JOHN F. KENEFICK]FK, Inc.

Indialantic, FL 32903DONALD E. JENNI 'GS

Analytic Photo Control, Inc.Indian Harbour Beach, FL 32937

WARREN FUSSELMAN, L.S.General Development Corporation

Miami, FL 33131ORMAN MILLICHAMP

Miami Aerial Photogrammetric Services, Inc.Miami, FL 33131

Bridging with IndependentHorizontal ControlAnalytical aerial triangulation performed with distances andazimuths proved to be less costly than that performed withconventional ground control.

INTRODUCTION

JUSTIFICATION FOR INDEPENDENT HORIZONTALCONTROL

T RADITIONALLY, aerial triangulation aspracticed in the commercial mapping

community is controlled by horizontal andvelikal control points. In the case of hori-

is viewed in this way one must necessarilyask whether this cost can be reduced butyet allow production of the maps in accor­dance with the project specifications. Inmany cases the answer to this question is adefinite yes, and a means by which this maybe accomplished is by utilizing independenthorizontal control instead of traverse control.

ABSTRACT: The concept of using distances and azimuths to controlaerial triangulation has been long established, but examples of prac­tical implementation in commercial mapping have not been widelypublicized. The underlying principles of one method of bridgingwith independent horizontal control are described. A block of foursidelapping flight lines containing 67 photographs at a scale of1 in. = 500 ft was initially controlled for and bridged by convention­al aerial triangulation procedures. The same project also was con­trolled and bridged according to the method of independent hori­zontal control. Comparison of coordinates of passpoints from thetwo methods of bridging showed rms differences of 0.58 and 0.60 ftin X and Y, reflecting good relative accuracy. Overall savings inproducing mapping control amounted to 33 percent when themethod of independent horizontal control was used as an alternateto the conventional method. Greater savings are anticipated forother projects.

zontal control points, these are most oftenestablished by traverse surveys. In mappingprojects, where permanent ground surveysare not required, such traverse work is mere­ly an expense item relative to producing themaps. That is, results of the field work arenot generally reusable. When the field effort

THE BASIC CONCEPT

Horizontal control for aerial triangulationand mapping simply serves three fundamen­tal purposes:

• to provide scale,• to provide azimuth orientation, and

687PHOTOGRAMMETRIC ENGINEERING AND REMOTE SENSING,Vol. 44, No.6, June 1978, pp. 687-695.

688 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1978

• to provide absolute reference to someadopted X-Y coordinate system.

Note that none of these dictate that X-Yhorizontal control points are an absolutenecessity. For example, scale can be provid­ed simpl\' by surveying horizontal distancesbetween a few pairs of points scatteredthroughout the project. Azimuth orientationcan be provided bv astronomic observationsof azimuth over lines between the same orseparate pairs of points. Absolute referencemay be established simply by assigningassumed coordinates to one point, in whichcase the coordinate system is a local or arbi­trary one. Alternately, one or more existingpoints of known position in, say, a stateplane coordinate system may be used. Thus,all of the fundamental hlllctions of horizon­tal control may be satisfied by new surveyswhich do not establish positions of controlpoints. Moreover, the only necessity forintervisibility is along lines over which dis­tances ancVor azimuths are observed. Sincethese lines need only be scattered through­out the project, they are totally independentof one another, that is, not tied together as ina traverse or triangulation network. Hence,the de~!gnation "independent horizontalcontrol.

It is well to make clear that the concept ofindependent horizontal control does notoriginate with the authors. In hlCt, the tech­nique has heretofore been described in theliterature by others (e.g., Brandenberger,1959; Colcord, 1961; Ghosh, 1962; andWong, 1972). Also, the method has beenused on some commercial mapping projectsover the past several years, but these appli­cations have not been widely publicized.Moreover, to the knowledge of the authors,there have never been documented studiesof the accuracy and cost-effectiveness of themethod based upon production experience.

