278
Subsequent analyses indicated that most of the residual error was in the form of a bias error resulting from the small
number of sample points (3) used to initially remove the bias between the GLC and the FASC. Statistical evaluations
have shown that increasing the number of sample points to as little as five would effectively eliminate the bulk of this
residual.
One final analysis performed was the non-linear least squares curve fit of the state vector estimates of the Kalman Filter
to the internal models of behavior after a simulated 2.5 years and 5 years on-orbit. Both sets of results indicate that RMS
errors were reduced to less than 196. Therefore, while not providing "real time" improvements, a posteriori back filtering
seems to have the potential to further improve radiometric estimates of historical data.
7. CONCLUSIONS
Although additional Monte Carlo computer runs could be made in order to provide a more statistically significant sample
set, these initial runs do provide evidence that a relatively simple Kalman Filter can synergistically combine information
from different types of radiometric calibrators both to track and compensate for variations in the sensor and calibrators,
and minimize residual errors. The key to success is a combination of sources with complementary strengths (initial
accuracy for the FASC, frequent updates and low randomness for the PASC, no drift in the GLC) which can be correlated
through the Kalman Filter. In this case, the FASC and PASC were correlated through the detector gain determined from
the GLC. The results are, of course, highly dependent upon the assumptions made in the study. The strongest sensitivity
seems to be to the random error in the estimated exoatmospheric GLC radiance and the degree to which it will hamper
determination of the bias error. (Note: Randomness in the exoatmospheric GLC radiance is not the variability in the
radiance, which is constantly changing, but in the error about the true value.) It is believed that such randomness can be
minimized through the judicious selection of a high, dry, ground calibration target.
Additionally, such a technique may be applicable to other radiometric remote sensing platforms with multiple calibration
sources. Several multispectral remote sensing platforms are planned for the next decade, and most of them will employ
several radiometric calibrators. In many cases, a technique for combining the different calibration results has not yet been
determined. This approach may provide one possible method for their combination.
8. ACKNOWLEDGEMENTS
This work was performed in support of NASA contract NAS532633.
The authors also wish to gratefully acknowledge the support of the engineers and scientists at Santa Barbara Research
Center, the Landsat Program Office at Goddard Space Flight Center, and the EROS Data Center, without whose help this
work would not have been possible.
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IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences", Zurich, March 22-24 1995
