magnetometers correction and magnetometers-aided

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Magnetometers Correction and Magnetometers-aided MINS Systems

Based on LabWindowsCVI and MATLAB

Long Wang1 a Xingcheng Li1 b Chuanjun Li1 c and Shuangbiao Zhang1 d

1

Key Laboratory of Dynamics and Control of Flight Vehicle Ministry of Education School ofAerospace Engineering Beijing Institute of Technology Beijing China

azilan862aliyuncom

bxingchlibiteducn

clichuanjunbiteducn

dgodtravel789163com

Keywords LabWindowsCVI MATLAB magnetometer MINS ActiveX virtual Instrument

Abstract Magnetometers-aided MINS could solve roll angle measurement of air vehicle at fast

spinning rate but magnetometers were easily disturbed and had measuring error so it was necessary

to establish tri-axial magnetometer correction system for magnetometers-aided MINS navigation

system Based on LabWindowsCVI and MATLAB fuzzy programming earth magnetic field and

ellipsoid fitting model were built to complete magnetometers correction system and its virtual

instrument On that basic magnetometers-aided MINS navigation system and its virtual instrumentwere established Results of correction and non-correction magnetometers-aided MINS navigation

test showed that the magnetometers correction system can compensate the error of interference

measuring and so on furthermore geomagnetic attitude computing become more accurate and the

higher precision of position and velocity for magnetometers-aided MINS system All of them are

significant for engineering and products

Introduction

Attitude information of air vehicle plays a great importance in navigation system and guidance system

Now inertial device canrsquot satisfy the measuring range of the spin rate for high rotation speed air

vehicle Magnetic sensor has the characteristic of good stability low drift low cost fast response etc

It can measure geomagnetic intensity for solving the attitude of high rotation speed air vehicle which

has been a hot research area [1] However magnetometers measurement include the effective

geomagnetism information the negative information of vehicle ferromagnetic error and own error

The vehicle ferromagnetic error mainly causes by hard magnetic materials and soft magnetic

materials magnetic field The own error causes by sensitivity zero offset and non-orthogonality [2 3]

Excluding the interference and error vehicle arbitrarily rotates at the origin The trace of the

magnetometers measurement about geomagnetism should be sphere surface of which original point

as the center the total geomagnetic intensity as the radius in three-dimensional space Since the

aforementioned interference and error the center of sphere shift and the sphere has aberration

changing to ellipsoid so in this paper magnetometers correction system and its virtual instrumentwere designed to calibrate and compensate composite error for gaining the actual measurement based

on the ellipsoid fitting method

LabWindowsCVI is a software development platform based on ANSI C as core and particularly

suitable for the development of detection data acquisition process monitoring virtual system It uses

event-driven and callback programming methods to implement complex data acquisition and

processing with a wealth of library functions and is easy to learn However in the areas of advanced

theories and methods of geomagnetism monitoring there is no available libraries At the same time

MATLAB has the aforementioned function with the strong capabilities of matrix computation and

data visualization In one hand it can achieve the numerical analysis optimization mathematical

statistics and equation solution in math On the other hand it can deal with a two-dimensional or

three-dimensional graphics image processing and other aspects [4]

This article is aimed at building up magnetometers correction system and its virtual instrument

taking advantage of that LabWindowsCVI collects sensor data MATLAB has powerful math

processing capability and MATLAB has earth magnetic field module Therefore the paper is aimed at

Applied Mechanics and Materials Vols 568-570 (2014) pp 374-379copy (2014) Trans Tech Publications Switzerland doi104028wwwscientificnetAMM568-570374



building up magnetometers-aided micro inertial navigation system (MINS) and its virtual instrument

utilizing LabWindowsCVI and C language for attitude and navigation computation The virtual

instruments can easily show or store the test data and result In this paper how to realize

LabWindowsCVI and MATLAB fuzzy programming is introduced such as how LabWindowsCVI

call MATLAB here their advantages fully embody for completing the development of

magnetometers correction system

System General Scheme Design

Magnetometers Correction System Fig 1 describes functional block diagram of the

Magnetometers correction system whose virtual instrument was built by LabWindowsCVI and

