1444 
A fundamental figure of merit for the estimates of the parameters can 
then be the determinant of the inverted normal equation matrix. Any 
measurement added to the solution will reduce the determinant of the 
inverted normal equation matrix and hence the volume of the hyper- 
ellipsoid. The measurement which should be added is the one which 
makes the volume as small as possible. Conversely, the candidate 
measurement which maximizes the determinant of the normal equation 
matrix will also give the hyperellipsoid with the smallest volume (2). 
A measure of efficiency will be defined as: 
= det (N^ 
V | v2] 3 
where, 
N. is the normal equation matrix after an additional observation 
is selected and added to the solution. 
N. is the normal equation matrix before the additional observation 
is included. 
If this ratio is computed for all the candidate measurements, the one 
which gives the largest value of v should be added to the solution since 
it will produce the hyperellipsoid with the smallest volume. 
Let us consider the currently available on-line system which 
utilizes a three-stage comparator. Equation 4 shows the structure of 
the normal equation matrix for an anaytical triangulation solution of