obtained, we can solve the elements of interior 
orientation x,,y,,f in Eqs. (1). However, in the case 
of vertical photography, the solution of the normal 
equations may be faced with singularities because 
X,,yo,f and X,,Y,,Z, offset each other. To overcome 
this weakness, the height differences between the 
ground control points in the test field need to be 
sufficiently large (Wang Zhizhuo, 1990). Generally 
speaking, it is very difficult to meet this condition in 
practice. Therefore, the conventional 
aerotriangulation solves only the elements of 
exterior orientation p,œ,x, Xs,Ys,Zs of photograph, 
whereas the elements of interior orientation X,,Y.,f of 
aerial camera are always determined in the 
laboratory. As the laboratory methods can not take 
into full account the actual conditions in 
aerophotography, large deviations often occur. 
Since GPS was applied to determine 3D coordinates 
(Xa, Ya Zy) of the camera station during a photo flight 
mission, revolutionary changes have taken place in 
the conventional aerotriangulation which had lasted 
60 years and more. The new investigations have 
shown that the accuracy of positioning with 
differential GPS carrier phase measurements is in 
the order of a few cm (Ackermann,F., 1991, 
Friess,P., 1991). If the GPS camera station 
coordinates are introduced to the adjustment of 
aerotriangulation, the strong correlation between 
Xo.Yo.f and Xs,Ys,Zs can be greatly weakened and the 
solution of normal equations is then unique. The 
elements of interior orientation and those of exterior 
orientation can be solved together in adjustment. 
The dynamic determination method for the elements 
of interior orientation can be performed in test field. 
2. THE BASIC IDEAS OF GPS-SUPPORTED 
DETERMINATION OF INTERIOR 
ORIENTATION ELEMENTS 
It is known from the principle of GPS kinematic 
carrier phase measurements that the real position 
determined by GPS is the center of the GPS 
antenna phase. The mathematical relationship 
between the coordinates (X,,Y,,Z,) and the 
coordinates (Xs,Ys,Zs) is written as (Li Deren, 1991): 
X, | u 
Y, |=| Y, |+R-|v (2) 
2, |Z, w 
214 
à, a, a; 
where, R zb, b, b,| is orthogonal transformation 
C, C C; 
matrix. u,v,w are the coordinates of GPS antenna 
phase center in image space coordinate system. 
In Eqs. (1) and Eqs. Q), x, y, X, Y, 4, are 
observables and x,, Yo, f, o, c, K, Xs, Ys, Zs, X, Y, Z, 
u, V, W are the parameters to be determined. After 
the substitution of the approximate values of these 
unknowns, the above equations can be linearized, 
after which, we can have the error equations which 
can be written in matrix form respectively as below: 
Number 
Weight ofEqs. 
V, =At+Bx+li -L 1.2 (@) 
Veran Ex 4 ren (3) 
Vi = EJ ysomkpiteuR isSrion de) 
V, = At HAE A 73 (d) 
where, 
t=[Ap Aœ AK AXs AYs AZs]" is the correction 
vector of exterior orientation elements. 
x-[AX AY AZ]' is the correction vector of object 
coordinates. 
i =[ 4x, dy, 4f]" is the correction vector of interior 
orientation elements. 
r =[Au Av Aw] is the correction vector of the 
coordinates of u,v,w. 
X - (X 
Li «56, (9, (y) are the computed values of x,y 
when the approximate values of the unknowns have 
been substituted into equations (1). 
X, "(X 
L; z|Y, -(QY) |, (XJ),(YJ).(Z) are the computed 
Z, -(2,) 
values of X,, Y,,Z, in Eqs (2). 
The meaning of coefficient matrices A and B refers 
to the reference [6]. 
E,, E, are unit matrix. 
According to Eqs.(1), we can obtain 
i 0 e] 
0 1 Q -yo)/f 
U u 
Letting | V |=R:|v |, we can derive from Eqs.(2) 
W W 
(Yuan Xiuxiao, 1994) 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B1. Vienna 1996 
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