MATLAB consisting of measuring unit data acquisition unit correction unit load parameters unit

and earth magnetic field model Three-axis magnetic sensor (Magnetic Measurement Unit MMU)

output digital local geomagnetic measurement which were received by data acquisition unit in the PC

via a serial port Data acquisition unit was generated by LabWindowsCVI MATLAB library

function has earth magnetic field model with lsquowrldmagmrsquo function It just needs to be input local

geography information (longitude latitude and altitude) and current time (year month and day) willobtain the geomagnetic information in the locality such as declination inclination geomagnetic total

intensity and so on A group of magnetic data collected by data acquisition unit can be ellipsoid fitted

by correction unit referenced the geomagnetic information with the ellipsoid fitting function But the

lsquowrldmagmrsquo function and the ellipsoid fitting function program and run in the MATLAB workspace

so here LabWindowsCVI must call MATLAB to work Finally the correction coefficients come out

with geomagnetism correction factors and bias that would be downloaded to or save in the vehicle

computer

Figure 1 Magnetometers correction system functional block diagram

Magnetometers-aided MINS System Most inertial measuring products are complete inertial

systems that include a tri-axial gyroscope a tri-axial accelerometer and a tri-axial magnetometer Fig

2 depicts functional block diagram of magnetometers-aided MINS navigation Themagnetometers-aided MINS virtual instrument was built by LabWindowsCVI The IMU and the

MMU both were digital output The sensor output was collected by digital data acquisition module of

the virtual instrument of Magnetometers-aided MINS navigation system via a serial port Before

calculating attitude the tri-axial magnetometers measurement value must be compensated by

equation [5]

H f = CH m － B (1)

Where C is a geomagnetic correction factors matrix of 3x3 B is a geomagnetic correction bias

matrix of 3x1 H m is a magnetometers measuring value and H f is an ideal value to calculate body

attitude The body attitudes are determined only with magnetometers if one attitude angle is knownThe yaw angle changes very little for the high-speed rotatable vehicle so the yaw angle is assumed to

be known or can be calculate from tri-axial gyroscope measuring value Magnetometers-aided

module works out the pitch and roll angles as the input of MINS to correct the attitude calculated by

Applied Mechanics and Materials Vols 568-570 375



INS With the more accurate attitude INS calculates velocity and position and output them to

guidance system

Figure 2 Magnetometers-aided MINS system functional block diagram

Virtual Instrument Design

Magnetometers correction system virtual instrument Magnetometers correction system virtual

instrument was programmed based on LabWindowsCVI and MATLAB mixed-language

programming Interface functions between LabWindowsCVI and MATLAB make

LabWindowsCVI can call MATLABrsquos functions to run in the MATLAB environment and return the

result to LabWindowsCVI Through building a data exchange service ActiveX LabWindowsCVI

would communicate with MATLAB [6]

ActiveX Generation Firstly in the LabWindowsCVI development environment we chooselsquoToolsrsquo click lsquoCreate ActiveX Controllerrsquo popup lsquoActiveX Controller Wizard-Welcomersquo dialog

click Next popup lsquoActiveX Controller Wizard-Choose Serverrsquo dialog select lsquoMATLAB Application

Type Libraryrsquo on the list click next popup lsquoActiveX Controller Wizard-Configurersquo set target file

name of suffix lsquofprsquo and path such as lsquoMATLABfprsquo Click next popup lsquoActiveX Controller

Wizard-Advanced Optionsrsquo dialog click lsquoAdvance Optionrsquo click lsquoCheck Allrsquo click next popup

lsquoActiveX Controller Wizard-Finishrsquo dialog click lsquoclosersquo at this moment system will automatically

generate five files of lsquoMATLABfp MATLABc MATLABh MATLABobj and MATLABsubrsquo in

the choice target directory

Select menu lsquoEdit-gtAdd Files to Project-gtAll Filesrsquo popup lsquoAdd Files to Projectrsquo dialog choose

the above five file click lsquoOKrsquo to finish At this point ActiveX service function contains the most basicfunctions that LabWindowsCVI and MATLAB use for fuzzy programming