COMPUTATIONAL METHODS

There are two basic methods for incorpo­rating independent horizontal control intothe aerial triangulation. The most rigorousmethod is to introduce such data directlyinto the aerial triangulation adjustment, suchas described by Wong (1972). This is doneby introducing condition equations whichmathematically impose additional con­straints within which the adjustment mustbe solved. As an example, an equation maybe set up which states that the computedcoordinates of a pair of passpoints must besuch that the inversed distance agrees withthe surveyed distance (in the least squaressense). Likewise, an equation can be set up

to express that a calculated azimuth mustagree with the surveyed value. Other condi­tion equations may be set up, including thevery basic one that the computed coordi­nates of a point must agree with known X-Yvalues. This paIticular equation, however,is not unique to the method of independenthorizontal control; it is a basic equation ofall aerial triangulation adjustments.

The second method is to impose the inde­pendent horizontal control condition equa­tions in a separate adjustment computation.This adjustment would be preceded by anormal aerial triangulation computation, butone which employs only two X-Y horizontalcontrol points or approximated X-Y horizon­tal control points. Results of this aerial tri­angulation are, of course, only provisionaland will be "warped" to some extent. Thefunction of the second adjustment, then, isto remove these deformations by using theindependent horizontal control data. Thistwo-step approach is the one employed bythe authors.

MATHEMATICAL FORMULATION

In the two-step approach to the use ofindependent horizontal control, the first step(i.e., aerial triangulation) is not affected inany way programming-wise. There is only aminor procedural difference owing to thesparse and/or approximated X-Y horizontalcontrol used in the aerial triangulation com­putations. Hence, it is necessary to consideronly the mathematical nature of the secondstep wherein the independent horizontalcontrol are used to "readjust" results of thefirst step.

BASIC MATH MODEL

It is a basic assumption that the result ofthe first step is systematically warped suchthat the def()rmations are representable bythe confo1111al equations:

(1)

in which,

X 2,Y2 = coordinates of a point after thesecond-step adjustment

PI = the coefficient matrix of the con­formal equations evaluated usingcoordinates of the same point result­ing from the first-step adjustment

= [1,O,X, - Y,(XL Y2), -2XY,(XL 3XY2),( -3X2y+Y3~

0,1,Y,X,2XY,(XL Y2),(3X2Y - Y3),(XL 3XY2) J1

BRIDGING WITH INDEPENDENT HORIZONTAL CONTROL 689

M x = the difference between the first rowsof the P I coefficient matricies gener­ated by the two endpoints of the line

M\· = the difference between the secondrows of the P I coefficient matriciesgenerated by the two endpoints ofthe line

Azimuths are also typically scatteredthroughout the project and these are anabsolute necessity as the basis for removingsystematic distortions which remain at theend of the first-step adjustment. Except forvery short strips, it is incorrect to assumethat azimuths can be dispensed with. Azi­muths are determined preferably throughobservations on Polaris, but careful solarobservations aided with a Roelofs prismmay also be used.

SOLUTION OF THE SYSTEM

The condition equations (Equations 2, 3,and 4) are linearized, evaluated, and accu­mulated into the normal equations in accor­dance with standard procedure for any leastsquares adjustment. The program used bythe authors allows individual weighting ofknown coordinates and distances in groundfeet (or meters) and azimuths in seconds ofarc. The coefficient matrix of the normaleq uations is of rank 8, so the inverse andcalculation of the solution vector is very fast.The solution vector is added to the previousvalues of the unknowns c" C'b •.. , Cs and theentire process is repeated. This iterativeprocedure continues until the solution vec­tor goes to zero.

POSITION CONDITIOi': EQUATIO:--i

For any point whose final coordinates areknown in advance, Equations 1 are simplyrearranged to form the position conditioneq uation:

[~t -P, . C = a (2)

in which the known coordinates are substi­tuted for X2 and Y2, since we desire the finalvalues to be equal to the known values.

As a minimum there must be one suchcondition equation. Otherwise, the solutionwill float around in the X-Y plane. That is,we mi.rst tie the solution down at least at onepoint. This point may be arbitrarily chosenand assigned artificial coordinates such as 0,0; or 1 000 000, 500 000; or the point may beone for which state plane coordinates areknown. If more than one point has knowncoordinates in the same coordinate system,all of these points may be used simply bywriting as many condition equations of thefonn of Eq uation 2.

