188 
In order to estimate the magnitude of the one gross 
error which have been localised in the i-th obser 
vation, the program adopts both the following for 
mulas : 
117- 
<>* 
ill 
(17) 
(18) 
where : 
v¡ is the i-th LS residual; 
q is the i-th local redundancy which is the i-th 
diagonal element of the Redundancy Matrix 
R = P . 
where a[ o) * 0 , the cofactor matrices are up 
dated 
Q<°» = ¿< 0) Q, Q?> = Q 2 
II) For v = 0 , 1 , 2 we compute sequentially 
zi v) = Qi v, +Qi> v) +Q3 
N (v) =A T (z[ v) )~ 1 A 
M (v) =(zj v) ) 1 [z, (v) -A(N <v) r 1 A T ](z, (v, )~ 1 
5. VARIANCE FACTORS BIQUE 
5.1 Rigorous method 
In order to perform the BIQUE estimate of the 
variance factors of the stochastic model (14), the 
rigorous method (Crocetto et al., 1998a) consists 
in solving, iteratively, the following system : 
HM = {h! 1 v| Mr(M< v >Q! v| M< v >Q{ v| )} 
f M = = I t M m q! v) M m I } (i, j = 1 ,2) 
¿(v+l) = [¿< v +i) a^ v+1| ] T = (H< v »r , f< v > 
Ha = f 
with 
H = {h,, = tr(MQ i MQ J )} 
(19) III) If aj v+1) * 1 then we update the cofactor ma 
trix 
(20) 
Q< v+1 > = a| v+1) Q< v > Q< v+1) = a ( 2 v+1) Q ( 2 v) 
fj = l T M Q¡ M I = 
= v T M Q, M v = ► 
= v T P Q, P v 
(i, j = 1,2) 
(21) 
and return to step II), else the final BIQUE of 
the variance components are computed 
v+l 
= n(éi) (a) 
a=o 
v+l 
<J 2 = n(a 2 ) <e0 
a=o 
where 
M = PS i P 
(22) 
P = (2ir‘ 
(23) 
v is the (n , 1) vector of least-squares residuals; 
£v the var-covariance (n, n) matrix of v. 
The iterative algorithm consists in the following 
steps: 
I) Starting with an initial vector of the variance 
factors 
¿<°>=(£f> ¿< 2 0) ) T 
6. EXAMPLE 
We present an application of our program to a GPS 
network in Po river Delta (Crocetto el al., 1998b), in 
which the coordinates of the main point "farogoro" 
are computed by the connection of this unknown 
local point with the I.G.S./A.S.I permanent GPS sta 
tions (Figure 2). 
We call the network by the name "goro". 
The tridimensional Cartesian geocentric coordinates 
of the I.G.S./A.S.I permanent GPS stations (in the 
ITRF94 at epoch 1997.6) are assumed as ob 
servable. 
The file "misgoro.dat" uses the Trimble output data 
format. 
In this example we consider only three I.G.S./A.S.I. 
stations : CAGLIARI, GRAZ and MATERA.