A Studyyy on an Accurate yet Simple Attitude Estimation S ... · A Studyyy on an Accurate yet Simple Attitude Estimation S h f N t llitScheme for Nanosatellites 1 HALIL ERSIN SOKEN

A Study on an Accurate yet y ySimple Attitude Estimation S h f N t llitScheme for Nanosatellites

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HALIL ERSIN SOKENT H E G R A D U A T E U N I V E R S I T Y F O R A D V A N C E D S T U D I E S

( S O K E N D A I )( S O K E N D A I )D E P A R T M E N T O F S P A C E A N D A S T R O N A U T I C A L S C I E N C E

S A G A M I H A R A / J A P A N

SHIN-ICHIRO SAKAI J A P A N A E R O S P A C E E X P L O R A T I O N A G E N C Y ( J A X A )

I N S T I T U T E O F S P A C E A N D A S T R O N A U T I C A L S C I E N C E ( I S A S ) S A G A M I H A R A / J A P A N

5th Nano-Satellite Symposium 20-22 November 2013 / Tokyo Soken&Sakai Nano-Sat 2013

Introduction

Main motivation is to provide an accurate attitude 2

Main motivation is to provide an accurate attitude determination method for a nanosatellite carrying;

Magnetometers,GGyro,Magnetorquers.

Step by step problems that arise for attitude d i i f hi lli k idetermination of this satellite are taken into consideration.

We first investigated the main reasons that reduce the ADCS gperformance.Then possible solution techniques for these problems are proposed, mainly based on the adaptation of the filters used for attitude determinationdetermination.In the final part, these techniques are integrated in order to propose an overall attitude determination scheme.

Soken&Sakai Nano-Sat 2013

Outline

Problem statement

3

Problem statementWhat do we aim?

Common ProblemsCommon ProblemsWhat do we propose?

Preliminaries: Briefly UKFSolutions

Magnetometer CalibrationS f l lSensor fault toleranceResidual Magnetic Moment Estimation

Proposed Attitude Estimation SchemeProposed Attitude Estimation SchemeDemonstrationConclusionConclusion


Problem Statement4

• For advanced small satellite • For advanced small satellite missions such as remote sensing, observation of astronomical objects the astronomical objects, the satellite must meet strict pointing accuracy requirements for obtaining the scientific data for obtaining the scientific data or the image.

• High accuracy sensors and actuators such as star-trackers actuators such as star trackers and reaction wheels cannot be easily used.

• The attitude must be determined Trend for Pointing Accuracy of Small Satellites• The attitude must be determined and controlled precisely by using coarse sensors and actuators which are smaller and lighter.

Trend for Pointing Accuracy of Small Satellites

Source: C. Pong, and et al., “High-Precision Pointing and Attitude Determination and Control of ExoplanetSat,” in Proc. AIAA Guidance,

Navigation, and Control Conference, Minneapolis, USA, 2012.

which are smaller and lighter.


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Magnetometer: Magnetorquer:Magnetometer:LightEconomicSmall

Magnetorquer:LightweightEnergy-efficientReliable

Onboard attitude sensors and actuators for nanosatellites launched as of 2010

Bouwmeester, J., and Guo, J. (2010). “Survey of Worldwide Pico- and Nanosatellite Missions, Distributions and Subsystem



Bouwmeester, J., and Guo, J. (2010). Survey of Worldwide Pico and Nanosatellite Missions, Distributions and Subsystem Technology,” Acta Astronautica, 67, 854-862. DOI:10.1016/j.actaastro.2010.06.004

Common Problems6

Main problem Reason Usual Solution Our method

Systematic error for magnetometers

- Disturbance fields by s/c electronics

Accurate in-flight calibration

- A single UKF to both estimate attitude and magnetometers s/c electronics.

- Modeling errors.- Compactness of the

s/c.

calibration estimate attitude and calibrate magnetometers.

- Tune the UKF with an adaptive algorithm to increase the performance.

Measurement faults ‐ External and internal Make the estimator An efficient method for robust for magnetometers disturbances.

‐ Compactness of the s/c.

robust against such faults.

Kalman filtering.

Changes in the RMM Variations in the onboard electrical current.

Excite the filter. A novel change detection and KF adaptation technique that regards the magnitude of the change.


What do we propose?p p7

Two stage filter Two-stage filter based attitude

estimation scheme

Algorithmic solutions which investigate the possible algorithm based possible algorithm based techniques to solve specific problems.

Propose an overall Propose an overall attitude estimation algorithm such that all these problems are these problems are solved.

