orientation of
>ngth of lines,
of equations
yy used in the
OWS:
(13)
es or in other
ys With errors
‘y to know (or
X ; into
Y
IEORETICAL
"tions, control
| are free from
(21
2)
(23)
(24
Natalia Moskal
additional unknown quantities
U'-U - AU (2.5)
Besides , the measured quantities Y , with the covariant matrix Dr are connected by the equations of corrections
with the vectors Y , U,so that
e, 7-By -SAU-W, (2.6)
The covariant matrix S of vector Y is known.
We consider the errors for Y, and Y 2 to be divided according to the Gauss law, and for y they differ a bit from the
Gauss. The dimensions of all the vectors do not cause the indetermination of the linear equations system, that is the
matrix possess the complete rang. Let us consider as well that the vectors Y. 15 yr are correlated with one
another.
, OF
As far as T'zT FATTO REF CTS Tae, (2.7)
1
Than AT ze, 2.8)
When carrying out the linearization (2.2) we get
dd à D 0d —
5 AT += NY +——AU + D(T’Y 'U')=0,
oT oY’ ol
or AAT + By + CAU +o, =0. (2.9)
Substituting expression (2.8) for AT' taking into account (2.6), we get the initial system if equations
De, +B, +CAU +w, = 0
(2.10)
E, +81} + SAU +0, =0
where D =A0 @11)
Let us make the adjustment for (2.10) under the condition of the minimization of function of losses, with
2 2 2+d
Pp (e,)=8,", P (&,)=e, p (v )=} (2.12)
where d - parameter of unsquareness.
Let us compose the function of Lagaran, for conditional equations (2.10) where we introduce the sum marked with Gauss
zi
symbols instead of'y ’ NS y
2+d
2+d 2+d 2+d
V. - [pv : |= mv, +py; ++p “, (2.13)
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 627