Ian Dowman 
  
  
  
  
  
  
  
  
  
Error parameter Sigma Time Const 
Along track 4 m 2000 s 
Cross track 8 m 3000 s 
Radial 2m 1000 s 
Rotation a .00001 rad 200 s 
Rotation b .00001 rad 100 s 
Rotation c .0002 rad 300 s 
Focal .001 m 5000 s 
  
  
  
  
  
Table 2. Sensor Support Data Error Characteristics 
A simultaneous, six image solution for the two arbitrarily located ground points was performed 100 times, with a 
different set of random numbers utilized each time consistent with all error sources, their standard deviations, and their 
correlations. (All error sources were assumed unbiased.) Besides sensor support data errors, mensuration errors (0.5 
pixel one-sigma) and errors in the a priori estimates of the two ground points (1000 m one-sigma) were also included. 
Each solution was actually performed using equation (4) two separate times: (1) the "original solution", using the 
original rigorous sensor model and its error covariance, and (2) the "replacement solution", using the replacement 
sensor model and its error covariance. 
Polynomial fitting error associated with the replacement sensor model were assumed zero — a reasonable 
approximation when using USM that also assures identical random errors affecting both solution techniques. In 
addition, prior to each of the 100 cases, the replacement sensor model's C, was generated consistent with equation 
[7] for use by the replacement solution. 
Table 3 presents the simulation results. The solutions' absolute and relative errors are presented as well as their 
corresponding accuracy estimates (standard deviations, or "sigmas"). (Absolute statistics refer to ground point 1, 
relative statistics to the ground point 1-ground point 2 pair; units are meters.) The errors were calculated as the root- 
mean-square (rms) error over the 100 cases. The sigmas were computed from the solutions' a posteriori error 
covariances and were virtually invariant over the 100 cases. The solution in the first row corresponds to the original 
solution. Note that the actual errors approach their corresponding sigma's, indicative of a well modeled solution. The 
solution in the second row corresponds to the replacements solution with a C, corresponding to a 6 term image space 
adjustment vector A. The replacement solution is virtually identical to the original solution, both in terms of the actual 
solution and its error propagation. 
  
  
  
  
  
  
Solution abs rms abs sigma rel rms rel sigma 
X-y-Z (m) X-y-Z (m) X-y-z (m) X-y-z (m) 
original 29 24 26 30 27 28 19 18 17 18 16 16 
replacement 29 24 26 30 27 28 19 18 17 18 16 16 
original S8 58 53 n/a 29 27 29 n/a 
eq wt 
replacement | 161 102 133 | 25 23 24 30 30 24 2 2,2 
2 adj par 
  
  
  
  
  
  
Table 3. Solution Performance 
Two other solutions are also presented in rows 3 and 4 of the table. Row 3 corresponds to the original solution 
artificially using equal weights for all image measurements, i.e., Cs is the identity matrix. Note the degradation in 
solution accuracy, and of course, the error propagation is not applicable. This solution illustrates the importance of 
proper weighting of the various image measurements using the correct error covariance matrix. Row 4 corresponds 
to the replacement solution using a C A corresponding to only a 2 term image space adjustment vector A. (The two 
  
264 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.