A 
REVIEW OF STRIP AND BLOCK ADJUSTMENT DURING 1964-1967 
2. TREATMENT OF CONTROL POINTS 
Both Brown [11] and Schmid [5] to [7] have 
now introduced the use of a covariance matrix 
for the coordinates of the control points in a 
block of aerial photographs. Unknown coordi 
nates are given a large variance and for the 
sake of simplicity, although unrealistically, 
one assumes that their estimated (observed) 
values are uncorrelated. If a rectangular 
coordinate system is used other than the one 
formed from planimetric coordinates and ter 
rain heights, the proper covariance matrix in 
that system can be easily computed from the 
relation between the two coordinate systems. 
With this procedure, the vector 5 contains 
also the corrections to the coordinates, known 
as well as unknown, of all control points. To 
retain the advantage that only one correction 
to an observation occurs in each condition 
equation, Equation 1 is supplemented with 
the equation 
v a = 0 (3) 
in which v g is the vector of corrections to 
observed coordinates of the control points and 
is the vector of corrections to their esti 
mated or given coordinates. The equation ex 
presses that one identifies the observed values 
with the estimated or given values. 
This procedure increases the size of the 
normal equations. However, it makes their 
formation simpler because now each terrain 
point receives three coordinate corrections, 
independent of whether it is completely 
known, partially known, or unknown. 
3. PARTITIONING OF THE NORMAL EQUATIONS 
The components of v, 5, and k may be par 
titioned into groups. If the condition equa 
tions contain a set of constraint equations in 
which no observations occur, the correspond 
ing ^-components will be equal to zero. In 
addition, the sequence of the groups in the 
normal equations may be rearranged. This 
can lead to a variety of formulas. 
It is customary to partition the vector 5 of 
Equation 2c into a vector 5i of corrections 
for improvement of the camera orientations 
and a vector 5 2 of corrections to approximate 
coordinates of terrain points. The attitude 
corrections included in 5i can be either the 
parameters of a correction matrix or correc 
tions to approximate values of attitude 
parameters. 
The corresponding partitioning of Equation 
2c gives: 
MiSx + Nl2§2 = £i 
Nnhi + N 2i ft2 = £2 
and elimination of d 2 gives 
(Nn — 2V12^2V22 — Wi 2 )5i = £i — Ni 2 t No2~ 1 £2- (2e) 
The components of 5i and of 5 2 can be par 
titioned into groups each of which contains 
only the corrections for one photograph or 
for one terrain point, respectively. The cor 
respondingly partitioned matrices Affi and 
N22 contain non-zero submatrices along their 
main diagonal only, while the submatrix of 
ÌV12 which corresponds to point i and photo 
graph j has non-zero elements only if point i 
has been measured in photograph j. 
Accordingly, the inverse of N2 2 can be 
computed by inverting its submatrices sep 
arately and Equation 2e can be computed 
directly from the Equation 1 by treating all 
the condition equations for one terrain point 
as a group and computing the contribution of 
this group to the normal equations separately. 
In this way, no space need be reserved for the 
matrices N22 and N i2 . If two photographs 
have no measured point in common, the cor 
responding off-diagonal submatrix in Equa 
tion 2e is equal to zero. 
Each of the block adjustment programs 
that have been coded along these lines em 
ploys a housekeeping routine, collapsing al 
gorithm, or indexing technique to avoid com 
puting and storing zero-submatrices and to 
keep track of the locations of the non-zero 
ones. 
4. DIRECT SOLUTION OF THE NORMAL EQUA 
TIONS 
Even for large blocks, the direct solution 
of the normal equations has proved to be 
entirely practical provided that a block- 
elimination procedure is used. This means 
that instead of the matrix elements the above- 
mentioned submatrices of Equations 2d or 2e 
are used as units in the computations. 
Both a Gauss-Cholesky type of elimination 
([91] and [21]) and a Gauss-Jordan type [16] 
are used. If S is an on-diagonal submatrix 
which is to be used as pivot in the elimination, 
the Gauss-Cholesky elimination involves the 
simple computation of an upper triangular 
matrix T such that T l T = S and of its in 
verse. The Gauss-Jordan elimination requires 
the computation of the inverse of S. The two 
elimination procedures perform equally well. 
5. ITERATIVE SOLUTION OF THE NORMAL 
EQUATIONS 
The iterative solution of a system of equa 
tions has the basic disadvantage that it is 
difficult to know when a sufficiently good 
approximation of the exact solution has been