design and analysis of transfer alignment algorithms

184 Pages·2005·1.07 MB·English

DESIGN AND ANALYSIS OF
TRANSFER ALIGNMENT ALGORITHMS

A THESIS SUBMITTED TO
THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES
OF
MIDDLE EAST TECHNICAL UNIVERSITY

BY

YİĞİTER YÜKSEL

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR
THE DEGREE OF MASTER OF SCIENCE
IN
ELECTRICAL AND ELECTRONICS ENGINEERING

FEBRUARY 2005

i
Approval of the Graduate School of Natural and Applied Sciences

Prof. Dr. Canan Özgen
Director

I certify that this thesis satisfies all the requirements as a thesis for the degree of
Master of Science.

Prof. Dr. İsmet Erkmen
Head of Department

This is to certify that we have read this thesis and that in our opinion it is fully
adequate, in scope and quality, as a thesis for the degree of Master of Science.

Prof. Dr. Mübeccel Demirekler
Supervisor

Examining Committee Members

Prof. Dr. Kemal Leblebicioğlu (Chairman), (METU, EE)
Prof. Dr. Mübeccel Demirekler, (METU, EE)
Prof. Dr. Aydan Erkmen, (METU, EE)
Assist. Prof. Dr. Yakup Özkazanç, (Hacettepe Unv., EE)
Dr. Ayşe Pınar Koyaz, (TÜBİTAK – SAGE)

ii
I hereby declare that all information in this document has been obtained
and presented in accordance with academic rules and ethical conduct. I also
declare that, as required by these rules and conduct, I have fully cited and
referenced all material and results that are not original to this work.

Yiğiter YÜKSEL

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ABSTRACT
DESIGN AND ANALYSIS OF TRANSFER ALIGNMENT
ALGORITHMS

YÜKSEL, Yiğiter
M.S., Department of Electrical and Electronics Engineering
Supervisor : Prof. Dr. Mübeccel Demirekler

February 2005, 169 Pages

Transfer Alignment is the process of simultaneously initializing and
calibrating a weapon inertial navigation system (INS) using data from host
aircraft’s navigation system. In general, this process is accomplished by
calculating the difference of navigation solutions between aircraft and weapon
INSs to form observations which are then used in a Kalman filter to generate
desired estimates. Numerous techniques about the problem of transfer alignment
exist in the literature. In this thesis, those techniques that can be applied in the
presence of elastic motion of aircraft wing were analyzed. Several transfer
alignment algorithms each of which process different measurement types were
designed and implemented. In order to evaluate the performance of implemented
algorithms under realistic conditions, a transfer alignment simulation environment
was developed. Using this simulation environment, the advantages and
disadvantages of each algorithm were analyzed and the dependence of transfer
alignment performance on Kalman filter system model, aircraft maneuvers and
alignment duration were investigated.

Keywords: Transfer Alignment, In-motion Alignment, Inertial Navigation
iv
ÖZ
YÖNELİM AKTARIMI ALGORİTMALARININ TASARIM VE
ANALİZİ

YÜKSEL, Yiğiter
Yüksek Lisans., Elektrik ve Elektronik Mühendisliği Bölümü
Tez Yöneticisi : Prof. Dr. Mübeccel Demirekler

Şubat 2005, 169 Sayfa

Yönelim aktarımı, uçağın seyrüsefer sistemi çıktılarını kullanarak
mühimmat üzerindeki ataletsel seyrüsefer sistemine ilk değer atama ve sistemin
kalibrasyonunun eş zamanlı yapılması işlemidir. Genel olarak bu işlem, uçağın ve
mühimmatın seyrüsefer sonuçları arasındaki farktan bir ölçüm oluşturulması ve bu
ölçümün Kalman süzgecinde işlenmesiyle gerçekleştirilir. Konuyla ilgili
kaynaklarda, aktarım yönlendirme ile ilgili birçok teknik ortaya konmuştur. Bu
tezde, uçak kanadının elastiki hareketinin mevcut olduğu durumlarda
uygulanabilecek aktarım yönlendirme teknikleri incelenmiştir. Farklı ölçüm
çeşitlerini işleyebilen birçok Kalman filtresi tasarlanmıştır. Tasarlanan Kalman
filtrelerinin performanslarını gerçekçi bir ortamda sınayabilmek için, bir yönelim
aktarımı benzetim ortamı geliştirilmiştir. Geliştirilen benzetim ortamı kullanılarak,
her bir yönelim aktarımı algoritmasının başarımı analiz edilmiş ve Kalman filtresi
sistem ve ölçüm modeli, uçak manevrası ve algoritma uygulama süresinin
yönelim aktarımı algoritmaları performansı üzerindeki etkileri incelenmiştir.

