- Email: [email protected]
Use of auxiliary data in aerial triangulation over long distances
38 Dr. S a n t o n i :
S y n c h r o n i z a t i o n to w i t h i n five milliseconds h a s been a t t a i n e d .
Mr. V a n Z a n d t : W h a t o r i e n t a t i o n p r o c e d u r e is followed in t h e solar m e t h o d ? Dr. S a n t o n i : Ideally no p a r a l l a x should be left a f t e r r e l a t i v e o r i e n t a t i o n . H o w e v e r , the p l o t t i n g m a c h i n e does i n t r o d u c e some p a r a l l a x , b u t t h i s is s y s t e m a t i c a n d c a n be t a k e n o u t by s m a l l c o r r e c t i o n s to both c a m e r a s . Mr. V a n Z a n d t : W o u l d n o t t h e u s e of t h i s p r o c e d u r e i n t r o d u c e d i f f i c u l t i e s in t h e a b s o l u t e o r i e n t a t i o n of t h e following model? Dr. S a n t o n i : T h e c o r r e c t i o n s so m a d e h a v e no b e a r i n g on t h e following model, w h i c h c a n be o r i e n t e d by t h e u s e of s u n d a t a . M r . Lo~'enz: W h a t w a s t h e f l y i n g h e i g h t e m p l o y e d in I)r. S a n t o n i ' s t e s t s ? Dr. S a n t o n i : T h e f l y i n g h e i g h t w a s 14,000 feet a n d 36 models w e r e used to cover t h e 100 k i l o m e t e r t e s t strip.
Use of auxiliary data in aerial triangulation over long distances p r e s e n t e d at the Ottawa-Con.fere~ce by T. J. B L A C H U T P h o t o g 1 ' a m m e t r i c R e s e a r c h , N a t i o n a l R e s e a r c h Council, O t t a w a . T h e p h r a s e " a e r i a l t r i a n g u l a t i o n over long d i s t a n c e s " r e q u i r e s closer d e f i n i t i o n since t h e i n t e : ' p r e t a t i o n of " l o n g d i s t a n c e " m a y v a r y f r o m a few k i l o m e t e r s up to s e v e r a l h u n d l e d k i l o m e t e r s d e p e n d i n g u p o n c i l c u m s t a n c e s . T h e following c o n s i d e r a t i o n s should be r e f e r r e d to t h e p r o b l e m s e n c o u n t e r e d in v e r y m a n y c o u n t r i e s w h i c h a r e not y e t s u r v e y ed, oi" which p o s s e s s a v e r y f r a g m e n t a r y f i r s t o r d e r t r i a n g u l a t i o n only. It is implied t h a t t h e d i s t a n c e s to be b r i d g e d will be of t h e o r d e r of a b o u t f i f t y k i l o m e t e r s to s e v e r a l h u n dred k i l o m e t e r s a n d t h e m a p to be p r o d u c e d will be at t h e scale 1 : 50,000 or s m a l l e r . F r o m a t h e o r e t i c a l p o i n t of view t h e r e is no d i f f e r e n c e b e t w e e n a e r i a l t r i a n g u l a t i o n on long a n d s h o r t d i s t a n c e s . Basic e r r o r s a n d t h e i r p r o p a g a t i o n a r e e x a c t l y t h e s a m e . A t r i a n g u l a t i o n on s h m ' t d i s t a n c e s m a y be r e g a r d e d as a p a r t of a t r i a n g u l a t i o n on long d i s t a n c e s a n d in c o n s e q u e n c e e v e r y t h i n g valid for long d i s t a n c e t r i a n g u l a t i o n m u s t also b2 valid for s h o r t d i s t a n c e b r i d g i n g . H o w e v e r , t h e r e is a q u a n t i t a t i v e d i f f e r e n c e w h i c h m u s t be t a k e n into a c c o u n t a n d w h i c h e n t e r s t h e p i c t u r e i m m e d i a t e l y w h e n one is conf r o n t e d w i t h a p r a c t i c a l o p e r a t i o n , partieula~:ly over v a s t t e r r i t o r i e s void of g r o u n d control or equipped only w i t h a v e r y s p a r s e n e t w o r k of g r o u n d control. A detailed s t u d y of e r r o r s a n d t h e i r p r o p a g a t i o n is v e r y i m p o r t a n t b u t does n o t solve t h e f u n d a m e n t a l p r o b l e m of aerial t r i a n g u l a t i o n b e c a u s e of o u r i n a b i l i t y at p r e s e n t to control n u m e r o u s er!'ors of a d i f f e r e n t n a t u r e w h i c h h a v e a b e a r i n g on a e r i a l t r i a n g u l a t i o n . T a k i n g into a c c o u n t all d e t e r m i n a b l e e r r o r s a priori or d u r i n g t h e f i n a l a d j u s t m e n t , it is possible m e r e l y to m i n i m i z e closure e r r o r s a n d to f l a t t e n c u r v e s of e r r o r s . In o t h e r words, t h e a b s o l u t e v a l u e of t h e a c c u m u l a t i v e eiu'ors in a b r i d g i n g c a n be reduced. T h i s j u s t i f i e s s u f f i c i e n t l y detailed s t u d y of v a r i o u s e r r o r s . H o w e v e r , e x p e r i e n c e h a s p r o v e n t h a t u s i n g even t h e m o s t precise t,"iangulation procedure, for i n s t a n c e a n a l y t i c a l t r e a t m e n t , it is i m p o s s i b l e a t p r e s e n t to p r e d i c t t h e e x a c t f o r m a n d m a g n i t u d e of accum u l a t i v e e r r o r s . In addition, t h e i r a b s o l u t e v a l u e is q u i t e large, so t h a t in o r d e r to g u a r a n t e e an a c c u r a c y d i c t a t e d by g e n e r a l m a p p i n g r e q u i r e m e n t s t h e t r i a n g u l a t i o n s t r i p m u s t be r e s t r i c t e d to r e l a t i v e l y s h o r t d i s t a n c e s . Since i n t e r m e d i a t e g r o u n d control p o i n t s provide t h e m o s t e f f i c i e n t m e a n s of i n c r e a s i n g f i n a l a c c u r a c y of a e r i a l t r i a n g u l a t i o n , t h e g e n e r a l t r e n d is to provide such a d d i t i o n a l g r o u n d control a l o n g t h e s t r i p - - s t r e t c h i n g in t u r n t h e total l e n g t h of t h e strip. T h i s p r o c e d u r e m a y be quite acceptable in developed a n d s u r v e y e d r e g i o n s b u t it is
39 not economical and practical in the remaining, and by f a r the largest, p a r t of the world. There is also no doubt that, f r o m the point of view of general p h o t o g r a m m e t r i c technique and its end goal, this approach m u s t be regarded a s a n u n s a t i s f a c t o r y answer. One would like to have a method which would make it possible to bridge practically unlimited distance and t h u s to m a p wide territories w i t h o u t h a v i n g recourse to field surveying. In the search for a solution the method proposed some time ago by Prof. P. Wiser, " L a M~thode des D~formation", should be mentioned. Wiser recognized the basic difficulty and shortcomings of the application of the general t h e o r y of errors to the problem of aerial t r i a n g u l a t i o n and devised a method which w a s intended to take into account errors "as t h e y are and not as one would like them to be". W i t h a f o r w a r d overlap of about '/0% he took a d v a n t a g e of a possibility of m e a s u r i n g d e f o r m a t i o n s which occur d u r i n g ins t r u m e n t a l t r i a n g u l a t i o n and he used deformation m e a s u r e m e n t s for the computation of corrections to strip co-ordinates. It seems t h a t the solution proposed by Wiser w a s the f i r s t a t t e m p t to give a complete a n s w e r to the aerial t r i a n g u l a t i o n problem, d i s r e g a r d i n g the question of w h e t h e r or not it w a s very convenient in a practical application, or even of how effective the proposed solution m i g h t be. A n o t h e r imaginable a n s w e r could be produced by the use of a u x i l i a r y d a t a which present convenient and efficient m e a n s of controlling the aerial t r i a n g u l a t i o n over long distances. This method, by the way, would not exclude f u r t h e r t r e a t m e n t such as e.g. proposd by Wiser. So far, d a t a from the solar camera, the horizon camera, the gyroscope and the statoscope h a s been used in aerial t r i a n g u l a t i o n . Their common characteristic is t h a t they control the elements of outer orientation of the photographic c a m e r a at the m o m e n t of exposure. As it is known, some very i n t e r e s t i n g results have been achieved with the use of this a u x i l i a r y e q u i p m e n t and corresponding data. U n f o r t u n a t e l y , practical experience is limited to certain countries only, which makes an e x h a u s t i v e discussion and wider spread of the methods quite difficult. The method of airborne controlled aerial t r i a n g u l a t i o n developed with p a r t i c u l a r concentration on the solution of problems outlined at the b e g i n n i n g of this p a p e r is quite d i f f e r e n t f r o m the above mentioned procedures. F i r s t of all, entirely new elements are used as a u x i l i a r y d a t a and, secondly, basic control is r e f e r r e d to the strip or ground coordinates r a t h e r t h a n to the elements of outer orientation. Similarly to the previous procedures, the a u x i l i a r y d a t a are recorded d u r i n g flight and t h e y include: 1. Distances f r o m the a i r c r a f t to the g r o u n d along the c a m e r a axis (clearances). 2. Profile of the t e r r a i n along the flight line. 3. Oblique p h o t o g r a p h s fore or a f t in the flight direction. The clearances between the a i r c r a f t and the g r o u n d control the scale in the triangulated strips a n d ipso facto also the x-strip co-ordinates. The profile of the t e r r a i n is identical with an infinite n u m b e r of vertical control points located along the strip axis. It is used therefore to control strip z-co-ordinates directly. Finally, s t r a i g h t line procedure based on the use of oblique p h o t o g r a p h s made in the flight direction is used as an independent control of strip y-co-ordinates. Clearances are the quantities m e a s u r e d directly d u r i n g flight and their values can be set on the plotting machine d u r i n g the t r i a n g u l a t i o n process. They are independent f r o m altimeter m e a s u r e m e n t s . Also used on the plotting machine are the altimeter (statoscope) indications on which r a d a r profile procedure is based. The procedure on the i n s t r u m e n t used so f a r h a s been described in an earlier publication 1) and need not be detailed here. The a d j u s t m e n t s t a r t s with the correction of elevations. It m u s t be noticed t h a t in our procedure used on the stereoplotter, the s e t t i n g of a clearance is done by the corre1) T. J. Blachut, Airborne controlled method of aerial t r i a n g u l a t i o n ; P h o t o g r a m m e t r i a , XII, 4, p. 294-302, 1955-56.
