inverse, several times, the following is a simple mathematical technique
that allows the modification of the matrix inverse of the normal equations
due to deleting some of the observation equations.
4.2 Modified Inverse of the Coefficient Matrix of Normal Equations After
deleting Some of the Original Observation Equations
Equation 4.08 can be rewritten as:
4.13
N D
-P
• • • •
where
4.14
N
B* U F
4.15
P
• • • •
The solution of equation 4.13 is:
4.16
D
• • • •
in which N -1 is assumed to have been previously evaluated and on the
basis of a total of n object points. We now divide n into two sets:
q points which are to be deleted and p points which are retained. (Note
that p must yield a number of equations that are equal to or more than
the number of unknowns.) The corresponding sets of observation equations
are:
for q points V+BC-CD = -F
4.17
• • • •
for p points V+BD-CÏÏ = -F
4.18
In view of the summation scheme given in the previous section and
expressed by equations 4.12 and 4.10, the system of normal equations
corresponding to 4.17 and 4.18 may be written as: