Transcript Folie 1 - TU Dresden

Technische Universität Dresden
•
Fakultät für Elektrotechnik und Informationstechnik
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Institut für Automatisierungstechnik
•
Prof. Dr. techn. Klaus Janschek
Titel  Fett  Univers 55  51  max. 2zeilig
Autoren  Fett  Univers 45  32
1. Hauptüberschriften  Univers 55  40
X±
y
y
k
X S±
k
X¤
X S¤
k
Die benötigten Univers Schriften können Sie sich von der Homepage der Technischen Universität Dresden
herunterladen. Rubrik: Coperate Design.
Haupttext  Univers 45  28, Textfluss  zweispaltig, blocksatz, Spalte jeweils 34 cm breit.
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X S¦
X¦
k
k
XS = X¤ \ X¦ \ X±
k
k
k
XS = X¤ \ X¦ \ X±
k
k
x
S
X ;XS ;XS
from the intersection
k
k
k
Abbildung 2: Computing the minimal circumscriptions
XS = X¤ \ X¦ \ X±
the two dimensional space.
k
k
k
k
¤
¦
k
k
k
x
in
±
Volume of the estimated sets
60
Multi-Model Estimation Filter
Combined EstimationFilter
Parallelepiped Set Technique
Interval Set Technique
Ellipsoid Set Technique
50
Mean of
r
in m
r
Deviation of in m
' ¡ '^
Mean of
in °
' ¡ '^
40
Volume
In many technical systems the internal states, which are for instance required for control or navigation purposes, are
not directly observable and have to be estimated on the basis of uncertain measurements of the system output.
Usually a stochastic description is selected and the searched states are calculated by use of a Kalman filter or one of
its variations. This work presents new results for state estimation based on noisy observations suffering from an
uncertainty, that is noted to be bounded but the exact underlying characteristics are unknown. Subjected to these
limitations a new estimator has been developed, that combines three different types of set theoretic state estimation
methods with the aim to improve the accuracy of the forecasted position without requiring advanced sensor
information.
k
30
Deviation of
in °
0.23
0.22
0.05
0.03
20
10
0
u
input
k
true output
¡
¢
System
x = f x
;u
k
noise
w
k¡ 1
k
noise
k
X¤
k¡ 1
X¦
k¡ 1
X±
k¡ 1
v
x
Propagation
fusion
Measure-ment
fusion
k
Table 1: Parameters
t0
in s
0
t
en d
in s
600
TA
in s
1
TM
in s
90
Estimated output
x~
k
X S¤ ; X S¦ ; X S±
k
k
300
Time in s
400
500
600
(x ¡ x^ ) 2 + (y ¡ y^) 2
k
k TM
! X±
200
r =
k
k
k
100
Figure 3: Figure 3a shows the trend of volume for three established forms of set theoretic estimation and the developed filter. In Table
3b the simulation results are qdisplayed with
.
! X¤
! X¦
0
k
Multi-Model Estimation Filter
Abbildung 1: Bildunterschriften  Univers 45  24
2. The multi-model estimation concept
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trajectory
circle
radius in m
v
in m/s
!
in 1/s
5
0.3
x
0
Ev
Ew
(2:1; 2:3; 0) T
§ (15cm; 15cm; 3± ) T
§ (0:25mm; 0:25mm; 0:0015± ) T
0.5
Simulation results shown in Figure 3 are achieved by using the parameters displayed in Table 1.  Auf dargestellte
Bilder oder Tabellen bitte im Text Bezug nehmen.
5. Zusammenfassung und Ausblick
Many estimation issues can be approached as noise problems, where the distribution of the uncertainty is unknown
but considered to be bounded. According to this the new estimator provides a framework for solving these problems
more precisely than using mentioned methods themselves. Therefor an in this field new method, the parallelepiped
set technique, has been combined with two more established procedures, the interval and ellipsoid set technique, in
order to compose the multi–model estimator. Furthermore analytical methods for executing the described
propagation and measurement fusion has been provided within this work.
This work focused on a combined set theoretic filter. In [3,4] a filter is introduced that deals with mixed noise –
noise with known distributions and noise with known bounds. A next step in the further development of the
introduced filter may be to transfer this attempt to broaden the potential area of application.
6. Quellenangaben
[1]
[2]
[3]
[4]
[5]
Alefeld G., Herzberger J., “Introduction to Interval Computations”, Academic Press, New York, (1983)
Hanebeck U.D., Schmidt G., “Mobile Robot Localization Based on Efficient Processing of Sensor Data and
Set-theoretic State Estimation“, Fifth International Symposium on Experimental Robotics (ISER'97), pp. 321332, Barcelona, Spain, (1997)
Hanebeck U.D., Horn J., “New Estimators for Mixed Stochastic and Set Theoretic Uncertainty Models: The
Vector Case”, Proceedings of the fifth European Control Conference (ECC’99), Karlsruhe, Germany,(1999)
Hanebeck U.D., Horn J., “New Results for State Estimation in the Presence of mixed Stochastic and Set
Theoretic Uncertainties ”, Proceedings of the 1999 IEEE International Systems, Man and Cybernetics
Conference (SMC’99), Tokyo, Japan, (1999)
Horn S., „Anwendung mengenbasierter Schätzverfahren zur Lokalisierung von mobilen Plattformen in ebenen
Umgebungen”, Diplomarbeit, Technische Universität Dresden, Fakultät für Elektrotechnik und
Informationstechnik, (2003)