Besides ActiveX NI company specially configures a friendly interface function file of

lsquoMATLAButilcrsquo which is at the directory of lsquo CVI80 Sample ActiveX MATLAB rsquo and make

fuzzy programming more easily

Functions Realization Introduction As shown in Fig 3 firstly click lsquoopen serial portrsquo button to

open the serial port through which MMU connect with PC then the vehicle with MMU respectively

rotates about xyx axis at the constant slow speed Magnetometers correction system collects

geomagnetic measuring data and store in the vehicle computer

Click lsquoLaunch MATLABrsquo to respond the function lsquoMLApp_NewDIMLApp (NULL 1

LOCALE_NEUTRAL 0 ampmMATLAB)rsquo for entering MATLAB work environment secondly Input

the local geography and time onto the panel click lsquoearth magnetic fieldrsquo to respond the function

lsquoRunMatlabCommand (mMATLAB ldquo[mag_t mag_h mag_dec mag_dip mag_f] = wrldmagm

(localinform(1) localinform(2) localinform(3) decyear (localinform(4) localinform(5)

376 Measurement Technology and its Application III



localinform(6)) lsquo2010rsquo)rdquo)rsquo to get the current earth magnetic field the local geomagnetic information

of which would show on the main panel

Click lsquoCorrectionrsquo button to respond the function lsquoRunMATLABScript (mMATLAB ldquoE

EllipsoidFittingmrdquo)rsquo to ellipsoid fit the collected data for obtaining the correction factors and bias

which can be returned to LabWindowsCVI environment from MATLAB environment using the

function lsquoGetMatrix (mMATLAB ldquomag_trdquo ampmatrixReal ampmatrixImag ampdim1 ampdim2)rsquo andfinally that would be loaded to PC or MINS via the serial port Click lsquoExitrsquo button to quit out of

system running

Figure 3 Magnetometers correction system virtual instrument user interface

Magnetometers-aided MINS virtual instrument Magnetometers-aided MINS Virtual Instrument

was made up with LabWindowsCVI Each button functions were programmed using C language It

provides the functions of sensors data acquisition timing initial alignment navigation showing

graphic and text and saving as shown in Fig 4

Figure 4 Magnetometers-aided MINS virtual instrument user interface

Data acquisition module turn on the switch of the serial port and receive the output of tri-axial

gyroscope tri-axial accelerometer and tri-axial magnetometer




Magnetometer-aided module after magnetometerrsquos measuring values are compensated by Eq 1

the bodyrsquos attitude can be determined with the known yaw angle the local declination inclination and

the total density of geomagnetism

In the INS the body attitude update used the tri-axial gyroscope output Then the body attitude

calculated in the Magnetometer-aided module replaces that calculated in the INS Next to estimate the

velocity and the position with the known attitude and the tri-axial accelerometer output The timer setthe sample rate and can be turn on or turn off It can be set initial alignment then turn to navigate The

magnetometer-aided MINS navigation system outputs the attitude velocity and position that all can

be display on the panel

Experimental Verification

In order to verify whether magnetometers correction could improve the performance of MINS based

on geomagnetic attitude-aided magnetometer-aided MINS integrated navigation test respectively

experiment with magnetometers correction and without magnetometers correction The navigation

tests adopt a group of IMU and MMU data that has error that INS update rate is at 500 Hz and that

rotational rate is at 10 rs Flight initial conditions set as latitude of 067020643 rad longitude of201410996 rad altitude of 139471 m the east velocity of 134969 ms the north velocity of 77943

ms the sky velocity of 108213 ms yaw angle of 30deg north by east pitch angle of 35deg and roll angle

of 0deg The IMU and MMU error model is that gyro bias is 75deg h gyro random walk is 05983216radich

accelerometer bias is 9 mg magnetometer bias is plusmn300 nT magnetometer axis non-orthogonality is