40 s p o n d i n g s e t t i n g of bz a n d o f t h e e l e v a t i o n of a profile p o i n t u s e d f o r t h e s c a l i n g o f t h e model in question. Since t h e r a d a r c l e a r a n c e s a r e n o t c o r r e c t v a l u e s a n d t h e r e a r e also ins t r u m e n t a l e r r o r s involved, t h e r e is a j u m p in scale a n d in e l e v a t i o n f r o m model to model. C o n s i d e r i n g model i + 1 ( F i g u r e 1) scaled, f o r i n s t a n c e , w i t h t h e c l e a r a n c e i ÷ 2 - - z ' ~ + 2 , p o i n t z~+ 1 will r e a d a n e l e v a t i o n i.i z'i.+l i n s t e a d of z~+ 1. I n o r d e r to derive c o r r e c t e l e v a t i o n s in model i + 1 all e l e v a t i o n r e a d i n g s m u s t be c o r r e c t e d b y t h e d i f f e r e n c e z~_!_, - - z'~+~ ~ Az~+ 1.
It is obvious t h a t t h e s e j u m p s in e l e v a t i o n could be e l i m i n a t e d during the instrumental process b y s i m p l y r e s e t t i n g t h e z-counter, but then the reference for the s e t t i n g of r a d a r c l e a r a n c e s w o u l d ........................ be lost. T h e r e f o r e , it s e e m s to be s i m p l e r to record t h e e l e v a t i o n s as Z~ Z',*I Z'i÷2 t h e y a r e a n d to i n t r o d u c e t h e Fig. 1. necessary corrections numerically l a t e r on. T h e elevation of a p o i n t in o v e r l a p N m u s t t h e n be c o r r e c t e d by 1;
A z I + Az.~ ÷ . . . + Az,~ = . ~ A z . 1
It should also be n o t e d t h a t scale e r r o r s h a v e a n e f f e c t on t h e e l e v a t i o n s . In f l a t c o u n t r y t h e s e e r r o r s a r e m o s t l y negligible b u t in hilly c o u n t r y scale e r r o r s a n d t h e r e s u l t i n g e f f e c t m a y be noticeable a n d t h e r e f o r e it m a y be n e c e s s a r y to i n t r o d u c e a n a d d i t i o n a l correction. C o m p a r i n g p h o t o g r a m m e t r i c e l e v a t i o n s w i t h c o r r e s p o n d i n g r a d a r elevations, disc r e p a n c i e s g r o w i n g w i t h i n c r e a s e d x ( d i s t a n c e f r o m t h e origin} become evident. T h i s e o m p a I i s o n c a n be best done g r a p h i c a l l y by p l o t t i n g t h e d i s t a n c e s a l o n g t h e x - a x i s a n d t h e above m e n t i o n e d d i s c r e p a n c i e s in t h e ~y-direetion. A s a r e s u l t a p o l y g o n is o b t a i n e d w h i c h could be r e g a r d e d a s a correction c u r v e if r a d a r e l e v a t i o n s w e r e t r u e . U n d e r o r d i n a r y f l i g h t conditions a n d f o r p o i n t s r e a s o n a b l y s e p a r a t e d , it is quite s a f e to a s s u m e t h a t t h e r a d a r e l e v a t i o n s a r e a f f e c t e d p r i m a r i l y by a c c i d e n t a l e r r o r s . C o n s e q u e n t l y t h e g r a d u a t i o n p r o c e s s is u s e d in o r d e r to d e t e r m i n e t h e p r o p e r s h a p e of t h e correction curve. R e m a r k a b l e r e s u l t s h a v e been o b t a i n e d so f a r f r o m s e v e r a l e x p e r i m e n t a l b r i d g i n g s over d i s t a n c e s r a n g i n g f r o m 30 u p to 200 miles, w h i c h of c o u r s e p r o v e s also t h e g r e a t reliability of r a d a r profiles. T h e i n t e n t i o n is to a p p l y t h e a n a l y t i c a l t r e a t m e n t to t h i s m e t h o d , as soon as t h e f i r s t s t e r e o c o m p a r a t o r s a r e a v a i l a b l e a n d t h e n t h e p r o c e d u r e m a y be altered. W e a r e t h i n k i n g f i r s t a b o u t t h e a l t i m e t e r d a t a w h i c h in s o m e of o u r e x p e r i m e n t s s h o w " s c a l e " e r r o r s t h a t a r e p r o b a b l y d u e to c a l i b r a t i o n e r r o r s in h e t A P R e q u i p m e n t . A l t i m e t e r i n d i c a t i o n s a r e in c e r t a i n r u n s s y s t e m a t i c a l l y too s m a l l or too large. T h e e f f e c t of t h i s on t h e r a d a r e l e v a t i o n p o i n t s u s e d in b r i d g i n g is p u r e l y a e c i d a n t a l a n d t h e r e f o r e is of n o t too s e r i o u s concern, b u t t h e w r o n g bz v a l u e s set on t h e p l o t t e r a c c o r d i n g to t h e a l t i m e t e r i n d i c a t i o n s d e c r e a s e t h e i n t e r i o r a c c u r a c y of a e r i a l t r i a n g u l a t i o n and, in consequence, also its f i n a l a c c u r a c y . T h e r e f o r e it a p p e a r s t h a t t h e a l t i m e t e r i n d i c a t i o n s s h o u l d be d r o p p e d f r o m t h e i n s t r u m e n t a l work. W h e r e a l t i m e t e r scale e r r o r s w e r e e s t a b l i s h e d , c o r r e c t i o n s to e l e v a t i o n s d e t e r m i n e d f r o m y - r o t a t i o n s of t h e p r e c e d i n g p r o j e c t o r s i m p r o v e d t h e f i n a l results.
41 C o r r e c t e d e l e v a t i o n s w e r e u s e d so f a r in o r d e r to i m p r o v e t h e c l e a r a n c e s s e t initially on t h e plotter, a n d t h e c o r r e s p o n d i n g c o r r e c t i o n s to t h e x a n d y model c o - o r d i n a t e s w e r e applied. U s i n g t h i s p r o c e d u r e , a n a c c u r a c y of a b o u t + 6 m e t e r s w a s o b t a i n e d on d i s t a n c e s u p to 330 k i l o m e t e r s . A m o r e c o r r e c t a d j u s t m e n t h o w e v e r s h o u l d be c a r r i e d out in a s l i g h t l y d i f f e r e n t way. T h e correction of c l e a r a n c e s b y c o r r e c t i o n s in r a d a r e l e v a t i o n s only is to a c e r t a i n
Fig. 2. S t r a i g h t line plotter. e x t e n t j u s t i f i e d b y t h e f a c t t h a t m o s t o f t h e e r r o r s in c l e a r a n c e s a r e c a u s e d b y f o r m s of t h e t e r r a i n a n d b y its c o v e r a g e . . H o w e v e r , in o r d e r to derive t h e b e s t possible value, r a d a r v a l u e s should be c o m p a r e d w i t h p h o t o g r a m m e t r i c c l e a r a n c e s a s o b t a i n e d f r o m a conventional bridging. I n t h e a n a l y t i c a l t r e a t m e n t we i n t e n d to u s e A P R d a t a f o r t h e f i n a l a d j u s t m e n t exclusively. I t is n o t clear w h e n t h e s t e r e o p l o t t e r s a r e u s e d w h e t h e r t h e r e j e c t i o n of t h e A P R d a t a f r o m t h e i n s t r u m e n t a l p r o c e d u r e is t h e r i g h t a n s w e r b e c a u s e of t h e i n s t r u m e n t a l e r r o r s w h i c h m u s t be considered. T h e e x p e r i m e n t s b e i n g c a r r i e d o u t a t p r e s e n t should supp]y the required information. T h e t r a n s v e r s a l bend of t h e s t r i p is a d j u s t e d to t h e " s t r a i g h t line" p r o d u c e d f r o m oblique p h o t o g r a p h s . T h e a d j u s t m e n t of z- a n d x - c o - o r d i n a t e s is e x t r e m e l y s i m p l e a n d c a n be done v e r y quickly, w h e r e a s t h e u s e of oblique p h o t o g r a p h s i n its p r e s e n t f o r m is a m u c h m o r e e l a b o r a t e p r o c e d u r e . I n p a r t i c u l a r , t h e c o n s t r u c t i o n of a s t r a i g h t line t h r o u g h o u t oblique p h o t o g r a p h s is a t a s k d e m a n d i n g t h e a t t e n t i o n of t h e m o s t reliable a n d skillful o p e r a t o r . I n o r d e r to e l i m i n a t e t h e p e r s o n a l f a c t o r involved a n d to f a c i l i t a t e a n d speed u p t h e s t r a i g h t line c o n s t r u c t i o n , a s t r a i g h t line p l o t t e r a s s h o w n in Fig. 2 w a s d e s i g n e d a n d b u i l t in o u r l a b o r a t o r i e s . A s in stereoscopic t y p e i n s t r u m e n t s , two s u c c e s s i v e oblique p h o t o g r a p h s a r e viewed a t t h e s a m e t i m e . V a r i a b l e m a g n i f i c a t i o n of t h e v i e w i n g s y s t e m combined w i t h t h e u s e of cylindrical l e n s e s p e r m i t s t h e o b s e r v a t i o n of selected detail on both p h o t o g r a p h s a t a p p r o x i m a t e l y e q u a l scales. A p p l y i n g , t h e n , t h e p r i n c i p l e of t h e
-20 m
"Horn"
,~110 m.
