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.