276 
(17) 
  
(18) 
In equation (18), DFk ODFkODPk, OpPKODFKk, and O?pPk are functions of the ground truth measurements, the state 
variables at the previous time step, and random variables with zero means and standard deviations of £G models £SF model: 
ESP model» EFG ‚model EPG,model, ANd NG,model (See Table 1). 
One last item of extreme importance was the initial procedure for "removing" bias errors in the estimated GLC radiance. 
During the first 48 days following (simulated) launch, it was assumed that the modeled radiance from the FASC was 
effectively correct (i.e. that the FASC had not yet begun to decay). The average difference between the first three GLC 
radiances and the corresponding FASC radiances was removed as a bias term in all of the GLC radiance estimates, thus 
providing an initial anchor, albeit an errored one, to a better estimate of the true radiance. 
Table 1 contains the parameters used for simulations discussed in this paper. Simulations were also conducted for a 
wide variety of other "truth" conditions, as part of a sensitivity analysis. Again, since the actual state dynamics process 
will not be characterized, the underlying Kalman Filter must be robust enough to provide satisfactory results with limited 
knowledge of the true system dynamics. 
The following section discusses the results obtained using the basic Kalman Filter under the conditions represented in 
Table 1. 
6. SIMULATION RESULTS 
Figure 1 presents six graphs of the results of one simulated run which used one random seed out of the twenty 
attempted. All of the graphs show results over time in units of days since launch. Graphs a, c, and e compare the true 
variation versus the variation estimated by the model for the FASC effective reflectivity (o), the PASC effective throughput 
(x), and the gain of a detector, respectively. In the case of o and Otrue, the curves overlap so that they are 
indistinguishable, although the random variability might appear to be greater than expected. Yet, at least superficially, the 
filter appears to be tracking the variation in the reflectivity. 
In the case of throughput, since the random component is smaller, it is easier to see the fidelity with which the filter tracks 
the actual variations. Here it is quite obvious that the filter is closely tracking reality. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
—596 error in oo -5% error in po —596 error in oo -5% error in oo 596 error in oo 596 error in og 596 error in oo 596 error in oo 
-596 GL bias -5% GL bias 5% GL bias 5% GL bias -5% GL bias -5% GL bias 5% GL bias 5% GL bias 
2.5% GL random 596 GL random 2.596 GL random 596 GL random 2.5% GL random 5% GL random 2.5% GL random 5% GL random 
u ag u g u ag u g u ag u o u o u ag 
A —1.84 1.69 | —2.03 2.23 2.73 1.39 1.02 1.9 -33 1.65 | —1.86 207 |} -132 1.49 0.65 1.92 
B —3.06 1.66 | -326 222 | -0.53 1.45 1.02 1.9 —0.98 1.47 | -5.84 227 | -552 1.67 | —5.84 227 
C -1.92 17 37 2.0 —0.55 1.5 0.75 1.96 —3.4 1.72 ] -2.01 2.16 —1.34 1.53 0.44 1.97 
D -321 1.71 3.7 1.9 —0.55 1.5 0.74 1.96 —3.4 173 | -5.99 238 ] -555 1.71 -1.55 2.08 
Model Descriptions 
A: Q asymptotic C: Q asymptotic 
t exponential T asymptotic 
B: 0 exponential D: p exponential 
t exponential t asymptotic 
Table 2. Results of Monte Carlo Analysis 
IAPRS, Vol. 30, Part SW1, ISPRS Intercommission Workshop "From Pixels to Sequences”, Zurich, March 22-24 1995