~oO!
Ioo
7oo
loo
llOO~
0 00- 007. 0 3O 0
40
la
60
o o~..j.C,,,.,/~
'~
80 0 0 0
0
o ~
140
Fig. 3
I~m
0°°
~ - e Gorteotl(m e a r n
0 Ground
120
o
0 0 0 0
Io
Fig. 4
~
Terroin Profile along Arizona FIiIM
I00
o ~.o°o~..J "--~
0
\
16Q \
O0~D A
0
I100 0
0
40
0 0 0
0
JoQ4k.~
O0 2100
m
220
- Xl[m
4~
43 f l o a t i n g m a r k , p o i n t s c a n be t r a n s f e r r e d f r o m one p h o t o g r a p h to t h e n e x t one w i t h a h i g h d e g r e e o f a c c u r a c y a n d in a s h o r t t i m e . No d o u b t t h e u s e o f t h i s e q u i p m e n t will be of g r e a t a s s i s t a n c e in p e r f o r m i n g t h e s t r a i g h t line c o n s t r u c t i o n . A t t h e s a m e t i m e , however, t h e r e a r e f u r t h e r t h o u g h t s on t h e q u e s t i o n of s i m p l i f y i n g a n d m a k i n g t h e b a s i c p r o c e d u r e m o r e s u i t a b l e f o r t h e electronic c o m p u t a t i o n s . I t h a s been decided to include t h e " p o l y g o n m e t h o d " in f u t u r e e x p e r i m e n t s . I n s t e a d of c o n s t r u c t i n g one s t r a i g h t line t h r o u g h o u t t h e s t r i p , s h o r t e r lines d r a w n on s i n g l e p h o t o g r a p h s will be joined in a p o l y g o n a n d u s e d l a t e r on f o r t h e control of t r a n s v e r s a l b e n d in t h e s t r i p . I t is hoped, b y u s i n g t h i s p r o c e d u r e , to r e t a i n t h e s a m e a c c u r a c y b u t c u t down t h e n u m b e r of c o m p u t a t i o n s necessary at present. T h e a u x i l i a r y d a t a m e n t i o n e d so f a r a r e n o t t h e only i n f o r m a t i o n p r o v i d e d b y t h e a i r b o r n e controlled m e t h o d o f a e r i a l t r i a n g u l a t i o n . I f t h e oblique p h o t o g r a p h s i n c l u d e t h e horizon, w h i c h is t h e case in t h e p r o c e d u r e p r e s e n t l y u s e d , t h e n a d d i t i o n a l e l e m e n t s q~ a n d o~ c a n be d e t e r m i n e d s i m i l a r l y to t h e horizon c a m e r a t e c h n i q u e . It i m p l i e s h o w e v e r t h a t t h e r e is no c h a n g e in r e l a t i v e position b e t w e e n t h e v e r t i c a l a n d oblique c a m e r a d u r i n g t h e f l i g h t , or a t l e a s t t h a t t h e i n s t a n t of c h a n g e if s u c h o c c a s i o n a l l y o c c u r s s h o u l d be recorded. T h u s t h e a u x i l i a r y d a t a c o n t a i n : 1. 2. 3. 4. 5. 6.
Altimeter (statoscope) data. Clearances. G r o u n d e l e v a t i o n s (profile) a l o n g t h e f l i g h t axis. S t r a i g h t line to control t h e t r a n s v e r s a l bend of t h e s t r i p . ~. 50.
It h a s to be e s t a b l i s h e d w h e t h e r or n o t is w o r t h while to u s e all t h i s a u x i l i a r y d a t a . T h e r e is, h o w e v e r , t h e o b v i o u s possibility of u s i n g oblique p h o t o g r a p h s in o r d e r to e l i m i n a t e t h e t w i s t f r o m t h e t r i a n g u l a t e d strip. In t h i s connection we a g a i n p r o p o s e t h e u s e of t h e s m o o t h i n g p r o c e s s in o r d e r to e l i m i n a t e t h e a c c i d e n t a l e r r o r s a f f e c t i n g h o r i z o n d a t a . S i n g l e i n d i c a t i o n s f r o m a u x i l i a r y e q u i p m e n t a r e p r i m a r i l y a f f e c t e d by a c c i d e n t a l e r r o r s w h i c h , in m o s t cases, a r e g r e a t e r t h a n t h e a c c i d e n t a l e r r o r s o f t h e s a m e e l e m e n t s e s t a b l i s h e d d u r i n g t h e p r o c e s s of i n s t r u m e n t a l b r i d g i n g . It s e e m s t h e r e f o r e t h a t a c e r t a i n g a i n in a c c u r a c y c a n be a c h i e v e d if b o t h m a g n i t u d e s a r e c o n f r o n t e d w i t h e a c h other. W e do n o t h a v e m u c h s t a t i s t i c a l m a t e r i a l to d e m o n s t r a t e t h e e f f i c i e n c y of t h e proposed m e t h o d of a e r i a l t r i a n g u l a t i o n u n d e r v a r i o u s conditions. H o w e v e r , t h e r e s u l t s o b t a i n e d so f a r a r e v e r y s a t i s f a c t o r y a n d q u i t e conclusive. T h e f i r s t s e r i e s of e x p e r i m e n t s c a r r i e d o u t o v e r f i a t c o u n t r y u s i n g Multiplex, S t e r e o p l a n o g r a p h C8 a n d W i l d A 7 p l o t t e r s c u l m i n a t e d in a b r i d g i n g a b o u t 330 k i l o m e t e r s tong, w i t h t h e f o l l o w i n g m e a n s q u a r e errors : = = m~ = m~ = m z m z
± 2.4 m e t e r s (checked on a p p r o x i m a t e l y 200 v e r t i c a l control p o i n t s ) , --+ 1.8 m e t e r s ( f o r p o i n t s located w i t h i n a c e n t r a l b a n d only 2 k i l o m e t e r s w i d e ) , ± 6.4 m e t e r s , ± 8.0 m e t e r s .
T h e s a m e s t r i p h a s been b r i d g e d b y t h e Colonial S u r v e y in E n g l a n d u s i n g M u l t i p l e x e q u i p m e n t . T h e a c c u r a c y in z w a s s l i g h t l y worse, a s w a s to be expected, b u t still e x c e l l e n t a n d r e a c h e d a v a l u e of m z = ± 3.4 m e t e r s . T h e opinion w a s , t h a t t h e u s e o f M u l t i p l e x did n o t allow a n y conclusion as f a r a s t h e d e t e r m i n a t i o n of x - c o - o r d i n a t e s w a s c o n c e r n e d a n d it s e e m s t h a t in c o n s e q u e n c e no a t t e m p t h a s been m a d e to a d j u s t t h e x - v a l u e s . H o w e v e r , t h e m a x i m u m error in x, a f t e r t h e s t r i p h a d been tied in a t b o t h e n d s w i t h o u t a n y f u r t h e r corrections, a m o u n t e d to a b o u t 32 m e t e r s on t h e g r o u n d , o r to a b o u t 0.6 m m on t h e m a p a t t h e scale of 1 : 50000,
44
o
o
!
