* 10 - 
t 
f=F+n+s (3) 
E fn] = (4) 
E [s] = (5) 
n is called noise or uncorrelated component and s is the signal 
or correlated part or f, Correspondingly, the noise covariance 
matrix Cnn (usually) is a diagonal matrix, whilst the signal 
covariance matrix Css is rather packed. In general, noise and 
signal are not correlated with each other (Che = 0). 
In the present case of self calibrating block adjustment the 
noise represents the purely random errors of the photogrammetric 
data. The signal s however, is interpreted as the effect of the 
additional parameters p on the image or model coordinates: 
s = Bp (6) e e 
The additional parameters p themselves are assumed as random 
variables with the expectation zero. 
E T5910 (7) 
With (7) the signal (6) meets the requirement (5). If the 
covariance matrix of the additional parameters p is denoted by 
Cpp» the signal covariance matrix Css follows from (6) as: 
Css "B Cup BT (8) 
The problem is solved by least squares. For that purpose the 
residual vectors vj, and v5 are attached to n and p. Considering 
(3) and (6) we then obtain: 
Ax - (f + (n+v; ) + B (p+v2)) = 
Ax. Wm Buuirof o0 (9) 
The minimum condition to be satisfied reads: 
T T.-1 Sa 
Vat à + VC ppY2 - min | (10) 
Equation (9) represents a conditioned adjustment with unknown 
parameters, which however, is equivalent to the observation 
equation system (1a), (1b): This can be shown by back substi- 
tution of (1b) into (1a) which directly leads to formula (9), 
For a detailed proof see Schwarz |17|. Because of (4) and (7) 
the obtained results x, vj and v», are unbiased, 
The additional parameters usually are common to many images or 
models occasionally. In this case formulation (1a), (1b) is 
superior to formulation (9), because it leads to normal equa- 
tion matrices of more favourable structure (banded bordered 
system) and of better numerical condition (see |18]).