MODIS and VIIRS Geolocation Error andLong-term Trend Analysis with Automated

Correction Techniques using Kalman Filtering

Masahiro NishihamaSigma Space Corporation

Lanham, Maryland, USA (20706)mash.nishihama@nasa.gov

Robert E. WolfeNASA Goddard Space Flight Center, Code 614.5

Greenbelt, Maryland, USA (20771) robert.e.wolfe@nasa.gov

IGARSS 2011 July 24-29, Vancouver Canada

INTRODUCTION - Accurate geolocation of remote sensing data is needed for Earth science

research and applications

- Initial on-orbit bias removal is performed immediately after launch

- Analysis and removal of long-term geolocation bias is needed to maintain accurate geolocation throughout multi-year missions

- Analysis and removal of the within-orbit trend is also needed because of thermal effects on instrument pointing

- Current approach is a manual least-squares analysis that uses linear and sinusoidal curves to remove both the long-term and within-orbit trends

- This presentation discusses two Kalman filtering approaches that are being considered to replace the current manual least-squares approach

- These new techniques can be applied to the Moderate-Resolution Imaging Spectroradiometer (MODIS) instruments and the future Visible Infrared Imaging Radiometer Suite (VIIRS) instrument.

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Background• MODIS - Launched on NASA’s Earth Observing System (EOS) Terra spacecraft in December 1999, and started collecting data in February 2000 - MODIS on Aqua spacecraft in May 2002, began collecting data in July 2002 - whisk-broom sensor with 36 spectral bands; 2 at 250 m, 5 at 500 m and 29 at 1 km nadir spatial resolution - “Ideal” band is located at the center of focal planes (1km resolution)

• Geolocation Components1) sensor geometry 2) spacecraft orbit-attitude relationship

3) ECI and ECR 4) Earth – Terrain height

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LWIR

SWIR/ MWIR

NIR

VIS

Scan

Track

Scan Track

Spacecraft velocity

Earth

MODIS scan mirror

To focal planes

One MODIS scan

Reference optical axis

12 11 4 3 8 9 10

32 31 36 35 34 33 27 29 28 30

23 22 21 20 5 6 7 25 26 24

19 18 13 13’ 2 1 14’ 15 14 16 17

Detector

• MODIS along-Scan Point Spread Function for 1km, 500 m and 250m Bands

Along-Scan

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• Geolocation Error Analysis Tools

- Use of Control Point Chip Library 1200 TM Landsat subscenes ( Red band Band 3)

- Estimation of Geolocation Residuals and Managementusing Band 1 (250m) - Red band

- Parameter (roll/pitch/yaw error ) Estimation Program

1) Non-linear sensor model for residuals to Linear model, 2) Estimation of roll/pith/yaw from along-track/scan errors

- Estimated Initial Geolocation Error 1) Terra Geo Error(March 2000)

roll: 243’’ pitch: -354” yaw: 0

2) Aqua Geo Error(July 2002) roll: 424” pitch: -26” yaw: -51”

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• Simulated MODIS-like Image with TM scene and MODIS Geolocation file - Use triangular weights and assemble TM samples to build a MODIS like pixel with 250m resolution

MOD02QKM.A2001199.0840.004.2003121094844.hdf 2001 Day 199 -- July 18 From TM: L5176039_03919840920_B10.TIF

L1B: 8160 lines x 5416 samples

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• Geolocation Residuals to Statistical Analysis - Convert along-scan/track shifts to Nadir view angle offsets- Convert them to ground distance and display by Scan Angle.

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• Long Term Geolocation Error Trend and Analysis - One year or more of accumulated residual records needed - Trend (linear and annual cyclic) with a combination of linear and sinusoidal curve to fit the scan and track directions - Remove additional smaller within-orbit variations caused by temperature variation - Reduced geolocation error to less than 50 m Root Mean Square Error (RMSE) for MODIS/Terra and 60 m RMSE for MODIS/Aqua.

Note: Difference in Geolocation Accuracy between Terra and Aqua

- Terra orbit is identical to Landsat orbit,

- Terra observes a similar Earth shadow as TM does (10:30 AM) - Motion of AMSR-E Parabolic Reflector 1.6 meters in diameter on top of Aqua

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• Terra/MODIS Adjusted Residuals - along Track and Scan

-75

-50

-25

0

25

50

75

0 1 2 3 4 5 6 7 8 9

Trac

k (a

dj.)

res.

(m) .

Years since Jan. 1, 2000

Daily 16-day Global 16-day Southern Hemisphere 16-day Northern Hemisphere

-75

-50

-25

0

25

50

75

0 1 2 3 4 5 6 7 8 9

Sca

n (a

dj.)

res.

(m) .

Years since Jan. 1, 2000

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• Two Kalman Filtering Approaches for Long-term Trend Analysis 1. Linear and Sinusoidal Filter - Replace the manual approach with the automated approach by a combination of linear and sinusoidal curves with a period of one year, day-by-day, - Estimate roll/pitch errors to the instrument alignment matrix to new geolocation ,

2. Satellite Attitude Error Estimation Filter: - Express the attitude variation(error) as differential equations of Euler angles and use residual errors as part of observations

- Estimate residual Roll/pitch/yaw error to alignment matrix correction to new geolocation .

