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.