C = the vector of conformal transforma­tion constants whose values must bedetermined in the second-stepadjustment

= [c he 2,C 3,C -be 5,C 6,C 7,C 8] T

DISTAi':CE co, DITIO ' EQUATION

For any pair of points, between which thehorizontal distance is known, Equations 1give rise to the condition equation:

d - [(M, . C)T (M, . C)] V2 = a (3)

in which,

d = the surveyed distance reduced tohorizontal (and grid if applicable)

M, = the difference between the P, coefH­cient matrices generated by the twoendpoints of the line

Typically, measured distances are scatteredthroughout the project just as X-Y horizontalcontrol points are in conventional aerial tri­angulation.

AZIMUTH CONDITION EQUATION

For any pair of points between which theazimuth is known, Equations 1 give rise tothe condition equation:

a - Tan-I [(Mx . C)/(My . C)] = a (4)

in which

a = the azimuth (reduced to grid, if appli­cable) from one point to the other

COOPERATIVE INVESTIGATION

BACKGROUND

Up until 1970, General Development Cor­poration (CDC) did not make use of aerialtriangulation of any kind. All stereomodelswere fully controlled by conventional hori­zontal and vertical ground surveys. At thistime, with the adoption of fully analyticalaerial triangulation via contracted services,CDC never again reverted to controllingstereomodels completely on the ground.

At first, aerial triangulation control wasestablished by GDC according to traditionalschemes, but it was not long before the firmtried the concept of perimeter control (hori­zontally) which had recently been investi­gated by Kunji (968) and Cyer and Kenefick(970). Actual field checks made by GDCthrough the interior of a 13-stIip block con­trolled horizontally only about the perimiterverified that the technique was suitable for

690 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1978

production work. Thereafter, CDC's policywas to run perimeter horizontal control only.In many instances, the boundary survey ofa tract also served as the horizontal controlsurvey for the aerial triangulation. In thesecases the horizontal control for aerial trian­gulation was obtained without any addedfield costs except for targetting of selectedturning points on the traverse.

There are situations, however, when CDCdesires to map an area where a boundarysurvey is not required. Heretofore, CDCwould nonetheless run a perimeter traversesolely for the purpose of controlling theaerial triangulation. It is this "special SUI:­

ey" situation that CDC preferred to avoidor, at least, reduce in terms of time and cost.It is precisely at this point at which CDCwas introduced to the concept of indepen­dent horizontal control.

ORGANIZATION OF PILOT PROJECT

As is evident from authorship of this aIti­c1e, four firms worked together to execute apilot project. Brief descriptions of theirresponsibilities are given here. It is well tomention, however, that this was an actualproduction mapping project being done forthe first time.

CDC assumed the responsibility for exe­cution of all field surveys. Also, time andcost figures for the field work were closelymonitored and compiled by CDC. MiamiAerial Photogrammetric Services (MAPS),who is responsible for all of CDC's photo­grammetric mapping, not only produced themaps but also coordinated the field surveyrequirements between Analytic Photo Con­trol (APC), their aerial triangulation special­ist firm, and CDC.

APC performs all of MAPS aerial triangu­lation work. APC planned the field controlscheme and then performed the point trans­fer work on their Wild PUC4, mensurationon their Kern MK2, and data processing ontheir NOVA 3/12. APC's aerial triangulationsoftware is the JFK-developed RABATS sys­tem which incorporates the adjustment toindependent horizontal control according tothe technique described earlier.*

JFK's participation was primarily con­cerned with analyses and repOlting of results.This included a number of experimentalaerial triangulation "runs" and transforma­tions between sets of resulting coordinates.

* RABATS is the acronym for Rapid AnalyticalBlock Aerial Triangulation. The adjustment toindependent horizontal control capability is anoptional "plug-in" module which can easily beinterfaced to any other aerial triangulation system.

GROUND SURVEYS

The pilot project is located in south Flori­da where CDC desired to map approximate­ly 8 400 acres at a scale of 1 in. = 100 ft fromaerial photographs of scale 1 in. = 500 ft.Horizontal control was established in twoseparate ways. First, a perimeter traversewas run even though a boundary survey wasnot required by CDC. This survey was exe­cuted solely to provide horizontal control forconventional aerial triangulation. Selectedturning points on the traverse were targettedfor this purpose (see Figure 1). Distanceobservations were made with an HP 3800distance meter and angles were observedwith a Wild T2.

