The normal equation system as shown in (35) is typical in its arrangement for
any photogrammetric triangulation problem. The number of points recorded at
any one station and the number of stations involved in a specific measuring
program will obviously influence the overall size of this matrix system but
will not change its basic character, A study of the corresponding matrix
(see Fig. 4) shows that we have along the diagonal, a sequence of fully
separated symmetrically arranged square submatrices, The fact that the two
types of submatrices which appear vary in size is less significant than the
fact that in each submatrix of the first group, By (AP! AT)" Bx , the
spatial coordinates of only one specific object point (in a general case up. to
3) are present, while in each submatrix of the second group Bl (AP~'AT yl Bo,
only the orientation elements of one specific camera station (in a general case
wp to 9), appear. The By (AP AT)! Bg and the BL (Ap^! AT y^! By
submatrices express the fact that a specific point was photographed from certain
camera stations, |
Viewing our system of normal equations with respect to the method of
partitioning as described in this report with formulas (22) through (50), a
Suitable point for partitioning is obviously that point on the diagonal, which
separates the parameters associated with the model, from the parameters con-
nected with the camera orientations, as indicated by the dotted lines in
formula (35). According to formula (27), we may write:
{85 tae" Y e, - [a5 (rA Y e, [e tne wr e] [estan Y Be] -
(eL ae"! -[BS cae A e [etae Me] [pta nr ])a 0
or, with reference to (32):
r r
à (CoBo); Ao = (695, (37)