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2) Crown Method 
The working unit is also the individual photo. We still 
take the photo as show in fig.1 to explain the method. 
Select two points from m points in the photo as base 
points, let other m-2 points relate to the base pointswe 
obtain 2m-4 co-angularity conditions, and let base points 
relate each other to get the (2m-3)th condition. By this 
means to form co-angularity conditions results the relations 
between the points as shown in fig.5. The shape of fig.5 
is like a crown of king, so we call our method as Crown 
Method. 
4 
     
3 5 
6 123456789 
2 [o] ij 
7 5 | 
E 
9 
11 
13 
15 | 
9 8 
Fig.5 Fig.6 
In fig.6, the column number presents the condition 
number, the line number stands for image point number. 
From fig.6 we know that the first (2m-3) X (2m-3) 
submatrix of matrix À is also a quasi-triangular matrix, 
according to the describtion of sector method, rank(A)=2m 
-3, so the conditions obtained from the Crown Method is 
also independent. 
The base of the crown consists of the selected points and 
their relation, so the selected image points are called as 
base image points, the corresponding ground points as 
base ground points, or all called as base points for short, 
the relation is called base condition. The vertexes of the 
crown consists of the other points, so they are called the 
vertexes. 
obviously, by the above two methods, the conditions are 
just formed one by one, needed no finding work, so the 
methods are simplest, safeest and easiest ones. 
3. GAUSS-MARKOFF MODELLING 
Refering back to section 1, we will find that eq. (39) is 
the same form as eq. (4), a general form of condition 
equations. If we directly use it to do adjustment, the 
computation work load will be very large, this is because 
the normal eguation matrix is very big. We must study 
further to get an available model. 
3.1 Principle 
To construct an available model, following three problems 
have to be solved, 
3.1.1 Equation Form 
The first problem is what equation form will be selected as 
our model. Both observation and condition equations are 
available to our model, though due to the following 
reasons, we will sellect observation one: 
1) Parameter vector can be direclly estimated. 
2) It is convenient to compensate syetematic errors, 
detect Blunders , estimate variance, include non-photo- 
grammetric data and evaluate the quality of the result. 
3) It is easy to construct and solve normal equation. 
4) almost all existing adjustment software are based on 
parameter adjustment. 
   
3.1.2 Finding 
The second problem is what method for finding conditions 
we will select to construct our available model. In 
preceding section, we recomended two method, which one 
is appropriate? Let's comparing fig.4 with fig.6. In fig.4, 
the matrix A; is a 14X14 matrix, its structure is banded. 
In fig.6, the matix A, is a 14X14 quasi-diagonal matrix. 
Of course, to inverse a quasi-diagonal matrix is much 
easier than a banded one. Therefore we select crown 
method to construct our model. 
3.1.3 Transformation 
The last problem is how to transform the condition 
equations with parameters into observation equations. 
consulting into section 1 and fig.6, we know that if we 
directly using eqs. (18) — (24) to transform, sub-matrix A; 
in eq. (18) of our case in fig.2 will be a 15X15 margined 
quasi-diagonal matrix, its inverse will be full-occupied. 
This will make the transformation difficult. Therefore we 
use a transformation with elimination technique to 
transform general form to observation form instead of a 
direct transformation in section 1. 
Above all. the principle of our modelling is that applying 
crown method to find conditions, using transformation 
with elimination technique transforms the general form into 
observation form. 
3.2 Modelling 
Acording to the above principle, we deal now with the 
observation modelling based on co-angularity condition. 
Because the observations related to each other by co- 
angularity condition are in the same photograph, we can 
take individual photograph as working unit. Furthermore, 
supposing that eq. (39) is for a photo with n image 
points, due to the crown finding method, from fig.6 we 
can see that the first 2(n-2) X2(n-2) sub-matrix A4 of 
matrix A in eq. (39) is a quasi-diagonal matrix, we can 
transform the first 2(n-2) equations of eq. (33) into 
corresponding observation equations with one by one vertex 
scheme. Now, we take the ith vertex together with the 
base of the crown to inquire into the transformation of 
general equation to observation equation. Here, eq. (39) 
can be written as 
  
  
  
  
  
AT, AB As Vi Wi 
| RS: | -0 (40) 
Fs Fc Vc Ws 
where 
Alim 32i a3im aml 0 
Anz AB; = Ac; = 
alin 32inl' asin |’ 0 as3in@4in 
  
  
  
  
  
  
FB =aimn ; FC = (a2 mn a3m na4mn) ; 
Buc biim D2in::** beim brim bsim boim 0 0 0 | 
biis bein *** bein O 0 O brin bein bein 1 * (4D) 
BB =(bimn bzma bama 0 0 0 b4ma b5mn *»* boma ) 
Vi =(vx, Vy, ); Vs ZVxm ; VE s (vy, Vx, Vy.) , 
WF = (Wim Win }, WB =Wm n ; i-1,2,--., (n-2) ; m=n-l, 
U"=(Xo Yo Zo Xi Yi Zi Xu Yn Zn Xa Ya Za). 
About the subs of askı,bs«xa and Wiz , j stands for the 
jth element ofthe matrix A and B in eq. (36), k meanses 
the hth point point in the plaoto,and 1 meanses that the 
the kth point in the photo, and 1 meanses that the kth 
point is related to the Ith point with co-angularity 
consdition in the photo. 
,