025983216 and magnetometer axis misalignment is 05983216

Magnetometers correction test simulation Before MagnetometerMINS integrated navigation test

we need to do magnetometers correction test following the steps of 212 chapter for obtaining

correction factor and bias and preparing them for MagnetometerMINS integrated navigation All the

MMU measuring value approximately distributes into an ellipsoid as shown in Fig 5

Figure 5 Tri-axial Magnetometers correction based on ellipsoid fitting

Magnetometers-aided MINS navigation test simulation Figs 6-7 show the simulation results of

position velocity and attitude errors of magnetometers-aided MINS navigation They present that the

navigation error of the correction magnetometers-aided MINS is smaller than that of the

non-correction magnetometers-aided MINS at the same spinning rate The attitude accuracy of the

correction magnetometers-aided MINS is greatly improved which imply that magnetometers

correction plays a role in the attitude estimation leading to more precise velocity and position

0 10 20 30 40 50 60 70-400

-300

-200

-100

0

100

200

300

400

500

600

X 6779Y 5417

Time (s)

P o s i t i o n E r r o r ( m )

X 6779Y -1455

X 6779Y -3755

Latitude

Longitude

Elevation

0 10 20 30 40 50 60 70-20

-15

-10

-5

0

5

10

15

20

25

30

X 6779Y 2259

Time (s)

V e l o c i t y E r r o r ( m s )

X 6779Y -8213

X 6779Y -1643

East

North

Sky

0 10 20 30 40 50 60 70-05

-04

-03

-02

-01

0

01

02

X 6779

Y -02391

Time (s)

A t t i t u d

e E r r o r ( d e g )

X 6779Y -04596

Yaw

Pitch

0 10 20 30 40 50 60 70-08

-06

-04

-02

0

02

04

06

X 6779Y -0004049

Time (s)

A t t i t u d


Roll

Figure 6 Magnetometers-aided MINS navigation test with non-correction




0 10 20 30 40 50 60 70-200

-150

-100

-50

0

50

100

150

X 6779Y 1219

Time (s)


X 6779Y 1055

X 6779Y -1805

Latitude

Longitude

Elevation

0 10 20 30 40 50 60 70-10

-8

-6

-4

-2

0

2

4

X 6779Y 3616

Time (s)


X 6779Y 3225

X 6779Y -9553

East

North

Sky

0 10 20 30 40 50 60 70-025

-02

-015

-01

-005

0

005

01

X 6779Y -006621

Time (s)

A t t i t u d e E r r o r ( d e g )

X 6779Y -02378

Yaw

Pitch

0 10 20 30 40 50 60 70

-005

0

005

01

015

02

025

X 6779Y 01104

Time (s)


X 6144Y 02019

X 5094Y -007565

Roll

Figure 7 Magnetometers-aided MINS navigation test with correction

Conclusions

The ActiveX controller of LabWindowsCVI allowed LabWindowsCVI to call MATLAB to realize

fuzzy programming which made magnetometers correction virtual instrument achievable according

to magnetometers correction system scheme Magnetometers-aided MINS and its virtual instrument

were developed for navigation test It turned out that magnetometers correction test could compensate

error and eliminate interference and magnetometers correction system could improve the

performance of magnetometers-aided MINS for higher precise navigation The visual virtualinstruments were readily exploited handled and convenient for display They had a good engineering

significance in the fields of measurement correction and navigation

Acknowledgements

This work was financially supported by the key laboratory of dynamics and control of flight vehicle

ministry of education school of aerospace engineering Beijing Institute of Technology

References

[1] GX Shi SX Yang and Z Su The Study on Attitude Algorithm of Rolling Projectile UsingGeomagnetic Information Journal of Projectiles Rockets Missiles and Guidance Vol 31

(2011) p 33-38 In Chinese

[2] J Xu The Study on Analysis of Hard Ferromagnetic Materials Interfere Geomagnetic

Measurement and Calibration Technology [D] Nanjing University of Science and Technology

Nanjing (2013) In Chinese

[3] Y Du The Research on Electronic Compass Measurement Error Analysis and Compensation

