The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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3D grid points cannot be established without physical model, so 
traditional methods (eg, field survey, map measurement or 
DEM) should be employed for the obtaining of GCP and CkP. 
Under this case, the result depends on the hypsography, number 
and distribution of GCP. It is a popular positioning method 
when the rigorous sensor model is unavailable or the accuracy 
is not demanding. 
4.2 IDKF Method 
Increment is used in this method for the accuracy improvement 
when the 80 parameters and the matrix P (in equation 11) are 
both available. With the new GCP, the RPC accuracy can be 
updated using this method. 
The value of RPC iteration is stable, of which the process and 
expression are as following (Hu and Tao, 2002) 
4. RPC CORRECTION METHOD 
Here the coorection method means to apply different 
mathematical models without changing the RPC model to the 
80 parameters to get the updated RPC parameters. If both the 
GCP calculating the RPC and the auxiliary GCP are available, 
BILSR is applied for a group of new RPC, otherwise if only the 
auxiliary GCP available, IDKF is employed. 
4.1 BILSR Method 
Both the original and new GCP are used in this method in batch 
process for the updated RPC. All the GCP are used in the 
equation 10 with different power for each point. 
time, there will be flexibility for the calculation if a non-zero 
Q k is provided (Hu and Tao,2002). 
The process (equation 13) and linearization (equation 14) are 
realized by adding new GCP using increment based on Kalman 
Filter to improved the initial RPC accuracy. Traditionally, 
Kalman Filter is used for the complicated time problems. 
Kalman Filter is used to space domain is based on its recursion 
character for the new GCP are obtained in sequence. 
1) Calculation of initial value and covariance matrix 
Ci = h + 
(12) 
n=c, 
C — ft k v k~t' k l k +v k ik —1,2 ) (13) 
Where: 
Equation 13 is transformed from equation 7, which denotes the 
linearity relation between the observations and parameters. 
W k is the noise vector, or white noise with known covariance 
matrix Q k ; V k is the measure error of image points, it is 
considered to be white noise with the known covariance matrix 
R k of new GCP. Vector W k and are independent. R k is 
usually based on experiences and tests in calculation. Test 
results show that even though RPC changes very little every 
GCP are divided into several groups, then repeated processes are 
needed. From the above we can see that the initial value of RPC 
covariance is very important for it decides the sensibility of new 
GCP and its covariance. 
5. RPC CORRECTION AND ACCURACY ANALYSIS 
The image is the same as mentioned above. 50 GCP distributed 
evenly were selected from the overall 139 surveyed points to 
calculate the initial RPC, the distribution of which was shown in 
figure 2. 26 points were selected randomly from the rest 
surveyed points as GCP and CkP for accuracy analysis, of which 
the distribution was as figure 4. 
Pk ~ ^K-1 + Qk-1 
(14) 
Where means the value is the previous result of the new one. 
2) Calculation of increment of Kalman Filter 
K t =P t TfT l p-Tj + R i y' 
(15) 
3) Updating I k by adding new GCP 
h ~ h + K k v k’ v k ~ Gk T k I k 
(16) 
4) Calculation of updated I k covariance 
P k =(E-K k T k )P k 
(17) 
There will be only one process from step (2) to (4) for the RPC 
updating if all new GCP are considered to a whole group. If the 
Figure 4 Distribution of 49 Auxiliary GCP