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MODIS and VIIRS Geolocation Error andLong-term Trend Analysis with Automated Correction Techniques using KalmanFiltering Masahiro Nishihama Sigma Space Corporation Lanham, Maryland, USA (20706) mash.nishihama@nasa.gov Robert E. Wolfe NASA Goddard Space Flight Center, Code 614.5 Greenbelt, Maryland, USA (20771) robert.e.wolfe@nasa.gov IGARSS 2011  July 24-29,  Vancouver Canada
INTRODUCTION  ,[object Object]
Initial on-orbit bias removal is performed immediately after launch
Analysis and removal of long-termgeolocation 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 twoKalmanfiltering 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.IGARSS’11-Nishihama et al.  2
Background ,[object Object],      -  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) ,[object Object],1) sensor geometry            	2) spacecraft orbit-attitude relationship          	3) ECI and ECR 		4) Earth – Terrain height  IGARSS’11-Nishihama et al.  3
[object Object],   Bands Along-Scan IGARSS’11-Nishihama et al.  4
[object Object],- Use of Control Point Chip Library   1200  TM Landsatsubscenes  ( Red band   Band 3)           -Estimation of Geolocation Residuals  and  Management using  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” IGARSS’11-Nishihama et al.  5
[object Object],    - 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 IGARSS’11-Nishihama et al.  6
[object Object],-  Convert along-scan/track shifts to Nadir view angle offsets 	-  Convert them to ground distance  and display by Scan Angle. IGARSS’11-Nishihama et al.  7
[object Object],-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 IGARSS’11-Nishihama et al.  8
[object Object],IGARSS’11-Nishihama et al.  9
[object Object],       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 . IGARSS’11-Nishihama et al. 10
[object Object],       -  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+ IGARSS’11-Nishihama et al. 11
[object Object],ω = 2π / 365.25 whereState vector  X:   where  x(t) is either along-scan or along-track error with observation equation z = HX + ν IGARSS’11-Nishihama et al. 12
IGARSS’11-Nishihama et al. 13
[object Object],	-  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) 	-  Kinetic equations based on Wertz (p765) and reordering parameters IGARSS’11-Nishihama et al. 14
[object Object],-  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 IGARSS’11-Nishihama et al. 15

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  • 1. MODIS and VIIRS Geolocation Error andLong-term Trend Analysis with Automated Correction Techniques using KalmanFiltering Masahiro Nishihama Sigma Space Corporation Lanham, Maryland, USA (20706) mash.nishihama@nasa.gov Robert E. Wolfe NASA Goddard Space Flight Center, Code 614.5 Greenbelt, Maryland, USA (20771) robert.e.wolfe@nasa.gov IGARSS 2011 July 24-29, Vancouver Canada
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  • 3. Initial on-orbit bias removal is performed immediately after launch
  • 4. Analysis and removal of long-termgeolocation bias is needed to maintain accurate geolocation throughout multi-year missions
  • 5. Analysis and removal of the within-orbit trend is also needed because of thermal effects on instrument pointing
  • 6. Current approach is a manual least-squares analysis that uses linear and sinusoidal curves to remove both the long-term and within-orbit trends
  • 7. This presentation discusses twoKalmanfiltering approaches that are being considered to replace the current manual least-squares approach
  • 8. These new techniques can be applied to the Moderate-Resolution Imaging Spectroradiometer (MODIS) instruments and the future Visible Infrared Imaging Radiometer Suite (VIIRS) instrument.IGARSS’11-Nishihama et al. 2
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  • 27. DISCUSSION Analysis of both Kalman filtering methods are preliminary, but results of the first method is very promising. The second method needs more tests and examination. Appearance of yaw in the second method is interesting and needs investigation. Further tests will be needed for Aqua data using both methods. Determination of the initial covariance matrices and other parameters is critical, and requires careful attention. The Kalman filters methods are computationally efficient, it took very little time to processing 3800 sample points (~250 ground points are acquired each day). Once fully tested, either of the methods could be implemented, enabling automated daily geolocation parameter updates. IGARSS’11-Nishihama et al. 21