Technology North University of China Taiyuan (2011) in press In Chinese

[4] YQ Guo C Chen DM Ma and L Li Establishment and Application of High-frequency

Channel Transmission Attenuation Model Based on LabWindowsCVI and MATLAB Journal

of Modern Electronics Technique Vol 34(2011) p 137-142 In Chinese

[5] L Long and H Zhang Automatic and Adaptive Calibration Method of Tri-axial Magnetometer

Chinese Journal of Scientific Instrument Vol 34 (2013) p 161-165 In Chinese

[6] Q Zhang QM Wu D Chen and Y Li ActiveX Creation and Application in the

LabWindowsCVI Journal of Mechanical and Electrical Engineering Technology Vol 35


[7] R Halir and J Flusser Numerically Stable Direct Least Squares Fitting of Ellipses Proc of the

6th International Conference in Central Europe on Computer Graphics Visualization and

Interactive Digital Media 1998 (WSCG98) University of West Bohemia Press Vol 1(1998) p

125-132

[8] L Qingde and JG Griffiths Least Squares Ellipsoid Specific Fitting Proc Geometric Modeling

and Processing 2004 (GMPrsquo04) IEEE Comput Soc Vol 18 (2004) p335-340




C o p y r i g h t o f A p p l i e d M e c h a n i c s amp M a t e r i a l s i s t h e p r o p e r t y o f T r a n s T e c h P u b l i c a t i o n s L t d

a n d i t s c o n t e n t m a y n o t b e c o p i e d o r e m a i l e d t o m u l t i p l e s i t e s o r p o s t e d t o a l i s t s e r v w i t h o u t

t h e c o p y r i g h t h o l d e r s e x p r e s s w r i t t e n p e r m i s s i o n H o w e v e r u s e r s m a y p r i n t d o w n l o a d o r

e m a i l a r t i c l e s f o r i n d i v i d u a l u s e



building up magnetometers-aided micro inertial navigation system (MINS) and its virtual instrument

utilizing LabWindowsCVI and C language for attitude and navigation computation The virtual

instruments can easily show or store the test data and result In this paper how to realize

LabWindowsCVI and MATLAB fuzzy programming is introduced such as how LabWindowsCVI

call MATLAB here their advantages fully embody for completing the development of

magnetometers correction system

System General Scheme Design

Magnetometers Correction System Fig 1 describes functional block diagram of the

Magnetometers correction system whose virtual instrument was built by LabWindowsCVI and

MATLAB consisting of measuring unit data acquisition unit correction unit load parameters unit

and earth magnetic field model Three-axis magnetic sensor (Magnetic Measurement Unit MMU)

output digital local geomagnetic measurement which were received by data acquisition unit in the PC

via a serial port Data acquisition unit was generated by LabWindowsCVI MATLAB library

function has earth magnetic field model with lsquowrldmagmrsquo function It just needs to be input local

geography information (longitude latitude and altitude) and current time (year month and day) willobtain the geomagnetic information in the locality such as declination inclination geomagnetic total

intensity and so on A group of magnetic data collected by data acquisition unit can be ellipsoid fitted

by correction unit referenced the geomagnetic information with the ellipsoid fitting function But the

lsquowrldmagmrsquo function and the ellipsoid fitting function program and run in the MATLAB workspace

so here LabWindowsCVI must call MATLAB to work Finally the correction coefficients come out

with geomagnetism correction factors and bias that would be downloaded to or save in the vehicle

computer

Figure 1 Magnetometers correction system functional block diagram

Magnetometers-aided MINS System Most inertial measuring products are complete inertial

systems that include a tri-axial gyroscope a tri-axial accelerometer and a tri-axial magnetometer Fig

2 depicts functional block diagram of magnetometers-aided MINS navigation Themagnetometers-aided MINS virtual instrument was built by LabWindowsCVI The IMU and the

MMU both were digital output The sensor output was collected by digital data acquisition module of

the virtual instrument of Magnetometers-aided MINS navigation system via a serial port Before

calculating attitude the tri-axial magnetometers measurement value must be compensated by

equation [5]