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• Linear Kalman Filter Key Parameters and Equations

- Definition of Time steps t0, t1, t2……. (days)

- Non-Linear Differential Equations to Linear Equations

- Observations or Meaurements z …… (along-track/scan residuals) - Initial State Vector X0

- System Noise (Q) and Measurement Noise (R) Covariance matrix - Initial State Error Covariance Matrix P0 ,

- Fundamental Matrix (Φ), Derived at tn+1 from tn

- A priori State Error Covariance Matrix (P-) and a priori Vector X-

- Kalman Gain Matrix (K) - Posteriori Error Covariance Matrix (P+) and best estimate X+

HXz

wAXX

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• Method 1. Linear and Sinusoidal Approach with

txtxtxxtx dcba cossin)(

dd

cc

bb

aa

dcb

xxxx

txtxxx

0000

sincos 0

)()( twXtAX

00001H

dcba xandxxxx ,,,,where State vector X:

where x(t) is either along-scan or along-track error with observation equation

Tdcba vvvvvw ),,,,( 0

ω = 2π / 365.25

z = HX + ν

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• Method 2. Euler Angle Differential Equation Approach

- Differential Equations in Euler Angles and Angular Velocity

- Along-Scan/Track Residuals in Observation Equations

- Estimate Roll/Pitch/Yaw Error at daily basis - Attitude Matrix with yaw (φ), roll (θ) and pitch (ψ)

coscoscossincossinsinsinsincoscossinsincoscossincos

cossincossinsinsincossinsinsincoscos

- Kinetic equations based on Wertz (p765) and reordering parameters

3

2

1

seccos0secsintancos1tansin

sin0cos

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• Method 2 (cont)

- Use of Approximation with small deviations f(θ, ψ, φ, ω) = f(θ0 + δθ, ψ0 + δψ, φ0 + δφ, ω0 + δω)

=

- Define State Vector X as

- Linear Differential Equations

ffff

f ),,,( 0000

0

3

2

1

03

02

01

0

3

2

1

, andX

)(twAXX

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• Method 2 (cont)- Determination of A

1. Express Euler angle matrix to (= B)

2. Use approximation to linearize contents of B:

333231

232221

131211

fffffffff

f11 = cψ = c(ψ0 + δψ) ≈ cψ0 – sψ0δψf12 = 0f13 = sψ = s(ψ0 + δψ) ≈ sψ0 + cψ0δψf21 = sψsθ/cθ = s(ψ0 + δψ)s(θ0 + δθ)/c(θ0 + δθ)

≈ sψ0sθ0/cθ0 + (cψ0sθ0)/cθ0)δψ + (sψ0/c2θ0 )δθf22 = 1f23 ≈ -cψ0sθ0/cθ0 + (sψ0sθ0)/cθ0)δψ - (cψ0/c2θ0 )δθf31 = -sψ secθ = -s(ψ0 + δψ) sec(θ0 + δθ)

≈ -sψ0/cθ0 – (cψ0/cθ0)δψ – ((sψ0sθ0)/c2θ0)δθf32 = 0f33 = c(ψ0 + δψ)/c(θ0 + δθ) ≈ cψ0/cθ0 – (sψ0/cθ0)δψ + ((cψ0sθ0)/c2θ0)δθ

3210

02

00

0

0

0

0

02

00

0

0

0

0

02

0

0

00

0

00

02

0

0

00

0

00

0000

0

1

0

GGGG

csc

cs

cc

css

cc

cs

cc

css

csc

cs

csc

css

cssc

B

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• Method 2 (cont)

- Determination of Matrix A

0

03

02

01

0

0030201

0000

andwhere

GGGG

0000

,

0030201 GGGGA

where

AXXhaveweX

- Observation Equation for Z 1) Non-trivial observation (measurement) matrix H

based on MODIS ground pointing algorithm.

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• Method 2 (cont)

2) View vector to Control Point(expected) and observed point

.

uorb = Torb/sc Tsc/inst uinst = F usc = F(θ, ψ, φ) usc

km705 where,0000

h

hh

E

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FuFuFuFuuZ scscsccpobsrv

321

||,

|| pXpX

upXpX

uobsrv

obsrvobsrv

cp

cpcp

• Method2 (cont)- Combining height matrix (E)and pre-observation equation ,

- Adding Angular velocity ω, observation becomes:

000000

where,232221

131211

3

2

1 hhhhhh

HHZ

..232221

131211

2

1

hhhhhh

FEZEzz

Z

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• Preliminary Results- From track/scan residuals over 10.4 years

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DISCUSSION

1. Analysis of both Kalman filtering methods are preliminary, but results of the first method is very promising.

2. The second method needs more tests and examination. Appearance of yaw in the second method is interesting and needs investigation.

3. Further tests will be needed for Aqua data using both methods.

4. Determination of the initial covariance matrices and other parameters is critical, and requires careful attention.

5. The Kalman filters methods are computationally efficient, it took very little time to processing 3800 sample points (~250 ground points are acquired each day).

6. Once fully tested, either of the methods could be implemented, enabling automated daily geolocation parameter updates.

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