first example. The second example gives worse 
results, since there are less points and the 
turbolence is higher. 
Table 4.1- Spatial analysis of turbolent flow fields (unit: mm) 
1st example (n - 811) 2nd example (n = 452) 
X y zZ X y z 
- a priori standard deviation: 2315 . 206 .286 «248 . 348 .348 
- 2nd order polynomial interpolation: 
a posteriori sigma naught .205 . 145 4259 -205 .208 . 344 
- covariance functions: (NS) (ES) (ES) (NS) (NS) (ES) 
(insignificant crosscovariances) 
a priori variance of the signal .144 .106 „142 4156 .148 . 149 
a priori variance of the noise „120 . 084 „174 . 104 „120 . 246 
best correlation coefficient 58% 54% 28% 68% 58% 24% 
optimal radius 10 10 10 5 5 5 
correlation length 30 20 10 20 15 10 
"Zero point" 100 100 100 50 50 50 
number of blunders (« = 1%) 26 26 20 12 15 15 
- collocation filtering: 
a posteriori variance of the signal . 145 :091 . 087 . 164 . 154 . 124 
a posteriori variance of the noise „114 .076 . 183 .094 115 . 266 
estimation error . 066 . 060 „112 :079 . 086 - 125 
number of outliers (œ = 5%) 38 36 33 25 34 41 
trimmed variance of the noise . 094 . 064 „148 . 073 . 092 . 185 
- finite element method by using tricubic splines: 
interpolation step 50 25 50 25 15 
number of knots 44 192 24 60 132 
a posteriori sigma naught x „152 . 123 «177 „153 . 128 
y 2193 „109 -189 .160 „133 
„253 . 224 „336 . 326 „316 
APPENDIX Note that it is necessary to perform preceding 
separate adjustments.Indeed the covariance matrix 
Least squares collocation with stochastic - and of the signal Cats obtained from estimates for 
non-stochastic parameters the unknown parameters or residuals; moreover the 
variance of the noise o is assumed equal to the 
(This appendix presents a development of basic sigma naught square obtained in the last preceding 
ideas of Barzaghi et al., 1988; and is quoted with separate adjustment. 
minor changes from Crippa/de Haan/Mussio, 1989). The use of both stochastic and non-stochastic 
parameters causes the need to introduce a hybrid 
In the above mentioned procedure different systems norm: 
are solved successively. In the integrated geodesy 
approach all systems are solved simultaneously. 
Thus after the linearization of the observation c 0 S 
and pseudo-observation equations, the observables 1176 7t ss t AS a A o 3 
> - n + A (Ax t Bs — - = 
and the other data « are collected in a unique zs (Ax S n g min 
m 
system containing uncorrelated unknowns x as well 0  P/o? 
as correlated unknowns that can be interpreted as n 
stochastic signal s to filter from the random 
noise n: o = A 
where « indicates the observations, x, s and n the 
estimated values of x, s and n respectively, P the 
œ = Ax * Bs weight matrix of the observations and A a vector 
of Lagrange multipliers. 
386