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COMBINING MULTIPLE SOURCES FOR RADIOMETRIC CALIBRATION OF LANDSAT 7 USING A KALMAN FILTER 
Ellis Freedman and Jennifer Byme 
Martin Marietta Corporation 
Management and Data Systems 
P.O. Box 8555 
Philadelphia, Pennsylvania U.S.A 19101 
Telephone: (610) 531-1684 
Fax: (610) 962-3698 
E-Mail: freedmae@land.vf.ge.com 
KEY WORDS: Kalman Filter, Radiometry, Calibration, Landsat 7 
ABSTRACT 
The Enhanced Thematic Mapper Plus, currently under development for Landsat 7, has a requirement to provide absolute 
radiometric information with errors of less than 5%. To meet this requirement, current plans call for the use of three differ- 
ent techniques for absolute radiometric calibration: Full Aperture Solar Calibration, Partial Aperture Solar Calibration, and 
Ground Look Calibration. Associated with each of these is its own set of uncertainties and errors which may, at times, 
exceed the system's allowable error margin. A Kalman Filter is proposed for combining the outputs of all three tech- 
niques, and for the optimal estimation and continual updating and tracking of the states of the associated hardware cali- 
brators. Results are presented which surpass the requirement and indicate the viability of the approach. 
1. INTRODUCTION 
The Thematic Mappers (TM) of Landsat 4 and 5 had goals of achieving less than 1096 error in absolute radiometric 
accuracy. To achieve this goal, the TMs were calibrated in the laboratory using equipment that had an estimated 
radiometric uncertainty of approximately 10%. Once on-orbit, the calibration coefficients were updated with an internal 
calibrator that provided both a dark shutter and various levels of light. While no definitive evaluation of performance is 
available, different studies indicate that as much as 10% - 15% additional drift may have occurred since launch. 
Landsat 7 will take a different approach. The Enhanced Thematic Mapper Plus (ETM+), while similar in its core design to 
the TM, will include not only an internal calibrator similar to that on the TM, but two additional radiometric calibration 
devices: the Full Aperture Solar Calibrator (FASC) and the Partial Aperture Solar Calibrator (PASC). Briefly, the FASC is 
a paddle that can be positioned in front of the ETM+ aperture covering the entire field of view. On the surface of the 
paddle facing the aperture is a panel of highly reflective, highly diffuse (nearly Lambertian), YB-71 white thermal control 
paint. The paddle is positioned during calibration in such a way as to reflect sunlight into the field of view providing a 
well-characterized source of radiance. Calibration is scheduled to take place approximately once every six weeks when 
the satellite passes over the (North Pole) terminator. 
The PASC is a completely different form of calibrator. It will consist of a small device in four parts which sits inside the 
sunshade. Each part will be made up of two reflecting surfaces and a small aperture. Approximately when the satellite 
passes over the North Pole and the Earth below is in darkness, sunlight will be reflected sequentially off the two surfaces 
and through the small aperture enabling the ETM+ to effectively create an image of the Sun through a combination of the 
whiskbroom scanning in one direction and the relative satellite motion in the other. This apparatus is duplicated four times 
to account for angular variations of Sun position with season (i.e. the Sun will be seen through different apertures at 
different times of the year). Current plans call for the PASC to be used once a day. 
The combination of all three techniques will provide a large amount of data on the radiometric response of the ETM+. 
However, each technique will have its own characteristic uncertainties, and questions quickly arise over how much the 
data from each form of calibration should be trusted and how the data should be combined to estimate the response of 
the sensor. Proper estimation of the errors and characteristics of each technique in combination with an optimal 
estimator, such as a Kalman Filter, can provide a better understanding of the sensor response than any single calibration 
technique might provide. This paper provides a description of some of the work done in developing that Kalman Filter. All 
work presented here is presumed to apply to band one (0.45um - 0.515 um) of the ETM+, although it is directly applicable 
to all of the other reflective bands (2 - 5, 7 and the new Panchromatic band). 
2. THE KALMAN FILTER 
A Kalman Filter is, in simple terms, a linear estimator/predictor which provides an optimized estimate of a set of measured 
parameters (the state vector) given certain characteristics about the system being measured and the measuring device. 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences", Zurich, March 22-24 1995