in measurements on the vehicle: position fixes, velocities and their error statis-
tics.
430
In next step we have:
= 2
C
matrix
(
2 x 2
)
(8)
= 2
C
(9)
where
=
0
0
=
0
0
(10)
(
)
=
(
)
;
(11)
(
)
=
;
(12)
=
,
=
,
(13)
= 2
(
)
(14)
= 2
(
)
(15)
= 2
(
)
(16)
= 2
(
)
(17)
Final solution is:
(
)
=
+
+
(
)
(
)
=
+
+
(
)
(18)
=
–
(19)
=
(20)
=
–
(21)
=
(22)
Our purpose is best estimation G and α from this
equation
(
,
)
=
{[
(
)
]
+
[
(
)
]
}
=
(23)
Figure 1. Visualization filter idea.
Figure 2. Alternative filter vs Kalman filter.
Figure 3. Powell Algorithm
431
1 TODAY'S NAVIGATION SYSTEMS AND
THE REQUIREMENTS PLACED ON THEM
Modern navigation are dominated by satellite sys-
tems and assist systems mainly including GPS -
NAVSTAR GPS (called the Global Positioning Sys-
tem - Navigation Signal Timing and Ranging), in
Europe EGNOS (called European Geostationary
Navigation Overlay Service), which de facto is a
service for GPS system and Russian GLONASS
(called Global Navigation Satellite System, or in
Russian Globalnaja Nawigacjonnaja Satelitarnaja
Sistemma). Each of these systems offers similar
functionality. Let focus on requirements that modern
navigation systems should met with reference to ex-
isting systems.
Satellite system which can be considered for nav-
igation must ensure:
− Accuracy; GPS does not meet expectations in
terms of its accuracy, which is required in avia-
tion - during landing approach. EGNOS is a sys-
tem that uses GPS position and corrections from
ground stations, offering greater level of accuracy
than GPS and it is to be used in civil aviation
starting 2008, but its accuracy is still between 2-3
meters, which is not fully satisfactory from Air
Navigation or even Waterways Navigation (riv-
ers) point of view. GLONASS is a system which
is right now exchanging it’s satellites constella-
tion, but to date no civilian usage is possible.
− The ability of immediately alert users about sys-
tem malfunction. A serious issue of GPS is lack
of any communication containing information
about its credibility (can we use it). Advanced us-
ers can view information from the various types
of satellites, including healthy/un-healthy status
but despite this, users can’t obtain data on the
state of the entire system. EGNOS in his assump-
tion, as a GPS service was intended to correct its
deficiencies, and so is about its ability to provide
warnings about improper functioning of the sys-
tem. EGNOS architecture based on the network
of ground stations collecting errors which GPS
generates can also determine the quality of the
GPS information and instantly send notice to its
three geostationary satellites, which will inform
the end user about inability to use the EGNOS
and in result GPS system.
− Continuity of service. GPS and so as the EGNOS
are systems/services which do not meet the de-
sired functionality even because of the fact that
GPS is an U.S. property and in any threat situa-
tion it can be disabled. EGNOS is in the testing
phase and its functionality is not yet complete
− Availability - is a factor expressed in percentage
representing the time within the system may be
used. The U.S. FAA (Federal Aviation Admin-
istration) organization demands availability for
air-route navigation, while approaching and land-
ing airports and during aerial surveillance no less
than 99,999%. As previously found GPS is dis-
qualified by lack of information about its credibil-
ity and availability at less than 99,999%, while
the European EGNOS at the moment is in testing
phase.
Unfortunately, none of these systems/services of-
fer the level of accuracy of 1 meter without the use
of differential techniques. Possible solution for this
is usage and development of already existing filters
or developing new ones or usage of mathematics and
information based on assumptions which will allow
individuals to increase the data accuracy regardless
of expanding space installations (GPS III and Gali-
leo).
2 EXISTING NAVIGATION FILTERS
Part of the problem is usually solved through a com-
bination of two different types of information, ob-
servation and vehicle traffic by creating a model
based on the basic rights of physics represented by
different equations. Existing filters in navigation
have been dominated by the Kalman filter in various
forms. Kalman filter will be thoroughly discussed in
chapter II. On the basis of experience and many pub-
lications related to navigation, especially in areas
where the navigation is performed many maneuvers
Kalman filter does not meet the requirements of ac-
curacy (positional error has repeatedly been growing
in the performance of maneuvers). The basis for
conducting further research traffic is a working hy-
pothesis that the existing model navigation filter
does not meet the accuracy requirements for the
movable object, it is assumed that the acquisition of
improvement in this regard will be developed when
submission to the new model navigation object
memory.
BIBLIOGRAPHY
1. Xu, B. 1996. „A new navigation filter”.
2. Vanìcek, P. & Omerbašic, M. 1999. „Does a navigation al-
gorithm have to use Kalman filter?” Department of Geode-
sy and Geomatics Engineering University of New Bruns-
wick