-& l
~
o
~o o
©l
=o
I
o
:J
|,
•
. o
Q
~o
ooo
o0o0 oa
0
o
o
o,
o
o J o
oo
.o
o
~D o
Jo
o
•
o
•
a n d to a b o u t 2.0 m a t t h e scale of t h e M u l t i p l e x plot• I n view of t h e equipment used, this extraordinary r e s u l t m u s t be r e g a r d e d a s p u r e l y accidental, despite the fact that somewhat similar results were a c h i e v e d in o u r f i r s t e x p e r i m e n t s , also c a r r i e d o u t on M u l t i p l e x . T h e r e is h o w e v e r no d o u b t t h a t t h e m e t h o d is o n l y s l i g h t l y s e n s i t i v e to t h e e q u i p m e n t u s e d . Oblique p h o t o g r a p h s w e r e n o t u s e d b y t h e Colonial S u r v e y f o r t h e a d j u s t m e n t of t h e t r a n s v e r s a l bend of t h e strip• Radar ground elevations and r a d a r c l e a r a n c e s d e p e n d f i r s t of all u p o n t h e t e r r a i n . I n o r d e r to p r o v e t h e e f f i c i e n c y of t h e m e t h o d over h i l l y c o u n t r y , a 240-kilometer A P R f l i g h t w a s a r r a n g e d over~ t e r r a i n h a v i n g d i f f e r e n c e s in elevations r a n g i n g u p to a b o u t 600 meters. About 100 boundary points, v e r y p r e c i s e l y d e t e r m i n e d by t h e Geodetic S u r v e y , w e r e u s e d a s h o r i z o n t a l control. T h e i r identif i c a t i o n on a e r i a l p h o t o g r a p h s w a s v e r y d i f f i c u l t since t h e y w e r e seld o m located close to a n y c h a r a c t e r istic, e a s i l y i d e n t i f i e d terrain points. In addition, s n o w c o v e r a g e further increased the difficulties of identification. Another unfort u n a t e circ~umstance w a s t h a t t h e v e r t i c a l control a t o u r d i s p o s a l included only 23 e l e v a t i o n p o i n t s , n o t v e r y reliable, u n e v e n l y d i s t r i b u t ed a n d m o s t l y selected f r o m a n existing map. The flight was made on a cold w i n t e r day. T h e f l y i n g h e i g h t w a s a b o u t 6000 m e t e r s a n d the camera used was a Wild RC5a. A c c o r d i n g to t h e o p e r a t i n g comp a n y t h e A P R e q u i p m e n t did n o t w o r k in a n e n t i r e l y s a t i s f a c t o r y m a n n e r b u t t h e r e w a s no opport u n i t y to r e p e a t t h e f l i g h t . T h e r e s u l t s of t h e b r i d g i n g w h i c h followed w e r e • m z = -- 5.6 m e t e r s , ,m~ = ± 6.4 m e t e r s , ~nv = ± 9.5 m e t e r s .
45 F~gure 3 shows the corresponding graph for x-adjustment. T h e m o s t r e c e n t e x p e r i m e n t w a s c a r r i e d o u t o v e r a v e r y s h o r t d i s t a n c e o f 60 kilom e t e r s b u t r i g i d l y controlled b y m e a n s o f a b o u t 65 h o r i z o n t a l a n d 130 v e r t i c a l control points. I n t h e c e n t r a l section t h e f l i g h t c r o s s e d v e r y r u g g e d m o u n t a i n s r e a c h i n g a n elevation o f over 1000 m. T h e p r o f i l e o f t h e t e r r a i n a l o n g t h e f l i g h t line is s h o w n in F i g u r e 4. F l i g h t d a t a w e r e a s follows: F l y i n g h e i g h t over s e a level, a b o u t 6000 m. C a m e r a u s e d : F a i r c h i l d T l l , f = 153 ram, size of p h o t o g r a p h s 230 X 230 m m . On t h e p l o t t i n g m a c h i n e , W i l d AT, a l t i m e t e r i n d i c a t i o n s a n d c l e a r a n c e s w e r e u s e d . H o w e v e r , f o r t h e f i n a l c o m p u t a t i o n of e l e v a t i o n s t h e s t a t o s c o p e d a t a w e r e rejected, x-coo r d i n a t e s w e r e a d j u s t e d as in p r e v i o u s e x p e r i m e n t s . T h e m e a n s q u a r e e r r o r s w e r e : m z = --+ 2.2 m, m x : --+ 2.8 m, m y = ± 2.4 m.
F r o m t h e d i s t r i b u t i o n of t h e e l e v a t i o n e r r o r s w i t h i n s i n g l e models, it is e v i d e n t t h a t in t h e m o u n t a i n o u s section of t h e s t r i p poor i d e n t i f i c a t i o n of control p o i n t s p r o d u c e d e r r o r s in e l e v a t i o n u p to a b o u t --+ 1 m e t e r . C o n s e q u e n t l y t h e t r u e a c c u r a c y of b r i d g i n g in e l e v a t i o n s is h i g h e r t h a n i n d i c a t e d above. All t h e r e s u l t s s e e m to p r o v e t h a t t h e choice of a u x i l i a r y d a t a a s g i v e n b y t h e a i r b o r n e controlled m e t h o d o f a e r i a l t r i a n g u l a t i o n is v e r y s u i t a b l e a n d e x p e d i e n t b e c a u s e t h e a u x i l i a r y d a t a a r e a p p l i c a b l e to t h e s t r i p c o - o r d i n a t e s r a t h e r t h a n to t h e v e r y s e n s itive e l e m e n t s of o u t e r o r i e n t a t i o n . T h e r e is also a f u r t h e r c o n s i d e r a t i o n w h i c h s t r e s s e s t h e i m p o r t a n c e of t h e m e t h o d p l o p o s e d a n d i t s d i s t i n c t l y d i f f e r e n t c h a r a c t e r a s c o m p a r e d w i t h all o t h e r p r o c e d u r e s u s e d so f a r . A i r b o r n e p r o f i l e m e t h o d s of a e r i a l t r i a n g u l a t i o n c h a n g e t h e basic c h a r a c t e r of a e r i a l p h o t o g r a m m e t r y . F r o m being' a relative m e t h o d o f m e a s u r i n g it becomes n o w a n cLbsolute m e t h o d . T h e c o n s e q u e n c e s a r e a l r e a d y visible. R a n g e a n d t h e a c c u r a c y h a v e been m u l t i p l i e d . W i t h f u r t h e r i n s t r u m e n t a l i m p r o v e m e n t s a l r e a d y e n v i s a g e d , s u c h a s a b s o l u t e c l e a r a n c e d e t e r m i n a t i o n , a n d w i t h all t h e a d v a n t a g e s w h i c h c a n be t a k e n f r o m t h e a n a l y t i c a l t r e a t m e n t , it m a y h a p p e n t h a t m a n y o f t h e s e c o n d a r y geodetic o p e r a t i o n s will be solved by p h o t o g r a m m e t r i c m e a n s .
Discussion of lMr. Blachut'$ paper. Professor Doyle : Mr. B l a c h u t h a s m e n t i o n e d t h a t no oblique p h o t o g r a p h s w e r e a v a i l a b l e to control t h e y - d e f o r m a t i o n s in t h e l a s t s t r i p a n d t h a t a p a r a b o l i c y - a d j u s t m e n t w a s m a d e o n c e n t r a l control. I t s e e m s , t h e n , t h a t one p o i n t in t h e middle o f t h e s t r i p is w o r t h a]l t h e a u x i l i a r y d a t a , since t h e m e a n e r r o r is of t h e s a m e m a g n i t u d e . M a k i n g t h e s t r i p twice as long, t h e s a m e a m o u n t o f c o n t r o l w o u l d be s u f f i c i e n t . T h e r e is no d o u b t of t h e v a l u e of a u x i l i a r y d a t a in c a n t i l e v e r e x t e n s i o n , h o w e v e r . Mr. B l a c h u t : R e a s o n i n g t h u s , e x t e n s i o n to s t r i p s of i n f i n i t e l e n g t h w o u l d be possible! W h e r e control is e s t a b l i s h e d b y S h o r a n it is g e n e r a l l y n o t located in s t r a i g h t lines a n d is t h u s n o t s u i t a b l e f o r p a r a b o l i c corrections. Colonel T h o m p s o n : Does P r o f e s s o r Doyle s u g g e s t t h a t all u s e of a u x i l i a r y d a t a be disc a r d e d ? I s h o u l d like to p o i n t o u t t h a t t h e r e s u l t s d e p e n d also on o t h e r a u x i l i a r y d a t a t h a n oblique p h o t o g r a p h s a n d t h a t w i t h o u t t h e s e t h e m e a n e r r o r w o u l d n o t h a v e b e e n so favourable. Mr. B l a c h u t : T h i s b r i n g s u p a n o t h e r i m p o r t a n t p o i n t w h i c h I f o r g o t to m e n t i o n . . G e n e r a l l y e r r o r s in a t r i a n g u l a t e d s t r i p do n o t follow a second o r d e r c u r v e . T h e r e f o r e , a p a r a b o l i c c o r r e c t i o n does n o t g i v e t h e b e s t a n s w e r . T h e a u x i l i a r y d a t a s u g g e s t e d in m y t a l k p e r m i t u s to m a k e s u i t a b l e c o r r e c t i o n s all a l o n g t h e s t r i p .
4
46 Mr. Lorenz: Mr. Blachut has mentioned t h a t in some strips a scale correction "was applied to the altimeter. How was this determined? Mr. B l a c h u t : Systematic discrepancies between altimeter indications and corresponding data from the plotter reveal a degree of "scale altimeter error". Mr. Lorenz: W h a t kind of r a d a r return points were selected to scale on in mountainous country? Mr. Blachut: Any convenient point, preferably on level ground. If absolutely necessary, a photogrammetric point from the preceding model can be used. Large errors can always be isolated. Mr. B a u s s a r t : W h a t weight should be applied to the auxiliary data as compared to the corresponding quantities from classical triangulation? Mr. S c h u t : In the adjustment the auxiliary data are followed, but the weight attached to each individual quantity will be determined by the degree of smoothing. Mr. Bau~ssart: How is block a d j u s t m e n t carried out in this method? Mr. Blachut: The method deals with strip triangulation. No specifications as to block adjustments are ma.de. Professor Thompsvn: Apparently in this method we are not concerned with systematic or accidental errors, but with systematic and accidental accuracy? Professor M c N a i r : The problem of w h a t weights should be applied to the various quantities comprising auxiliary d a t a and the data of classical triangulation is still unsolved.
