9
Improved Stereotriangulation Ad Justments
. o J . X
with Electronic Computers
ALBERT L. NOWICKI and CARL J. BORN,
Army Map Service, L-
Washington, D. C.
is
ABSTRACT: The UNIVAC plays an important role in the stereotriangulation s
adjustment process. For this reason, thoughts are always directed toward im-
proving the existing programs as well as devising new ones. Considerable time
and study have been devoted to the deficiencies of the vertical adjustment pro-
gram. The results have led to a revised program with the required flexibility.
Work is also underway for programming a horizontal block adjustment, which
shows considerable promise.
N APRIL 1952 the Army Map Service ac- where
I quired one of the first major commercial He = [1 + (a — 4 — aojalZC
electronic computers (UNIVAC), developed C — Scale conversion factor
in the United States for use in its Geodetic Z —Stereophotogrammetric height
and Photogrammetric Divisions. At that time x =Stereophotogrammetric x
programming was initiated for the analytical y=Stereophotogrammetric y
computations incidental to the horizontal ad- Xo — Origin for vertical scale correction
justments of stereophotogrammetric exten- a — Scale coefficient
sions; however, the classical-graphic method He = Adjusted-computed heights
for vertical adjustments was continued. Dur- A; & Bj; — Coefficients (2—90, 1, 2)
ing the ensuing period additional first-order
stereoplotting
It was assumed, at the time, that the terms
of the quadratic equation satisfied the sys-
tematic error accumulation due to earth
curvature and imperfect optical compensa-
tion. The B»x?y term had been included to
partially compensate for accidental errors.
Inconsistencies in results led to further re-
search and testing in order to arrive at a
more accurate and economic solution.
After a large number of tests, involving
y many combinations of flight lengths, control
spacing patterns and number of control points
available per strip, it became apparent that
these three factors had a definite bearing on
the extent to which the residual errors were
removed in the UNIVAC adjustment. For
example, whenever the strips of photographs
exceeded fifteen models and the distribution
of control occurred in four or more bands,
with each band consisting of two or more ver-
tical control points, a “poor fit” to the con-
instruments were acquired
specifically for use in extension work; at
present over thirty such instruments (Stereo-
planigraphs, Autographs, etc.) are being used
for that purpose.
To date successful use has been made of
the conformal transformation equations
(quadratic in (x)) for the horizontal adjust-
ment of extensions (see equation (1)).
*X =x + Ka? 4+ Hx + D (2Ax + B)
Y = y+Ax+Br+D+(2Kx4 I1),
Steps were taken, subsequently, to program
the mathematical adjustment of the vertical
errors in a stereotriangulated strip utilizing
the equation of a ruled surface (quadratic in
(x)). (See equation 2.)
*Ao + Boy + Ax F Bixy + Aon?
+ Bax?y + H, = H. j
; trol, on a least squares solution, resulted.
The acceptable standard error of the residual
errors after a least squares fit to the control
was considered to be 1/5,000 of the flight
height; this value of H/5,000 will be recog-
* In actual computing x and y are replaced by
V — 3) «& (y— 5) where £, ? are mean values of the
stereophotogrammetric coordinates of the vertical
control points in the strip.
Presented at the Society's 26th Annual Meeting, Hotel Shoreham, Washington, D. C..
March
23 26, 1960.
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