Mulawa - 6
It is interesting to note, if the above equation is included in a least squares estimation
The fixed point C could have a large covariance matrix Z cc . This can be caused by a
the line 1L which is closest to the origin 0 as determined by the equation C • (5 = 0. A
fixed point C determined by the equation C • p = 0 may fall well outside the observed
segment of the line IL. This forces the estimation of the fixed point C position to be a
large extrapolation from the measured portion of the line IL. An example of this offset
can be shown when the coordinate system is based on a map projection and the origin 0
is hundreds of kilometers from the measurement area. The effect of extrapolation on the
covariance matrix 2 PP of a point P can be seen in equation (7). In particular, the
covariance Z PP increases as a quadratic function in the arc length s as the point P moves
away from the best fixed point C®. This quadratic growth also effects the covariance
matrix 2 CC of the fixed point C. A large covariance matrix Z cc will have large
eigenvalues and can make the least squares normal equations NA = t somewhat difficult
to invert. The solution to this possible instability is to replace the equation C • p = 0 with
one that determines a fixed point C that is much closer to the best fixed point C®. This
can be done by using a local reference origin C° and the equation:
or by some a priori knowledge about the measurement area. In general, some reasonable
approximation of the location of a local fixed point C° can be made. In a project that
forali the lines { IL, }.
Calculation of a Set of Initial Approximations for EL:
process, then as 5® -*■ 0 it follows that t^Zcp)-* 0. It is in this sense that the best
fixed point C® has a reduced correlation with p.
process, then as 5®
r: r-«© „
Use of a Local Reference Origin C°
large separation between the best fixed point C® and the fixed point C that is the point on
A local reference origin C° could be determined by measurement of a nearby point feature
measures many lines j IL, ]■, it may be possible to use a single local reference origin C°
Given two photographs each with two photogrammetric rays: {Lj, pj i,pi 2 } and