The publication of the texts of communications will be continued in the next i~sue o] Photogrammetria.
S y n c h r o n i z a t i o n to w i t h i n five milliseconds h a s been a t t a i n e d .
Mr. V a n Z a n d t : W h a t o r i e n t a t i o n p r o c e d u r e is followed in t h e solar m e t h o d ? Dr. S a n t o n i : Ideally no p a r a l l a x should be left a f t e r r e l a t i v e o r i e n t a t i o n . H o w e v e r , the p l o t t i n g m a c h i n e does i n t r o d u c e some p a r a l l a x , b u t t h i s is s y s t e m a t i c a n d c a n be t a k e n o u t by s m a l l c o r r e c t i o n s to both c a m e r a s . Mr. V a n Z a n d t : W o u l d n o t t h e u s e of t h i s p r o c e d u r e i n t r o d u c e d i f f i c u l t i e s in t h e a b s o l u t e o r i e n t a t i o n of t h e following model? Dr. S a n t o n i : T h e c o r r e c t i o n s so m a d e h a v e no b e a r i n g on t h e following model, w h i c h c a n be o r i e n t e d by t h e u s e of s u n d a t a . M r . Lo~'enz: W h a t w a s t h e f l y i n g h e i g h t e m p l o y e d in I)r. S a n t o n i ' s t e s t s ? Dr. S a n t o n i : T h e f l y i n g h e i g h t w a s 14,000 feet a n d 36 models w e r e used to cover t h e 100 k i l o m e t e r t e s t strip.
Use of auxiliary data in aerial triangulation over long distances p r e s e n t e d at the Ottawa-Con.fere~ce by T. J. B L A C H U T P h o t o g 1 ' a m m e t r i c R e s e a r c h , N a t i o n a l R e s e a r c h Council, O t t a w a . T h e p h r a s e " a e r i a l t r i a n g u l a t i o n over long d i s t a n c e s " r e q u i r e s closer d e f i n i t i o n since t h e i n t e : ' p r e t a t i o n of " l o n g d i s t a n c e " m a y v a r y f r o m a few k i l o m e t e r s up to s e v e r a l h u n d l e d k i l o m e t e r s d e p e n d i n g u p o n c i l c u m s t a n c e s . T h e following c o n s i d e r a t i o n s should be r e f e r r e d to t h e p r o b l e m s e n c o u n t e r e d in v e r y m a n y c o u n t r i e s w h i c h a r e not y e t s u r v e y ed, oi" which p o s s e s s a v e r y f r a g m e n t a r y f i r s t o r d e r t r i a n g u l a t i o n only. It is implied t h a t t h e d i s t a n c e s to be b r i d g e d will be of t h e o r d e r of a b o u t f i f t y k i l o m e t e r s to s e v e r a l h u n dred k i l o m e t e r s a n d t h e m a p to be p r o d u c e d will be at t h e scale 1 : 50,000 or s m a l l e r . F r o m a t h e o r e t i c a l p o i n t of view t h e r e is no d i f f e r e n c e b e t w e e n a e r i a l t r i a n g u l a t i o n on long a n d s h o r t d i s t a n c e s . Basic e r r o r s a n d t h e i r p r o p a g a t i o n a r e e x a c t l y t h e s a m e . A t r i a n g u l a t i o n on s h m ' t d i s t a n c e s m a y be r e g a r d e d as a p a r t of a t r i a n g u l a t i o n on long d i s t a n c e s a n d in c o n s e q u e n c e e v e r y t h i n g valid for long d i s t a n c e t r i a n g u l a t i o n m u s t also b2 valid for s h o r t d i s t a n c e b r i d g i n g . H o w e v e r , t h e r e is a q u a n t i t a t i v e d i f f e r e n c e w h i c h m u s t be t a k e n into a c c o u n t a n d w h i c h e n t e r s t h e p i c t u r e i m m e d i a t e l y w h e n one is conf r o n t e d w i t h a p r a c t i c a l o p e r a t i o n , partieula~:ly over v a s t t e r r i t o r i e s void of g r o u n d control or equipped only w i t h a v e r y s p a r s e n e t w o r k of g r o u n d control. A detailed s t u d y of e r r o r s a n d t h e i r p r o p a g a t i o n is v e r y i m p o r t a n t b u t does n o t solve t h e f u n d a m e n t a l p r o b l e m of aerial t r i a n g u l a t i o n b e c a u s e of o u r i n a b i l i t y at p r e s e n t to control n u m e r o u s er!'ors of a d i f f e r e n t n a t u r e w h i c h h a v e a b e a r i n g on a e r i a l t r i a n g u l a t i o n . T a k i n g into a c c o u n t all d e t e r m i n a b l e e r r o r s a priori or d u r i n g t h e f i n a l a d j u s t m e n t , it is possible m e r e l y to m i n i m i z e closure e r r o r s a n d to f l a t t e n c u r v e s of e r r o r s . In o t h e r words, t h e a b s o l u t e v a l u e of t h e a c c u m u l a t i v e eiu'ors in a b r i d g i n g c a n be reduced. T h i s j u s t i f i e s s u f f i c i e n t l y detailed s t u d y of v a r i o u s e r r o r s . H o w e v e r , e x p e r i e n c e h a s p r o v e n t h a t u s i n g even t h e m o s t precise t,"iangulation procedure, for i n s t a n c e a n a l y t i c a l t r e a t m e n t , it is i m p o s s i b l e a t p r e s e n t to p r e d i c t t h e e x a c t f o r m a n d m a g n i t u d e of accum u l a t i v e e r r o r s . In addition, t h e i r a b s o l u t e v a l u e is q u i t e large, so t h a t in o r d e r to g u a r a n t e e an a c c u r a c y d i c t a t e d by g e n e r a l m a p p i n g r e q u i r e m e n t s t h e t r i a n g u l a t i o n s t r i p m u s t be r e s t r i c t e d to r e l a t i v e l y s h o r t d i s t a n c e s . Since i n t e r m e d i a t e g r o u n d control p o i n t s provide t h e m o s t e f f i c i e n t m e a n s of i n c r e a s i n g f i n a l a c c u r a c y of a e r i a l t r i a n g u l a t i o n , t h e g e n e r a l t r e n d is to provide such a d d i t i o n a l g r o u n d control a l o n g t h e s t r i p - - s t r e t c h i n g in t u r n t h e total l e n g t h of t h e strip. T h i s p r o c e d u r e m a y be quite acceptable in developed a n d s u r v e y e d r e g i o n s b u t it is
39 not economical and practical in the remaining, and by f a r the largest, p a r t of the world. There is also no doubt that, f r o m the point of view of general p h o t o g r a m m e t r i c technique and its end goal, this approach m u s t be regarded a s a n u n s a t i s f a c t o r y answer. One would like to have a method which would make it possible to bridge practically unlimited distance and t h u s to m a p wide territories w i t h o u t h a v i n g recourse to field surveying. In the search for a solution the method proposed some time ago by Prof. P. Wiser, " L a M~thode des D~formation", should be mentioned. Wiser recognized the basic difficulty and shortcomings of the application of the general t h e o r y of errors to the problem of aerial t r i a n g u l a t i o n and devised a method which w a s intended to take into account errors "as t h e y are and not as one would like them to be". W i t h a f o r w a r d overlap of about '/0% he took a d v a n t a g e of a possibility of m e a s u r i n g d e f o r m a t i o n s which occur d u r i n g ins t r u m e n t a l t r i a n g u l a t i o n and he used deformation m e a s u r e m e n t s for the computation of corrections to strip co-ordinates. It seems t h a t the solution proposed by Wiser w a s the f i r s t a t t e m p t to give a complete a n s w e r to the aerial t r i a n g u l a t i o n problem, d i s r e g a r d i n g the question of w h e t h e r or not it w a s very convenient in a practical application, or even of how effective the proposed solution m i g h t be. A n o t h e r imaginable a n s w e r could be produced by the use of a u x i l i a r y d a t a which present convenient and efficient m e a n s of controlling the aerial t r i a n g u l a t i o n over long distances. This method, by the way, would not exclude f u r t h e r t r e a t m e n t such as e.g. proposd by Wiser. So far, d a t a from the solar camera, the horizon camera, the gyroscope and the statoscope h a s been used in aerial t r i a n g u l a t i o n . Their common characteristic is t h a t they control the elements of outer orientation of the photographic c a m e r a at the m o m e n t of exposure. As it is known, some very i n t e r e s t i n g results have been achieved with the use of this a u x i l i a r y e q u i p m e n t and corresponding data. U n f o r t u n a t e l y , practical experience is limited to certain countries only, which makes an e x h a u s t i v e discussion and wider spread of the methods quite difficult. The method of airborne controlled aerial t r i a n g u l a t i o n developed with p a r t i c u l a r concentration on the solution of problems outlined at the b e g i n n i n g of this p a p e r is quite d i f f e r e n t f r o m the above mentioned procedures. F i r s t of all, entirely new elements are used as a u x i l i a r y d a t a and, secondly, basic control is r e f e r r e d to the strip or ground coordinates r a t h e r t h a n to the elements of outer orientation. Similarly to the previous procedures, the a u x i l i a r y d a t a are recorded d u r i n g flight and t h e y include: 1. Distances f r o m the a i r c r a f t to the g r o u n d along the c a m e r a axis (clearances). 2. Profile of the t e r r a i n along the flight line. 3. Oblique p h o t o g r a p h s fore or a f t in the flight direction. The clearances between the a i r c r a f t and the g r o u n d control the scale in the triangulated strips a n d ipso facto also the x-strip co-ordinates. The profile of the t e r r a i n is identical with an infinite n u m b e r of vertical control points located along the strip axis. It is used therefore to control strip z-co-ordinates directly. Finally, s t r a i g h t line procedure based on the use of oblique p h o t o g r a p h s made in the flight direction is used as an independent control of strip y-co-ordinates. Clearances are the quantities m e a s u r e d directly d u r i n g flight and their values can be set on the plotting machine d u r i n g the t r i a n g u l a t i o n process. They are independent f r o m altimeter m e a s u r e m e n t s . Also used on the plotting machine are the altimeter (statoscope) indications on which r a d a r profile procedure is based. The procedure on the i n s t r u m e n t used so f a r h a s been described in an earlier publication 1) and need not be detailed here. The a d j u s t m e n t s t a r t s with the correction of elevations. It m u s t be noticed t h a t in our procedure used on the stereoplotter, the s e t t i n g of a clearance is done by the corre1) T. J. Blachut, Airborne controlled method of aerial t r i a n g u l a t i o n ; P h o t o g r a m m e t r i a , XII, 4, p. 294-302, 1955-56.