H f = CH m － B (1)

Where C is a geomagnetic correction factors matrix of 3x3 B is a geomagnetic correction bias

matrix of 3x1 H m is a magnetometers measuring value and H f is an ideal value to calculate body

attitude The body attitudes are determined only with magnetometers if one attitude angle is knownThe yaw angle changes very little for the high-speed rotatable vehicle so the yaw angle is assumed to

be known or can be calculate from tri-axial gyroscope measuring value Magnetometers-aided

module works out the pitch and roll angles as the input of MINS to correct the attitude calculated by





guidance system








































system running









































0 10 20 30 40 50 60 70-400

-300

-200

-100

0

100

200

300

400

500

600

X 6779Y 5417

Time (s)


X 6779Y -1455

X 6779Y -3755

Latitude

Longitude

Elevation

0 10 20 30 40 50 60 70-20

-15

-10

-5

0

5

10

15

20

25

30

X 6779Y 2259

Time (s)


X 6779Y -8213

X 6779Y -1643

East

North

Sky

0 10 20 30 40 50 60 70-05

-04

-03

-02

-01

0

01

02

X 6779

Y -02391

Time (s)

A t t i t u d


X 6779Y -04596

Yaw

Pitch

0 10 20 30 40 50 60 70-08

-06

-04

-02

0

02

04

06

X 6779Y -0004049

Time (s)

A t t i t u d


Roll





0 10 20 30 40 50 60 70-200

-150

-100

-50

0

50

100

150

X 6779Y 1219

Time (s)


X 6779Y 1055

X 6779Y -1805

Latitude

Longitude

Elevation

0 10 20 30 40 50 60 70-10

-8

-6

-4

-2

0

2

4

X 6779Y 3616

Time (s)


X 6779Y 3225

X 6779Y -9553

East

North

Sky

0 10 20 30 40 50 60 70-025

-02

-015

-01

-005

0

005

01

X 6779Y -006621

Time (s)


X 6779Y -02378

Yaw

Pitch

0 10 20 30 40 50 60 70

-005

0

005

01

015

02

025

X 6779Y 01104

Time (s)


X 6144Y 02019

X 5094Y -007565

Roll


Conclusions








Acknowledgements



References



















125-132













guidance system








































system running









































0 10 20 30 40 50 60 70-400

-300

-200

-100

0

100

200

300

400

500

600

X 6779Y 5417

Time (s)


X 6779Y -1455

X 6779Y -3755

Latitude

Longitude

Elevation

0 10 20 30 40 50 60 70-20

-15

-10

-5

0

5

10

15

20

25

30

X 6779Y 2259

Time (s)


X 6779Y -8213

X 6779Y -1643

East

North

Sky

0 10 20 30 40 50 60 70-05

-04

-03

-02

-01

0

01

02

X 6779

Y -02391

Time (s)

A t t i t u d


X 6779Y -04596

Yaw

Pitch

0 10 20 30 40 50 60 70-08

-06

-04

-02

0

02

04

06

X 6779Y -0004049

Time (s)

A t t i t u d


Roll





0 10 20 30 40 50 60 70-200

-150

-100

-50

0

50

100

150

X 6779Y 1219

Time (s)


X 6779Y 1055

X 6779Y -1805

Latitude

Longitude

Elevation

0 10 20 30 40 50 60 70-10

-8

-6

-4

-2

0

2

4

X 6779Y 3616

Time (s)


X 6779Y 3225

X 6779Y -9553

East

North

Sky

0 10 20 30 40 50 60 70-025

-02

-015

-01

-005

0

005

01

X 6779Y -006621

Time (s)


X 6779Y -02378

Yaw

Pitch

0 10 20 30 40 50 60 70

-005

0

005

01

015

02

025

X 6779Y 01104

Time (s)


X 6144Y 02019

X 5094Y -007565

Roll


Conclusions








Acknowledgements



References



















125-132


















system running









































0 10 20 30 40 50 60 70-400

-300

-200

-100

0

100

200

300

400

500

600

X 6779Y 5417

Time (s)