Anahtar Kelimeler: Yönelim Aktarımı, Ataletsel Seyrüsefer, Hareket
Halinde İlklendirme
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To my mother and father who still love me despite of my endless
peevishness.

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ACKNOWLEGMENTS

I am greatly thankful to my supervisor Prof. Dr. Mübeccel Demirekler for
her guidance throughout the preparation of this thesis. Thanks to her advices and
appreciated criticisms, I had the chance of improving my studies.
I am also grateful to Uğur Topay, Burak Kaygısız, Yüksel Subaşı and
Ayhan Erdim for their help and friendship during this period.
I would like to express my sincere thanks to my family for their support and
understanding.
Finally, I would like to thank my brother. Even his sole existence makes
me feel more confident.
TÜBİTAK-SAGE who supported this work is greatly acknowledged.

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TABLE OF CONTENTS

ABSTRACT...........................................................................................................iv
ÖZ...........................................................................................................................v
ACKNOWLEGMENTS..........................................................................................vii
TABLE OF CONTENTS.......................................................................................viii
LIST OF SYMBOLS...............................................................................................xi
LIST OF ABBREVATIONS...................................................................................xv
1 INTRODUCTION.................................................................................................1
1.1 Thesis Objectives...............................................................................4
1.2 Organizatıon of the Thesis.................................................................5
2 INERTIAL NAVIGATION SYSTEM.....................................................................7
2.1 Slave Navigation System Structure...................................................8
2.2 Navigation System Errors................................................................10
2.2.1 Slave IMU Errors...................................................................11
2.2.2 Initialization Errors.................................................................13
2.2.3 Computational Errors............................................................14
2.3 Navigatıon System Error Analysis...................................................15
2.3.1 Linear Error Propagation Models..........................................15
2.3.1.1 Attitude Error Propagation...............................................15
2.3.1.2 Velocity Error Propagation..............................................16
2.3.1.3 Position Error Propagation..............................................17
2.3.2 Verification of Linear Error Propagation Models...................17
3 KINEMATICS OF MASTER AND SLAVE SYSTEMS AND
CHARACTERIZATION OF VIBRATION ENVIRONMENT...................................21
3.1 Trajectory Generation......................................................................22
3.1.1 Trajectory Regeneration Function.........................................24
3.1.2 Trajectory Shaping Function.................................................28
3.1.2.1 Level Flight......................................................................29
3.1.2.2 Vertical Turn....................................................................29
3.1.2.3 Coordinated Turn............................................................29
3.2 KINEMATIC RELATIONS BETWEEN MASTER AND SLAVE........34
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3.2.1 Velocity Relation...................................................................34
3.2.2 Attitude Relation....................................................................36
3.2.3 Acceleration Relation............................................................37
3.2.4 Rotation Rate Relation..........................................................37
3.2.5 Position Relation...................................................................38
3.3 Characterization of Vibration Environment......................................38
3.4 Analysis of Vibration Dependent Errors...........................................42
4 DESIGN OF TRANSFER ALIGNMENT ALGORITHMS....................................44
4.1 Introduction......................................................................................44
4.2 Transfer Alıgnment Simulation Environment....................................48
4.3 Acceleration / Rotation Rate Matching Method................................53
4.4 Velocity Matching Method................................................................63
4.5 Integrated Velocity Mathcing Method...............................................68
4.6 Attitude Matching Method................................................................83
4.7 Velocity and Attitude Matching Method............................................95
5 ANALYSIS OF TRANSFER ALIGNMENT ALGORITHMS BASED ON
VELOCITY OBSERVATIONS............................................................................108
5.1 Comparision of Velocity and Integrated Velocity Matching Methods
109
5.2 Effect of Kalman Filter Update Rate..............................................119
5.3 Effect of Aircraft Maneuvers on Kalman Filter Estimates...............126
6 CONCLUSIONS & FUTURE WORKS.............................................................143
6.1 Recommended Future Works........................................................144
REFERENCES...................................................................................................147
APPENDICES
A SUMMARY OF CONING AND SCULLING ALGORITHMS............................150
A.1 Coning Algorithm...........................................................................150
A.2 Sculling Algorithm..........................................................................155
A.3 Total Algorithm Error under General Motion..................................158
B VIBRATION MODELS.....................................................................................161
B.1 X Axes Linear Vibration Model.......................................................162
B.2 Y Axes Linear Vibration Model.......................................................163
B.3 Z Axes Linear Vibration Model.......................................................163
B.4 Roll Axes Rotational Vibration Model.............................................165
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B.5 Pitch & Yaw Axes Rotational Vibration Model................................166
C KALMAN FILTER STRUCTURE USED IN TRANSFER ALIGNMENT
ALGORITHMS....................................................................................................168

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