40 s p o n d i n g s e t t i n g of bz a n d o f t h e e l e v a t i o n of a profile p o i n t u s e d f o r t h e s c a l i n g o f t h e model in question. Since t h e r a d a r c l e a r a n c e s a r e n o t c o r r e c t v a l u e s a n d t h e r e a r e also ins t r u m e n t a l e r r o r s involved, t h e r e is a j u m p in scale a n d in e l e v a t i o n f r o m model to model. C o n s i d e r i n g model i + 1 ( F i g u r e 1) scaled, f o r i n s t a n c e , w i t h t h e c l e a r a n c e i ÷ 2 - - z ' ~ + 2 , p o i n t z~+ 1 will r e a d a n e l e v a t i o n i.i z'i.+l i n s t e a d of z~+ 1. I n o r d e r to derive c o r r e c t e l e v a t i o n s in model i + 1 all e l e v a t i o n r e a d i n g s m u s t be c o r r e c t e d b y t h e d i f f e r e n c e z~_!_, - - z'~+~ ~ Az~+ 1.
It is obvious t h a t t h e s e j u m p s in e l e v a t i o n could be e l i m i n a t e d during the instrumental process b y s i m p l y r e s e t t i n g t h e z-counter, but then the reference for the s e t t i n g of r a d a r c l e a r a n c e s w o u l d ........................ be lost. T h e r e f o r e , it s e e m s to be s i m p l e r to record t h e e l e v a t i o n s as Z~ Z',*I Z'i÷2 t h e y a r e a n d to i n t r o d u c e t h e Fig. 1. necessary corrections numerically l a t e r on. T h e elevation of a p o i n t in o v e r l a p N m u s t t h e n be c o r r e c t e d by 1;
A z I + Az.~ ÷ . . . + Az,~ = . ~ A z . 1
It should also be n o t e d t h a t scale e r r o r s h a v e a n e f f e c t on t h e e l e v a t i o n s . In f l a t c o u n t r y t h e s e e r r o r s a r e m o s t l y negligible b u t in hilly c o u n t r y scale e r r o r s a n d t h e r e s u l t i n g e f f e c t m a y be noticeable a n d t h e r e f o r e it m a y be n e c e s s a r y to i n t r o d u c e a n a d d i t i o n a l correction. C o m p a r i n g p h o t o g r a m m e t r i c e l e v a t i o n s w i t h c o r r e s p o n d i n g r a d a r elevations, disc r e p a n c i e s g r o w i n g w i t h i n c r e a s e d x ( d i s t a n c e f r o m t h e origin} become evident. T h i s e o m p a I i s o n c a n be best done g r a p h i c a l l y by p l o t t i n g t h e d i s t a n c e s a l o n g t h e x - a x i s a n d t h e above m e n t i o n e d d i s c r e p a n c i e s in t h e ~y-direetion. A s a r e s u l t a p o l y g o n is o b t a i n e d w h i c h could be r e g a r d e d a s a correction c u r v e if r a d a r e l e v a t i o n s w e r e t r u e . U n d e r o r d i n a r y f l i g h t conditions a n d f o r p o i n t s r e a s o n a b l y s e p a r a t e d , it is quite s a f e to a s s u m e t h a t t h e r a d a r e l e v a t i o n s a r e a f f e c t e d p r i m a r i l y by a c c i d e n t a l e r r o r s . C o n s e q u e n t l y t h e g r a d u a t i o n p r o c e s s is u s e d in o r d e r to d e t e r m i n e t h e p r o p e r s h a p e of t h e correction curve. R e m a r k a b l e r e s u l t s h a v e been o b t a i n e d so f a r f r o m s e v e r a l e x p e r i m e n t a l b r i d g i n g s over d i s t a n c e s r a n g i n g f r o m 30 u p to 200 miles, w h i c h of c o u r s e p r o v e s also t h e g r e a t reliability of r a d a r profiles. T h e i n t e n t i o n is to a p p l y t h e a n a l y t i c a l t r e a t m e n t to t h i s m e t h o d , as soon as t h e f i r s t s t e r e o c o m p a r a t o r s a r e a v a i l a b l e a n d t h e n t h e p r o c e d u r e m a y be altered. W e a r e t h i n k i n g f i r s t a b o u t t h e a l t i m e t e r d a t a w h i c h in s o m e of o u r e x p e r i m e n t s s h o w " s c a l e " e r r o r s t h a t a r e p r o b a b l y d u e to c a l i b r a t i o n e r r o r s in h e t A P R e q u i p m e n t . A l t i m e t e r i n d i c a t i o n s a r e in c e r t a i n r u n s s y s t e m a t i c a l l y too s m a l l or too large. T h e e f f e c t of t h i s on t h e r a d a r e l e v a t i o n p o i n t s u s e d in b r i d g i n g is p u r e l y a e c i d a n t a l a n d t h e r e f o r e is of n o t too s e r i o u s concern, b u t t h e w r o n g bz v a l u e s set on t h e p l o t t e r a c c o r d i n g to t h e a l t i m e t e r i n d i c a t i o n s d e c r e a s e t h e i n t e r i o r a c c u r a c y of a e r i a l t r i a n g u l a t i o n and, in consequence, also its f i n a l a c c u r a c y . T h e r e f o r e it a p p e a r s t h a t t h e a l t i m e t e r i n d i c a t i o n s s h o u l d be d r o p p e d f r o m t h e i n s t r u m e n t a l work. W h e r e a l t i m e t e r scale e r r o r s w e r e e s t a b l i s h e d , c o r r e c t i o n s to e l e v a t i o n s d e t e r m i n e d f r o m y - r o t a t i o n s of t h e p r e c e d i n g p r o j e c t o r s i m p r o v e d t h e f i n a l results.
41 C o r r e c t e d e l e v a t i o n s w e r e u s e d so f a r in o r d e r to i m p r o v e t h e c l e a r a n c e s s e t initially on t h e plotter, a n d t h e c o r r e s p o n d i n g c o r r e c t i o n s to t h e x a n d y model c o - o r d i n a t e s w e r e applied. U s i n g t h i s p r o c e d u r e , a n a c c u r a c y of a b o u t + 6 m e t e r s w a s o b t a i n e d on d i s t a n c e s u p to 330 k i l o m e t e r s . A m o r e c o r r e c t a d j u s t m e n t h o w e v e r s h o u l d be c a r r i e d out in a s l i g h t l y d i f f e r e n t way. T h e correction of c l e a r a n c e s b y c o r r e c t i o n s in r a d a r e l e v a t i o n s only is to a c e r t a i n
Fig. 2. S t r a i g h t line plotter. e x t e n t j u s t i f i e d b y t h e f a c t t h a t m o s t o f t h e e r r o r s in c l e a r a n c e s a r e c a u s e d b y f o r m s of t h e t e r r a i n a n d b y its c o v e r a g e . . H o w e v e r , in o r d e r to derive t h e b e s t possible value, r a d a r v a l u e s should be c o m p a r e d w i t h p h o t o g r a m m e t r i c c l e a r a n c e s a s o b t a i n e d f r o m a conventional bridging. I n t h e a n a l y t i c a l t r e a t m e n t we i n t e n d to u s e A P R d a t a f o r t h e f i n a l a d j u s t m e n t exclusively. I t is n o t clear w h e n t h e s t e r e o p l o t t e r s a r e u s e d w h e t h e r t h e r e j e c t i o n of t h e A P R d a t a f r o m t h e i n s t r u m e n t a l p r o c e d u r e is t h e r i g h t a n s w e r b e c a u s e of t h e i n s t r u m e n t a l e r r o r s w h i c h m u s t be considered. T h e e x p e r i m e n t s b e i n g c a r r i e d o u t a t p r e s e n t should supp]y the required information. T h e t r a n s v e r s a l bend of t h e s t r i p is a d j u s t e d to t h e " s t r a i g h t line" p r o d u c e d f r o m oblique p h o t o g r a p h s . T h e a d j u s t m e n t of z- a n d x - c o - o r d i n a t e s is e x t r e m e l y s i m p l e a n d c a n be done v e r y quickly, w h e r e a s t h e u s e of oblique p h o t o g r a p h s i n its p r e s e n t f o r m is a m u c h m o r e e l a b o r a t e p r o c e d u r e . I n p a r t i c u l a r , t h e c o n s t r u c t i o n of a s t r a i g h t line t h r o u g h o u t oblique p h o t o g r a p h s is a t a s k d e m a n d i n g t h e a t t e n t i o n of t h e m o s t reliable a n d skillful o p e r a t o r . I n o r d e r to e l i m i n a t e t h e p e r s o n a l f a c t o r involved a n d to f a c i l i t a t e a n d speed u p t h e s t r a i g h t line c o n s t r u c t i o n , a s t r a i g h t line p l o t t e r a s s h o w n in Fig. 2 w a s d e s i g n e d a n d b u i l t in o u r l a b o r a t o r i e s . A s in stereoscopic t y p e i n s t r u m e n t s , two s u c c e s s i v e oblique p h o t o g r a p h s a r e viewed a t t h e s a m e t i m e . V a r i a b l e m a g n i f i c a t i o n of t h e v i e w i n g s y s t e m combined w i t h t h e u s e of cylindrical l e n s e s p e r m i t s t h e o b s e r v a t i o n of selected detail on both p h o t o g r a p h s a t a p p r o x i m a t e l y e q u a l scales. A p p l y i n g , t h e n , t h e p r i n c i p l e of t h e
-20 m
"Horn"
,~110 m.
