to the output of any sensor producing observations serving ultimately to Ü
interrelate coordinates of photographed points. Parameters for self- F
calibration of external sensors of likely practical interest can be
assigned to the border of the normal equations in just the same way as
parameters for the self-calibration of the camera itself. As a result
of the practical success reported by Ackermann (1974b) with the incorpo-
ration of observations made by a statoscope into the PAT-M-43 program for
adjustment of independent models, it is logical that the statoscope be
considered a prime candidate for similar incorporation into programs for
bundle adjustment. A possibly worthwhile refinement of Ackermann's develop-
ment might be the treatment of successive errors in statoscopic heights as
being subject to a significant degree of serial correlation (as, indeed,
they seem to be). If the serial correlation along each strip is considered
to be governed by an autoregressive process, the rigorous adjustment of
such errors in the bundle adjustment can be effected without disturbing the
bandwidth of the normal equations. This is so even though the covariance
matrix of the errors in statoscopic heights along each strip would be com-
pletely filled with nonzeroes, for, as pointed out in Brown and Trotter
(1969), the inverse of such a covariance matrix is a banded matrix, the
bandwidth being equal to £+1 where £ is the order of the autoregressive o
process. Hence, a more rigorous treatment of errors in statoscopic heights
can be implemented without unduly burdensome consequences.
Another external sensor that is likely to emerge to prominence
in the next few years is the inertial navigational system. Such a system
has been adapted to applications to ground surveying with almost unbeliev-
able success. It is produced by Litton Corporation under the trademark
'Autosurveyor'. Gregerson (1975) reports tests in which traverses were
performed by the Autosurveyor to accuracies in excess of 1:100,000. The
inertial navigator employed in the Autosurveyor is essentially the Litton
LN-15, a unit developed in the mid 1960's and rated in accuracy at a little
better than one nautical mile per hour in normal applications to aerial
navigation. The state-of-the-art of inertial navigation has progressed to
the point (see Figure 12 below) where accuracies of 0.08 nm/hr have been
demonstrated in routine operations by the Honeywell SPN/GEANS (Standard
Precision Navigation/Gimbaled Electrostatic gyro Aireraft Navigation System).
2.0 md
1.0. 7
POSITION ERROR (NM)
ONE SIGMA SPEC
T
. 68 HOURS
TIME
FIGURE 12. Error in aircraft positioning by Honeywell SPN/GEANS as
determined from composite of nine laboratory tests (from Hall (1975)).
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