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273 
Developing the filter requires a degree of knowledge of the random error associated with the measuring device for each 
parameter to be estimated (the measurement noise), a similar knowledge of the randomness in the parameter being 
measured (the process noise), and a model of how the parameters change from one state to the next (the transition 
operation). In the basic Kalman Filter, noise is assumed to be white and Gaussian. From this information (which is never 
perfectly known), the filter will dynamically determine, with each new measurement, the weight (i.e. trust) that should be 
placed on each new measurement versus that of its own internal model/prediction. The first step in developing a Kalman 
Filter is, therefore, to characterize the system. Development of the filter after that step is relatively straightforward. Finally, 
the filter must be tested in a simulation which models a true world, which differs from that assumed by the filter, in order to 
evaluate its ability to adapt to unknowns and still determine the correct state of the system. 
3. CHARACTERIZATION OF DIFFERENT CALIBRATION TECHNIQUES 
In addition to calibrating with the FASC and PASC, plans also call for performing Ground Look Calibration (GLC). In that 
case a ground truth team will be located at a prearranged site taking a variety of readings of surface radiance and 
reflectivity and atmospheric conditions while ETM+ images the scene. Calculations will be performed on the ground truth 
data to determine the effective radiance seen by the sensor at the top of the atmosphere. GLC will be nominally 
scheduled once every two to six months after initial on-orbit calibration. 
Based upon estimates from Santa Barbara Research Center (SBRC), the developer of the ETM+ and its solar calibrators, 
the FASC will initially have two error sources which, when combined, will provide a total of 3.2%(10) radiometric error: 
uncertainties in the measured Bidirectional Reflectance Distribution Function (BRDF), and geometric alignment errors. 
Approximately 1.5% (10) radiometric error is due to the randomness in positioning the FASC in the field of view with each 
calibration. Thus it varies with time. The remainder of the total can be considered an initial bias error. As a conservative 
measure, the larger values of 4.4% and 1.7% were chosen to represent the true initial and random errors. 
In addition to the initial bias error and a random component over time, it is also known that the effective reflectivity of 
YB-71 is altered with exposure to UV, atomic oxygen, and contamination. The degree and rate of this change is, 
however, open to debate. Results from the LDEF satellite (Bruegge, 1991), as well as from various laboratories differ in 
magnitude, and generally do not represent the conditions expected for Landsat 7. Therefore, a worst case condition was 
chosen to represent the simulated true band 1 degradation (the most sensitive band) in effective reflectivity of 22% over 5 
years. 
Also based upon SBRC estimates, the PASC was assumed to have a small degradation in its effective throughput 
(transmission) of 5% over 5 years due to the effects of contamination. The random component was assumed to be very 
small, due to a lack of random contributors. However, because of contamination problems encountered with early 
Landsat vehicles with similar devices, to be conservative, a true initial error of 10% was assumed. 
Estimation of the accuracy of exoatmospheric radiometry using ground truth and atmospheric modeling is somewhat 
subjective due to the dependence on the type of modeling, and the type and precision of the ground truth collected. No 
decision has yet been made about the source for such measurements. However, based upon estimates from other 
studies, both in-house and external (Green, 1994 and Hartmann, 1983), a true constant bias error of 5% and a 
time-varying random error of 2.5% (10) with no long term drift was assumed. 
Collections were assumed to take place at the following intervals: 
1. FASC atdays 16, 24, 32, 40, and 48 days after launch and every 45 days thereafter. 
2. PASC every day after launch starting with day 16. 
3. GLC atdays 16, 32, and 48 days after launch and every 90 days thereafter. 
4. TRUTH MODEL 
The truth model was developed based on engineering insight, experience, and analysis of "worst case" conditions. It 
served as the basis for evaluating the potential for achieving the desired absolute radiometric accuracy in the face of 
anticipated uncertainty in the dynamics and measurement models incorporated into the Kalman Filter. The variables 
estimated at each time step, i.e., the state variables, were the reflectivity of the FASC paddle as a function of time, o, and 
the effective throughput of the PASC optics as a function of time, x. The true value of these quantities change dynamically 
and are not known exactly, even at the initial time step. To simulate the true dynamics, however, the following equations 
were used. 
24.154589 
ome) = 7595077005 + 97 + Cruel) | (1) 
IAPRS, Vol. 30, Part SW1, ISPRS Intercommission Workshop "From Pixels to Sequences", Zurich, March 22-24 1995