Keep it simple and easy to apply.


pp y

Unscented Kalman Filter8

UKF is advantageous in case of li d i d/nonlinear dynamics and/or

measurement model.Unlike the EKF, the UKF does not

i J bi i require any Jacobian matrix calculation, which may mean;

hard and time consuming process,possibility of filter divergence because of possibility of filter divergence because of linearization assumptions,usually computational burden,a filter which is prone to human errors.

h f l h hHence the UKF is a filter that has;a higher estimation accuracy and convergence characteristic,more robustness against the initial

Example of mean and covariance propagationmore robustness against the initial estimation errors.

Not so many application examples for the UKF while the EKF has been

l d d f l i i

Source: Van der Merwe ,R. and Wan, E.A. The Square-root Unscented Kalman Filter for State and Parameter Estimation, Proceedings of: IEEE International Conference onAcoustics, Speech, and Signal Processing, Salt Lake City, USA, 2001.


already used for several missions.

Magnetometer Calibrationg9

We can estimate the t t bi t th

10x 10

-6 bxm Estimation

Kalman Estimation

magnetometer biases together with the attitude using the UKF.However the estimation accuracy for especially the magnetometer bi t i t hi h

5

0

5

bxm

(T) Actual Value bias terms is not so high.

The main problem is the difficult tuning procedure for the Q matrix.

It is usually tuned by trial-error.0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

-5

10x 10-6

y yThat is difficult for state vectors with high dimension.Adaptive UKF is a possible solution technique.

0

5

erro

r (T)

The Q matrix should be tuned adaptively to

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

-5

time(sec)

tuned adaptively to increase the calibration

and so attitude estimation performance


performance

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Based on Maximum Likelihood Estimator [ ]Based on Maximum Likelihood Estimator [ ]

( ) ( ) ( )

Observation for the PNCM

( ) ( ) ( )( 1) ( 1) 1 1 1TQ k k P k k P k k Q k∗ = Δ + Δ + + + − + + −x x

Residual as the difference between the estimated and predicted state.

We perform Q adaptation

for

( ) ( )ˆ ˆ( 1) 1 1 - 1k k k k kΔ + = + + +x x x

Estimation within a window (or by low-pass filter)

for optimizing

the UKF and use it for s/c

( ) ( ) ( )11Q k Q k Q Q kγ

∗⎡ ⎤+ = + −⎣ ⎦

Estimation within a window (or by low-pass filter) f /attitude

estimation.γ

Window size (determined by either trial-error method or numerical optimization)

•P.S. Maybeck, Stochastic Models, Estimation and Control. Vol. II. Academic Press, New York, USA,


.S. aybec , Stoc ast c ode s, st at o a d Co t o . Vo . . cade c ess, New o , US ,1982, Chap.10.

Sensor Fault Tolerance11

S i i t Space is a severe environment so the measurement faults are always possible. The measurement sensors may

Proposing novel techniques for R The measurement sensors may

be easily affected from the other subsystems considering the size of the nanosatellites and necessity for placing the

techniques for R adaptation to make

the filter robust necessity for placing the subsystems closely to each other.External disturbances such as ionospheric currents may have The essence of the proposed o osp e c c e s y egreat deteriorating effect on the measurement performance. Making the filter insensitive ( b t) t th h f il t

The essence of the proposed method is;

Detecting the fault.(robust) to the such failures at the measurement channel is necessary in order to keep attitude estimation accuracy.

Calculating the scale factor(s). Tuning the R matrix to decrease the Kalman gain.


y the Kalman gain.

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( )1 k

∑ ( ) ( ) ( ) ( ) ( )1

1 1 1 1 1 .Tyy

j k

j j P k k S k R kξξ = − +

+ + = + + +∑ e e

1 k⎧ ⎫ ( )S diag s s s∗ ∗ ∗ ∗=

{ }max 1, 1,i iis S i z∗ = =

( ) ( ) ( ) ( ) ( )1

1

1 1 1 1 1 .k

Tyy

j k

S k j j P k k R kξξ

−

= − +

⎧ ⎫= + + − + +⎨ ⎬⎩ ⎭

∑ e e ( )1 2, , , zS diag s s s= …

Scaling matrix for

( ) ( ) ( ) ( ) ( )1

1 1 1 1xy yyK k P k k P k k S k R k−∗⎡ ⎤+ = + + + +⎣ ⎦

making the filter robust

In normal conditions filter operates optimally

At each step we test the statistical function of;

Normal condition

( ) 20 : sk αγ β χ≤ k∀p ;

Measurement malfunction( ) ( ) ( ) ( )1

( ) 1 1 1 1Tyyk e k P k k R k e kβ

−⎡ ⎤= + + + + +⎣ ⎦

( )0 ,sαγ β χ

( ) 21 ,: sk αγ β χ> k∃by comparing with chi square distribution

2χ


by comparing with chi-square distribution.,sαχ

Residual Magnetic Momentg13

satellite size smalleraerodynamic torque,

i disatellite size smaller gravity gradient torque and solar radiation

pressure torque

RMM caused by the current loop small permanent magnet loop, small permanent magnet

in some devices or some special material on the

satellite does not strongly satellite does not strongly depend on the satellite size.

