AL PY WT 
  
  
  
277 
Rho and Estimated Rho Percent Error for Estimated Rho 
10 
  
  
(b) 
  
  
750 1000 1250 3500 1750 
Estimated 
586 True 
.055 | 
  
.054 | 
  
  
(c) (d) 
Gain and Estimated Gain Percent Error in Estimated Gain 
Estimated 2 
  
  
  
True ; -3 
-4 
(e) (f) 
Figure 1: Kalman Filter Output with GLC bias estimated from data, Random Seed - 29. (a) Rho Estimate 
and Rho True. (b) Percent Error in Rho Estimate. (c) Tau Estimate and Tau True. (d) Percent Error 
in Tau Estimate. (e) Gain and Estimated Gain. (f) Percent Error in Estimated Gain. 
Graph e presents the most important result, the comparison of estimated detector gain and actual detector gain. It is 
clearly evident that, despite initially large errors in the PASC, and errors which rise dramatically in the FASC, the filter has 
managed to closely track (usually within 396), and therefore enable the calibration of the detector. 
Graphs b, d, and f present the percentage differences between the curves in a, c, and e, respectively. 
A series of several hundred simulated Monte Carlo runs (see Table 2.) indicated that the filters are relatively insensitive to 
errors in estimating the magnitude of the noise (measurement and process) statistics. In Table 2., the mean and standard 
deviation over one hundred sample runs of the detector gain error is presented for various combinations of initial FASC 
reflectivity error, exoatmospheric ground look radiance bias and random errors, and assumed FASC and PASC 
degradation modeling characteristics. Where the model is labeled as asymptotic, the characteristic was assumed to have 
degraded inversely with time, as in equation (1), and where it is labeled as exponential, the modeled degradation takes 
the exponential form of equations (15) and (16). In most cases, the residual mean/bias error is well below the 5% goal, 
and in all cases, the random is less than 2.396. Also, although not detailed here, tripling the estimates of the noise caused 
no significant changes in either the settling time or residual error magnitude. The filters were also insensitive to the 
degradation model assumed for the FASC, primarily because of its infrequent measurements. All of the filters stabilized 
quickly. The 5% error limit goal was usually reached within 48 simulated days of launch, with quantitative indications of 
stability occurring within 150 days. 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences", Zurich, March 22-24 1995