~oO!
Ioo
7oo
loo
llOO~
0 00- 007. 0 3O 0
40
la
60
o o~..j.C,,,.,/~
'~
80 0 0 0
0
o ~
140
Fig. 3
I~m
0°°
~ - e Gorteotl(m e a r n
0 Ground
120
o
0 0 0 0
Io
Fig. 4
~
Terroin Profile along Arizona FIiIM
I00
o ~.o°o~..J "--~
0
\
16Q \
O0~D A
0
I100 0
0
40
0 0 0
0
JoQ4k.~
O0 2100
m
220
- Xl[m
4~
43 f l o a t i n g m a r k , p o i n t s c a n be t r a n s f e r r e d f r o m one p h o t o g r a p h to t h e n e x t one w i t h a h i g h d e g r e e o f a c c u r a c y a n d in a s h o r t t i m e . No d o u b t t h e u s e o f t h i s e q u i p m e n t will be of g r e a t a s s i s t a n c e in p e r f o r m i n g t h e s t r a i g h t line c o n s t r u c t i o n . A t t h e s a m e t i m e , however, t h e r e a r e f u r t h e r t h o u g h t s on t h e q u e s t i o n of s i m p l i f y i n g a n d m a k i n g t h e b a s i c p r o c e d u r e m o r e s u i t a b l e f o r t h e electronic c o m p u t a t i o n s . I t h a s been decided to include t h e " p o l y g o n m e t h o d " in f u t u r e e x p e r i m e n t s . I n s t e a d of c o n s t r u c t i n g one s t r a i g h t line t h r o u g h o u t t h e s t r i p , s h o r t e r lines d r a w n on s i n g l e p h o t o g r a p h s will be joined in a p o l y g o n a n d u s e d l a t e r on f o r t h e control of t r a n s v e r s a l b e n d in t h e s t r i p . I t is hoped, b y u s i n g t h i s p r o c e d u r e , to r e t a i n t h e s a m e a c c u r a c y b u t c u t down t h e n u m b e r of c o m p u t a t i o n s necessary at present. T h e a u x i l i a r y d a t a m e n t i o n e d so f a r a r e n o t t h e only i n f o r m a t i o n p r o v i d e d b y t h e a i r b o r n e controlled m e t h o d o f a e r i a l t r i a n g u l a t i o n . I f t h e oblique p h o t o g r a p h s i n c l u d e t h e horizon, w h i c h is t h e case in t h e p r o c e d u r e p r e s e n t l y u s e d , t h e n a d d i t i o n a l e l e m e n t s q~ a n d o~ c a n be d e t e r m i n e d s i m i l a r l y to t h e horizon c a m e r a t e c h n i q u e . It i m p l i e s h o w e v e r t h a t t h e r e is no c h a n g e in r e l a t i v e position b e t w e e n t h e v e r t i c a l a n d oblique c a m e r a d u r i n g t h e f l i g h t , or a t l e a s t t h a t t h e i n s t a n t of c h a n g e if s u c h o c c a s i o n a l l y o c c u r s s h o u l d be recorded. T h u s t h e a u x i l i a r y d a t a c o n t a i n : 1. 2. 3. 4. 5. 6.
Altimeter (statoscope) data. Clearances. G r o u n d e l e v a t i o n s (profile) a l o n g t h e f l i g h t axis. S t r a i g h t line to control t h e t r a n s v e r s a l bend of t h e s t r i p . ~. 50.
It h a s to be e s t a b l i s h e d w h e t h e r or n o t is w o r t h while to u s e all t h i s a u x i l i a r y d a t a . T h e r e is, h o w e v e r , t h e o b v i o u s possibility of u s i n g oblique p h o t o g r a p h s in o r d e r to e l i m i n a t e t h e t w i s t f r o m t h e t r i a n g u l a t e d strip. In t h i s connection we a g a i n p r o p o s e t h e u s e of t h e s m o o t h i n g p r o c e s s in o r d e r to e l i m i n a t e t h e a c c i d e n t a l e r r o r s a f f e c t i n g h o r i z o n d a t a . S i n g l e i n d i c a t i o n s f r o m a u x i l i a r y e q u i p m e n t a r e p r i m a r i l y a f f e c t e d by a c c i d e n t a l e r r o r s w h i c h , in m o s t cases, a r e g r e a t e r t h a n t h e a c c i d e n t a l e r r o r s o f t h e s a m e e l e m e n t s e s t a b l i s h e d d u r i n g t h e p r o c e s s of i n s t r u m e n t a l b r i d g i n g . It s e e m s t h e r e f o r e t h a t a c e r t a i n g a i n in a c c u r a c y c a n be a c h i e v e d if b o t h m a g n i t u d e s a r e c o n f r o n t e d w i t h e a c h other. W e do n o t h a v e m u c h s t a t i s t i c a l m a t e r i a l to d e m o n s t r a t e t h e e f f i c i e n c y of t h e proposed m e t h o d of a e r i a l t r i a n g u l a t i o n u n d e r v a r i o u s conditions. H o w e v e r , t h e r e s u l t s o b t a i n e d so f a r a r e v e r y s a t i s f a c t o r y a n d q u i t e conclusive. T h e f i r s t s e r i e s of e x p e r i m e n t s c a r r i e d o u t o v e r f i a t c o u n t r y u s i n g Multiplex, S t e r e o p l a n o g r a p h C8 a n d W i l d A 7 p l o t t e r s c u l m i n a t e d in a b r i d g i n g a b o u t 330 k i l o m e t e r s tong, w i t h t h e f o l l o w i n g m e a n s q u a r e errors : = = m~ = m~ = m z m z
± 2.4 m e t e r s (checked on a p p r o x i m a t e l y 200 v e r t i c a l control p o i n t s ) , --+ 1.8 m e t e r s ( f o r p o i n t s located w i t h i n a c e n t r a l b a n d only 2 k i l o m e t e r s w i d e ) , ± 6.4 m e t e r s , ± 8.0 m e t e r s .
T h e s a m e s t r i p h a s been b r i d g e d b y t h e Colonial S u r v e y in E n g l a n d u s i n g M u l t i p l e x e q u i p m e n t . T h e a c c u r a c y in z w a s s l i g h t l y worse, a s w a s to be expected, b u t still e x c e l l e n t a n d r e a c h e d a v a l u e of m z = ± 3.4 m e t e r s . T h e opinion w a s , t h a t t h e u s e o f M u l t i p l e x did n o t allow a n y conclusion as f a r a s t h e d e t e r m i n a t i o n of x - c o - o r d i n a t e s w a s c o n c e r n e d a n d it s e e m s t h a t in c o n s e q u e n c e no a t t e m p t h a s been m a d e to a d j u s t t h e x - v a l u e s . H o w e v e r , t h e m a x i m u m error in x, a f t e r t h e s t r i p h a d been tied in a t b o t h e n d s w i t h o u t a n y f u r t h e r corrections, a m o u n t e d to a b o u t 32 m e t e r s on t h e g r o u n d , o r to a b o u t 0.6 m m on t h e m a p a t t h e scale of 1 : 50000,
44
o
o
!
