Jen-Jer Jaw
Yet from the prediction point of view, the closer the unknown object point is to the registered surface point, the more
reliable the constraint information would become . The error-propagated uncertainty assessment of the surface constraint
based on the aforementioned model does not find itself the same conclusion. Therefore a modification of the stochastic
model compromising the likely conflict due to the imperfect analytical model is needed [Jaw, 1999]. The modification
performs in a way such that the X,,, as shown below, reflects the deviation of the plane formation by three surface
points from the fitting plane by all the neighboring surface points. We therefore come to the modified model as follows,
? -1
weBemAxtE, — e Y.-BnH 4X9 Bp 05s, 7B.) (5)
where
P. :the weight matrix of the added uncertainty;
oo
P, stands for the weight matrix of surface constraint after the modification;
Due to the restricted space in this paper, the author encourages the interested readers refer [Jaw, 1999] for more detailed
explanation of the model modification.
3 CONTROL SURFACE IN AERIAL TRIANGULATION
3.1 Aerial Triangulation System Formulation
With the formulation of surface constraint model, the photogrammetric measurements can be joined into the system
performing the aerial triangulation task. The combined model is expressed as below,
Yı A, A, [Hern e 6
Dum 7 = + > > 0,X , e
Y x +m) x1 b | lo i 3C nx) fo fo | ( )
-1
>
2 12k2k) =8 of A 0 o xm)
2. (2k-+m)x(2k +m) = -
(mx2k ) Y oo (mxm) =s 00 Poo
where
y, : increments of the photo observations, namely the difference between the original observations
and the derived observation via the approximations;
k : number of the photo point measurements;
p : number of the photos ; n : number of the object points to be determined;
A, : the coefficient matrix derived from taking partial derivatives with
respect to the exterior orientation parameters;
A, : the coefficient matrix derived from taking partial derivatives with respect to the object point
coordinates ;
x, =[AX, AY, , AZ, , Aw,
01
Aj, » BK, ys BX
orientation. A indicates the increment of the parameters; x, =[AX ,, AY,, AZ,, AX, , AY, AZ,.... AX, , AY, AZ 1":
unknowns of object points;
e, : the random errors of the photo point measurements;
op AY, ‚AZ, ‚Aw, Aj, Ak, ]' : unknowns of exterior
; 2
1
s :the variance component of the photo point measurements;
01
P, :the weight matrix of the photo point measurements; w : the discrepancy of the surface constraint;
A,, is A in equation (4) plus 0 for those object points unable to find registered surface
mx3(n-m)
planes;
m : number of the surface constraints ; e, : the random errors of the registered surface points;
S, :the variance component of registered surface points;
P,, :the weight matrix of the modified surface constraints;
0
446 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
