187 
i = (X|,Y |t Zi) T (3) 
. or in the case of a GPS vectors between a 
known (I.G.S./A.S.I. or local) station and a un 
known point; then the (3,1) observation sub 
vector is 
Ijk = (^Xjk + Xj , AYj k + Yj , AZj k + Zj) (4) 
The A block row and the (3,1) observation sub 
vector are respectively: 
a, = [0 ... -I ... I ... 0] (5) 
lj k ~ (AXj k * AYj k ' AZj k ) (®) 
if the GPS vector is between two unknown points. 
The A block row and the (3,1) observation sub 
vector are respectively: 
a, = [0 ... -I ... 0 ... 0] (7) 
lj k = (AXj ~ Xk , AYj k — Yk , AZj k - Zk j (8) 
when the GPS vector is between a unknown point 
and a known (I.G.S./A.S.I. or local) station. 
the (3,3) variance-covariance matrix of the GPS 
baseline vector between the j-th and k-th points, 
where the coordinates of the j-th point are known 
and not assumed as observables. 
Thus the variance-covariance (n , n) matrix of the 
observation is the block diagonal matrix is : 
El = diag 
(12) 
Denoting with 
ct = (g?! Gq2) T = (g-i a 2 ) T (13) 
the unknown vector (2,1) of the variance factors of 
the measured GPS baseline vectors, the stocha 
stic model can be put in the following form : 
E| = o-| Q-i + a 2 Q2 Q3 
(14) 
where the known block diagonal cofactor (semi- 
definite positive) (n , n) matrices Qj are respecti 
vely : 
Q 1 formed by the known (3,3) block cofactor 
Qjk < 
Q 2 by the known (3,3) block cofactor bj k Qj k , 
Q 3 by the known (3,3) block variance Q M . 
3.2 Stochastic model 
4. BLUNDERS DETECTION 
If the Cartesian coordinates of the i-th point are 
assumed as observables, then we put: The a P° s f er i° r global variance factor 
Qü = Qii 
(9) 
Sq =(v T Pv)/(n-u) 
(15) 
where Qj j is the (3,3) known variance matrix of 
the coordinates of the i-th point. 
Let 
Qjk =(<*01 +Go 2 bf k )Qjk 
(10) 
is computed in order to verify the absence of gross 
errors in the observations by the Fisher Global Test. 
Since the observations are correlated, in order to 
localise one blunder in the set of observations by 
the Baarda’s Test, the program performs the com 
putation of the normalised weighted LS residuals 
the (3,3) variance-covariance matrix of the GPS 
baseline vector, whose length is bj k, between the 
j-th and k-th points, where the coordinates of the 
both points are unknown and none of them is assu 
med as observable. 
Let 
Qjk - 
(G§i+G§ 2 bf k )Qjk 
+ Qi 
(11) 
Wj/a Wj = (ej T w)/(ej T S w ej ) (16) 
where : 
ei is the (n , 1) vector whose i-th com 
ponent is 1 and zero everywhere, 
w = Pv is the weighted LS residual (n,1) 
vector, 
E w = P Zy P is the variance-covariance (n , n) 
matrix of w.