-& l
~
o
~o o
©l
=o
I
o
:J
|,
•
. o
Q
~o
ooo
o0o0 oa
0
o
o
o,
o
o J o
oo
.o
o
~D o
Jo
o
•
o
•
a n d to a b o u t 2.0 m a t t h e scale of t h e M u l t i p l e x plot• I n view of t h e equipment used, this extraordinary r e s u l t m u s t be r e g a r d e d a s p u r e l y accidental, despite the fact that somewhat similar results were a c h i e v e d in o u r f i r s t e x p e r i m e n t s , also c a r r i e d o u t on M u l t i p l e x . T h e r e is h o w e v e r no d o u b t t h a t t h e m e t h o d is o n l y s l i g h t l y s e n s i t i v e to t h e e q u i p m e n t u s e d . Oblique p h o t o g r a p h s w e r e n o t u s e d b y t h e Colonial S u r v e y f o r t h e a d j u s t m e n t of t h e t r a n s v e r s a l bend of t h e strip• Radar ground elevations and r a d a r c l e a r a n c e s d e p e n d f i r s t of all u p o n t h e t e r r a i n . I n o r d e r to p r o v e t h e e f f i c i e n c y of t h e m e t h o d over h i l l y c o u n t r y , a 240-kilometer A P R f l i g h t w a s a r r a n g e d over~ t e r r a i n h a v i n g d i f f e r e n c e s in elevations r a n g i n g u p to a b o u t 600 meters. About 100 boundary points, v e r y p r e c i s e l y d e t e r m i n e d by t h e Geodetic S u r v e y , w e r e u s e d a s h o r i z o n t a l control. T h e i r identif i c a t i o n on a e r i a l p h o t o g r a p h s w a s v e r y d i f f i c u l t since t h e y w e r e seld o m located close to a n y c h a r a c t e r istic, e a s i l y i d e n t i f i e d terrain points. In addition, s n o w c o v e r a g e further increased the difficulties of identification. Another unfort u n a t e circ~umstance w a s t h a t t h e v e r t i c a l control a t o u r d i s p o s a l included only 23 e l e v a t i o n p o i n t s , n o t v e r y reliable, u n e v e n l y d i s t r i b u t ed a n d m o s t l y selected f r o m a n existing map. The flight was made on a cold w i n t e r day. T h e f l y i n g h e i g h t w a s a b o u t 6000 m e t e r s a n d the camera used was a Wild RC5a. A c c o r d i n g to t h e o p e r a t i n g comp a n y t h e A P R e q u i p m e n t did n o t w o r k in a n e n t i r e l y s a t i s f a c t o r y m a n n e r b u t t h e r e w a s no opport u n i t y to r e p e a t t h e f l i g h t . T h e r e s u l t s of t h e b r i d g i n g w h i c h followed w e r e • m z = -- 5.6 m e t e r s , ,m~ = ± 6.4 m e t e r s , ~nv = ± 9.5 m e t e r s .
45 F~gure 3 shows the corresponding graph for x-adjustment. T h e m o s t r e c e n t e x p e r i m e n t w a s c a r r i e d o u t o v e r a v e r y s h o r t d i s t a n c e o f 60 kilom e t e r s b u t r i g i d l y controlled b y m e a n s o f a b o u t 65 h o r i z o n t a l a n d 130 v e r t i c a l control points. I n t h e c e n t r a l section t h e f l i g h t c r o s s e d v e r y r u g g e d m o u n t a i n s r e a c h i n g a n elevation o f over 1000 m. T h e p r o f i l e o f t h e t e r r a i n a l o n g t h e f l i g h t line is s h o w n in F i g u r e 4. F l i g h t d a t a w e r e a s follows: F l y i n g h e i g h t over s e a level, a b o u t 6000 m. C a m e r a u s e d : F a i r c h i l d T l l , f = 153 ram, size of p h o t o g r a p h s 230 X 230 m m . On t h e p l o t t i n g m a c h i n e , W i l d AT, a l t i m e t e r i n d i c a t i o n s a n d c l e a r a n c e s w e r e u s e d . H o w e v e r , f o r t h e f i n a l c o m p u t a t i o n of e l e v a t i o n s t h e s t a t o s c o p e d a t a w e r e rejected, x-coo r d i n a t e s w e r e a d j u s t e d as in p r e v i o u s e x p e r i m e n t s . T h e m e a n s q u a r e e r r o r s w e r e : m z = --+ 2.2 m, m x : --+ 2.8 m, m y = ± 2.4 m.
F r o m t h e d i s t r i b u t i o n of t h e e l e v a t i o n e r r o r s w i t h i n s i n g l e models, it is e v i d e n t t h a t in t h e m o u n t a i n o u s section of t h e s t r i p poor i d e n t i f i c a t i o n of control p o i n t s p r o d u c e d e r r o r s in e l e v a t i o n u p to a b o u t --+ 1 m e t e r . C o n s e q u e n t l y t h e t r u e a c c u r a c y of b r i d g i n g in e l e v a t i o n s is h i g h e r t h a n i n d i c a t e d above. All t h e r e s u l t s s e e m to p r o v e t h a t t h e choice of a u x i l i a r y d a t a a s g i v e n b y t h e a i r b o r n e controlled m e t h o d o f a e r i a l t r i a n g u l a t i o n is v e r y s u i t a b l e a n d e x p e d i e n t b e c a u s e t h e a u x i l i a r y d a t a a r e a p p l i c a b l e to t h e s t r i p c o - o r d i n a t e s r a t h e r t h a n to t h e v e r y s e n s itive e l e m e n t s of o u t e r o r i e n t a t i o n . T h e r e is also a f u r t h e r c o n s i d e r a t i o n w h i c h s t r e s s e s t h e i m p o r t a n c e of t h e m e t h o d p l o p o s e d a n d i t s d i s t i n c t l y d i f f e r e n t c h a r a c t e r a s c o m p a r e d w i t h all o t h e r p r o c e d u r e s u s e d so f a r . A i r b o r n e p r o f i l e m e t h o d s of a e r i a l t r i a n g u l a t i o n c h a n g e t h e basic c h a r a c t e r of a e r i a l p h o t o g r a m m e t r y . F r o m being' a relative m e t h o d o f m e a s u r i n g it becomes n o w a n cLbsolute m e t h o d . T h e c o n s e q u e n c e s a r e a l r e a d y visible. R a n g e a n d t h e a c c u r a c y h a v e been m u l t i p l i e d . W i t h f u r t h e r i n s t r u m e n t a l i m p r o v e m e n t s a l r e a d y e n v i s a g e d , s u c h a s a b s o l u t e c l e a r a n c e d e t e r m i n a t i o n , a n d w i t h all t h e a d v a n t a g e s w h i c h c a n be t a k e n f r o m t h e a n a l y t i c a l t r e a t m e n t , it m a y h a p p e n t h a t m a n y o f t h e s e c o n d a r y geodetic o p e r a t i o n s will be solved by p h o t o g r a m m e t r i c m e a n s .
Discussion of lMr. Blachut'$ paper. Professor Doyle : Mr. B l a c h u t h a s m e n t i o n e d t h a t no oblique p h o t o g r a p h s w e r e a v a i l a b l e to control t h e y - d e f o r m a t i o n s in t h e l a s t s t r i p a n d t h a t a p a r a b o l i c y - a d j u s t m e n t w a s m a d e o n c e n t r a l control. I t s e e m s , t h e n , t h a t one p o i n t in t h e middle o f t h e s t r i p is w o r t h a]l t h e a u x i l i a r y d a t a , since t h e m e a n e r r o r is of t h e s a m e m a g n i t u d e . M a k i n g t h e s t r i p twice as long, t h e s a m e a m o u n t o f c o n t r o l w o u l d be s u f f i c i e n t . T h e r e is no d o u b t of t h e v a l u e of a u x i l i a r y d a t a in c a n t i l e v e r e x t e n s i o n , h o w e v e r . Mr. B l a c h u t : R e a s o n i n g t h u s , e x t e n s i o n to s t r i p s of i n f i n i t e l e n g t h w o u l d be possible! W h e r e control is e s t a b l i s h e d b y S h o r a n it is g e n e r a l l y n o t located in s t r a i g h t lines a n d is t h u s n o t s u i t a b l e f o r p a r a b o l i c corrections. Colonel T h o m p s o n : Does P r o f e s s o r Doyle s u g g e s t t h a t all u s e of a u x i l i a r y d a t a be disc a r d e d ? I s h o u l d like to p o i n t o u t t h a t t h e r e s u l t s d e p e n d also on o t h e r a u x i l i a r y d a t a t h a n oblique p h o t o g r a p h s a n d t h a t w i t h o u t t h e s e t h e m e a n e r r o r w o u l d n o t h a v e b e e n so favourable. Mr. B l a c h u t : T h i s b r i n g s u p a n o t h e r i m p o r t a n t p o i n t w h i c h I f o r g o t to m e n t i o n . . G e n e r a l l y e r r o r s in a t r i a n g u l a t e d s t r i p do n o t follow a second o r d e r c u r v e . T h e r e f o r e , a p a r a b o l i c c o r r e c t i o n does n o t g i v e t h e b e s t a n s w e r . T h e a u x i l i a r y d a t a s u g g e s t e d in m y t a l k p e r m i t u s to m a k e s u i t a b l e c o r r e c t i o n s all a l o n g t h e s t r i p .
4
46 Mr. Lorenz: Mr. Blachut has mentioned t h a t in some strips a scale correction "was applied to the altimeter. How was this determined? Mr. B l a c h u t : Systematic discrepancies between altimeter indications and corresponding data from the plotter reveal a degree of "scale altimeter error". Mr. Lorenz: W h a t kind of r a d a r return points were selected to scale on in mountainous country? Mr. Blachut: Any convenient point, preferably on level ground. If absolutely necessary, a photogrammetric point from the preceding model can be used. Large errors can always be isolated. Mr. B a u s s a r t : W h a t weight should be applied to the auxiliary data as compared to the corresponding quantities from classical triangulation? Mr. S c h u t : In the adjustment the auxiliary data are followed, but the weight attached to each individual quantity will be determined by the degree of smoothing. Mr. Bau~ssart: How is block a d j u s t m e n t carried out in this method? Mr. Blachut: The method deals with strip triangulation. No specifications as to block adjustments are ma.de. Professor Thompsvn: Apparently in this method we are not concerned with systematic or accidental errors, but with systematic and accidental accuracy? Professor M c N a i r : The problem of w h a t weights should be applied to the various quantities comprising auxiliary d a t a and the data of classical triangulation is still unsolved.
The publication of the texts of communications will be continued in the next i~sue o] Photogrammetria.