Joz Wu 
  
2.1 Radargrammetric Equations 
The following range and Doppler expressions are frequently utilized for radargrammetric image processing 
(Curlander et al., 1987; Dowman, 1992; Leberl, 1979): 
1 
R jz[(X; -X)^ * (Y; -Y4)? *(Zi -Z4)1? (1) 
Rj 2 My,r(t;) t R, (3) 
where RA; (m) is the measured one-way slant range from radar path/station ( X a> Loi <a; } to point target 
( X;, Y;,Z; ); for the same point i, there may be multiple flight paths j over i; 7 (deg) stands for the squint 
angle/parameter; ( 4,,u,,u. ) in m/s units is the instantaneous unit radar velocity; M, (m/pixel) represents the 
pixel spacing; A, (m) is the constant slant-range delay 7r; (pixels) is the cross-track image coordinate 
measurement, with the along-track image coordinate f j» acting as an argument, in pixels (or in seconds). 
The time polynomial expansions are used to model the exterior orientation parameters, as follows: 
X — dg tat +a,t; +astj 
2 3 
Zo Beat Olio rest] 
The higher-order coefficients ( a, ,b,,c, ,***) are to be statistically tested for their parametric significance, on a 
one-by-one basis. 
2.2 Parameter Estimation 
By reviewing Eqs. (1-4), the line and pixel coordinate measurements ( ---1 js ^7), and the unknown 
parameters (T,M,,ap,**,bp ,***, Co, **) are readily identified. In general, initial approximations for the 
parameters can be made available. An iterative least-squares adjustment algorithm provides us with both the 
measurement and the parameter solutions (Koch, 1999; Leick, 1995). The relevant formulae are listed here: 
Bv+Ax=l; 0Q (5a) 
Q, =BQB’ (5b) 
x=Q,A"Q;" (6a) 
v-Q,B/Q;!/ (6b) 
62 x v'Q vio -u) (7) 
where the n-vector v contains the image control point measurement residuals; the nxn matrix B consists of the 
corresponding partial derivatives; the u-vector x represents the parameter corrections; the nxu design matrix A 
holds the corresponding partial derivatives (gradients); the n-vector I is a reduced observation vector: Ga 
represents the unit-weight reference variance, serving as a scaling factor. 
  
348 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000. 
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