Joz Wu 
  
It is noted that the suitable/stable criteria (9a-9c) are commonly used to select an optimal regression equation 
(Zhong, 1997). The optimization criteria could successfully be applied to the selection of polynomial 
parameters involving the GPS geoid height interpolation. 
After the deletion of a least significant polynomial parameter by means of Eq. (8), the resulting model is 
checked out as to its optimality on the basis of Eq. (9). This process is iterated until no improvements on 
model optimization can be made. | By analogy, an optimal set of model parameters can be determined by using 
some other statistical methods. The discrimination test given by Wang et al. (1998) represents an interesting 
alternative. 
4. EXPERIMENTS 
The C-band HH-polarized 6-look SAR image of Yangmei town and its neighboring area was a result of the 
Canadian CV-580 GlobeSAR campaign in Taiwan. The 7.0-km high aerial flight, cruising at around 240 
knots (120 m/s), was flown on 28 October, 1993. The nominal ground resolution was 4.0 m by4.0m. The 
experimental slant-range SAR image was of 9.0 km along-track by 12.0 km cross-track, and had 35 distributed 
image/ground control points, reflecting the modest terrain height variations from 75.1 m to 210.9 m. 
Both the image-space and the object-space control point coordinates were carefully measured by two 
independent operators, leading to an averaged input dataset needed for any radargrammetric processing. In 
fact, the same set of image/ground coordinate measurements were once used to study the time-dependent 
orientation parameters. The feasibility study by Wu and Lin (2000) was focused on the linear prediction 
parameter-modeling. In the current paper, the existing Fortran-software program YeSir has been edited to 
implement the significance test (8) and the optimization checks (9) on the polynomial model parameters (4). 
4.1 Parameter Estimates 
The fourth-order time polynomials were initialized, creating an unknown 17-paramete x-vector. By utilizing 
a set of 30 image control points, each involving a pair of the line and pixel coordinates ( t ji). there were 60 
independent and identically-distributed measurements. The degree of freedom was 43, well over a generally 
acceptable number of 30. Table 1 summarizes the corresponding stage-by-stage results. 
Table 1 Significant parameter determination with a set of 30 image/ground control points 
  
  
Stage-1 Stage-2 Stage-3 Stage-4 
Parameter set T. M,. T. M,, T, M,, TM p. 
49» "+a, Ag: *$04; dg» ly» dys***,ds3, 
bos ‘Da, 50:54. boo 234. b... 
CQsCi5€25€34€4 Cos» C3» C4 Coss CoC Cx 
Parameter with Cy 64 a, - 
minimum F test 
statistic 
Criteria: 
é2 0.471 0.460 0.454 0.478 
V 121.0 117.7 115.7 121.4 
AIC 665.2 663.0 662.4 671.5 
Optimization No No Yes No 
  
  
350 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part Bl. Amsterdam 2000. 
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