Hence for the nanosatellites the RMM is a dominant disturbance source. Nano-Jasmine Satellite: An Example for

astrometry mission where high pointing accuracy is needed.


accuracy is needed.

Source: http://www.jasmine-galaxy.org/index-ja.html

Time difference for

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Time difference for exceeding these

successive thresholds gets smaller for larger gets smaller for larger

changes

When the change is detected, calculate a weighting function using the GMA steepness as input.The value of the function changes between zero to one.

( )( 1) exp /k t t ϑ⎡ ⎤Ω + = ⎣ ⎦Then adapt the covariance of the UKF such that;

( )1 2( 1) exp /k t tξ ξ ϑ⎡ ⎤Ω + = − −⎣ ⎦

( )1 1P k k { } ( ) ( ) ( ) ( )1 ( 1) 1 1 1 1 ( 1)Tk P k k K k P k k K k k P⎡ ⎤Ω + + + + + +Ω +⎣ ⎦( )1 1P k k+ + ={ } ( ) ( ) ( ) ( ) 01 ( 1) 1 1 1 1 ( 1)Tvvk P k k K k P k k K k k P⎡ ⎤−Ω + + − + + + +Ω +⎣ ⎦

Overall Attitude Estimation Scheme15

Each problem, which were addressed individually were addressed individually, were solved. Now the main issue is to show the proposed methods are working as a part of the whole estimation

RAUKFTwo-stage Filter

RAUKF

pscheme.So we integrate different adaptation methods.The overall estimation scheme is b d fil f based on two filters: a RAUKF for attitude estimation and sensor calibration and an UKF for RMM estimation.

Unique filter

MED 2009

Unique filter integration

scheme


MED 2009

Demonstrations16

A 3U cubesat (10cm x 10cm x A 3U cubesat (10cm x 10cm x 30cm) - 3kg - inertia matrix: TURKSAT

3U-SAT of Istanbul 2(0 055 0 055 0 017)J di k

1000km altitude, 31deg inclinationh b h

Technical University

2(0.055 0.055 0.017) . .J diag kg m=

The bias in the magnetometers:[ ] 40.14 0.019 0.37 10 .T

mb nT= × 1) Reijneveld, J. and Choukroun, D. (2012) “Attitude Control of the Delfi-

Magnetometer noise:[ ]

300nTσ =

(2012). Attitude Control of the Delfi-n3Xt Satellite”.

2) Sakai, S., Fukushima, Y., Ohno, A. and Saito, H. (2006). “In-orbit Performance Evaluation of Temperature

Gyro characteristics:300m nTσ

2 47[ / ] 4 36 36 10 [ / ]−&

pControlled Small Fiber Optical Gyro on Microsatellite <REIMEI>”.

3) Sakai S. and et al. (2011) "Real-time estimation of the bias error of the


2.47[ / ]arcsec sνσ = 4 36.36 10 [ / ]u arcsec sσ −= ×& magnetometer only with the gyro sensors“.

Effects of Q Adaptationff f Q p17

B tt ttit d Better attitude estimation accuracy

by the AUKF (the UKF for which the Q UKF for which the Q is adaptively tuned)


Effects of R Adaptationff f p18

In case of possible measurement faults

the regular filter deteriorates while h fil b the filter robust to

faults keeps giving accurate results.


Effects of P Adaptationff f p19

In case of change in the estimated RMM

parameters the regular algorithm is late about catching

the new value, while the RAUKF with the

proposed change d i ddetection and P

adaptation quickly converges

MED 2009MED 2009


Conclusion

Algorithm based solutions are proposed for common

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Algorithm based solutions are proposed for common problems about attitude determination of a nanosatellite which has magnetometers and nanosatellite which has magnetometers and magnetorquers as the primary attitude hardware.Problems such as magnetometer calibration and ob e s suc as ag eto ete ca b at o a d RMM estimation are addressed.Investigated solution techniques are integrated using g q g gan unique scheme to propose an overall attitude estimation method.The method is validated by demonstrations for a hypothetical nanosatellite.


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THANK YOU

Acknowledgment

This work was supported in part by Japanese Government with MONBUKAGAKUSHO scholarship and also by Japan Aerospace Exploration Agency (JAXA) with a research grant.


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A Studyyy on an Accurate yet Simple Attitude Estimation S ... · A Studyyy on an Accurate yet Simple Attitude Estimation S h f N t llitScheme for Nanosatellites 1 HALIL ERSIN SOKEN