X 6779Y -1455

X 6779Y -3755

Latitude

Longitude

Elevation

0 10 20 30 40 50 60 70-20

-15

-10

-5

0

5

10

15

20

25

30

X 6779Y 2259

Time (s)


X 6779Y -8213

X 6779Y -1643

East

North

Sky

0 10 20 30 40 50 60 70-05

-04

-03

-02

-01

0

01

02

X 6779

Y -02391

Time (s)

A t t i t u d


X 6779Y -04596

Yaw

Pitch

0 10 20 30 40 50 60 70-08

-06

-04

-02

0

02

04

06

X 6779Y -0004049

Time (s)

A t t i t u d


Roll





0 10 20 30 40 50 60 70-200

-150

-100

-50

0

50

100

150

X 6779Y 1219

Time (s)


X 6779Y 1055

X 6779Y -1805

Latitude

Longitude

Elevation

0 10 20 30 40 50 60 70-10

-8

-6

-4

-2

0

2

4

X 6779Y 3616

Time (s)


X 6779Y 3225

X 6779Y -9553

East

North

Sky

0 10 20 30 40 50 60 70-025

-02

-015

-01

-005

0

005

01

X 6779Y -006621

Time (s)


X 6779Y -02378

Yaw

Pitch

0 10 20 30 40 50 60 70

-005

0

005

01

015

02

025

X 6779Y 01104

Time (s)


X 6144Y 02019

X 5094Y -007565

Roll


Conclusions








Acknowledgements



References



















125-132









































0 10 20 30 40 50 60 70-400

-300

-200

-100

0

100

200

300

400

500

600

X 6779Y 5417

Time (s)


X 6779Y -1455

X 6779Y -3755

Latitude

Longitude

Elevation

0 10 20 30 40 50 60 70-20

-15

-10

-5

0

5

10

15

20

25

30

X 6779Y 2259

Time (s)


X 6779Y -8213

X 6779Y -1643

East

North

Sky

0 10 20 30 40 50 60 70-05

-04

-03

-02

-01

0

01

02

X 6779

Y -02391

Time (s)

A t t i t u d


X 6779Y -04596

Yaw

Pitch

0 10 20 30 40 50 60 70-08

-06

-04

-02

0

02

04

06

X 6779Y -0004049

Time (s)

A t t i t u d


Roll





0 10 20 30 40 50 60 70-200

-150

-100

-50

0

50

100

150

X 6779Y 1219

Time (s)


X 6779Y 1055

X 6779Y -1805

Latitude

Longitude

Elevation

0 10 20 30 40 50 60 70-10

-8

-6

-4

-2

0

2

4

X 6779Y 3616

Time (s)


X 6779Y 3225

X 6779Y -9553

East

North

Sky

0 10 20 30 40 50 60 70-025

-02

-015

-01

-005

0

005

01

X 6779Y -006621

Time (s)


X 6779Y -02378

Yaw

Pitch

0 10 20 30 40 50 60 70

-005

0

005

01

015

02

025

X 6779Y 01104

Time (s)


X 6144Y 02019

X 5094Y -007565

Roll


Conclusions








Acknowledgements



References



















125-132












0 10 20 30 40 50 60 70-200

-150

-100

-50

0

50

100

150

X 6779Y 1219

Time (s)


X 6779Y 1055

X 6779Y -1805

Latitude

Longitude

Elevation

0 10 20 30 40 50 60 70-10

-8

-6

-4

-2

0

2

4

X 6779Y 3616

Time (s)


X 6779Y 3225

X 6779Y -9553

East

North

Sky

0 10 20 30 40 50 60 70-025

-02

-015

-01

-005

0

005

01

X 6779Y -006621

Time (s)


X 6779Y -02378

Yaw

Pitch

0 10 20 30 40 50 60 70

-005

0

005

01

015

02

025

X 6779Y 01104

Time (s)


X 6144Y 02019

X 5094Y -007565

Roll


Conclusions








Acknowledgements



References



















125-132










magnetometers correction and magnetometers-aided

Documents