The second horizontal survey consisted ofmeasuring independent distances and azi­muths as indicated in Figure 2. Preliminaryselection of these lines was based upon thedesire to scatter the independent horizontalcontrol throughout the project and upon astudy of accessability as best as this could bedetermined from 1:24 000 U.S. CeologicalSurvey quadrangle sheets. The same fieldequipment was used for these measure­ments as was used in the traverse work.Astronomic observations were on Polariswith time being kept by means of an accu­rate stopwatch synchronized (at the office)with WWV prior to and upon completion ofthe field work.

Calculation of both surveys was perforn1edon the Florida State plane coordinate sys­tem. However, the project did not requirethat a tie be made to the State plane system.The traverse closure amounted to 1:57000in position after adjustment of each angle by0.7 sec of arc.

Inasmuch as the mapping project requiredcontours, elevation control was establishedby differential leveling. Selected turningpoints were targetted to control the aerialtriangulation (see Figure 1). The same ele­vation control was used for the conventionalaerial triangulation and for aerial triangula­tion with independent horizontal control.

STRIP ADJUSTMENTS

In production, block aerial triangulationnormally would be performed without inter­mediate adjustment of individual strips. Itwas desired, however, to evaluate the effec­tiveness of independent horizontal controlon a single strip as well as on the entireblock. Hence, flight line 1 was computed byitself in two ways. In the first calculation thestrip was bridged in the usual way using the12 X-Y horizontal control points which fellwithin the strip (Figure 1). The resultant

[•

BRIDGING WITH INDEPENDE T HORIZO TAL CO TROL 691

• • • • • •~---+-------<-------+-~--.-------<---+-~-~--.--__---+-+-I 0

• •

•

-+---+---+---+---+---+---+----_--..--~-~--,-.-+I----·=.,-----<~-®•

••~--.---.-~~-~-----~-....--~--.------.------+-~~-0

•

••

-+--~-~---+------+--------+---~-..--~---+-~~-~-0

• •• • • • • •

• Horizontal a V,rtical ConIIo4

• Vertical Control

FIG. 1. Layout of the pilot project showing flight lines and horizontal and veltical control forconventional aerial triangulation.

RMS "fit" to the control was 0.30, 0.29, and0.23 ft in X, Y, and Z, respectively. Maximummisfits amounted to 0.57, 0.53, and 0.51 ft.

In the second calculation the strip wasrebridged and initially adjusted to only twoX-y control points. These two control pointswere actually the endpoints of the indepen­dently measured distance near the center ofthe strip (Figure 2); they were not traversestations. Assigned coordinates of the endpoints were aItificial except for the fact thattheir inverse produced the measured dis­tance (reduced to the State plane grid). Thiscalculation of the strip is that which wasreferred to earlier as the "first-step adjust­ment".

/

Before proceeding with the second-stepadjustment to the independent horizontalcontrol, results from the first-step adjust­ment were mathematically translated androtated (but not scaled) to the results fi'omthe conventionally controlled aerial triangu­lation. RMS differences existing betweenthe two sets of data were found to be 1.04and 1.72 ft in X and Y, with maximum differ­ences amounting to 2.79 and 4.54 ft. Thistransformation was performed using allpoints to obtain the overall best-fit in theleast squares sense. Moreover, the patternof these differences was markedly systematicowing to yet uncorrected varying scale andazimuth drift in the strip. But, by rescaling

-

\

-FIG. 2. Locations of measured distances and azimuths for aerial triangulation with independenthorizontal control. Vertical control is the same as in Figure 1.

692 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1978

J1

using an average scale based on all threedistances, it was possible to reduce the RMSvalues to 0.89 and lAO ft with maximumdifferences of 2.14 and 3.20 ft.

The next step was to perform the second­step adjustment to the three distances andthree azimuths which fell within the strip.One endpoint of one distance was also as­signed artificial X-Y coordinates to preventthe strip from "floating" in the X-Y plane.These control data generated eight condi­tion equations, which theoretically wouldallow a determination' of the eight transfor­mation constants (c" C2, ... , cs) of Equations1. But, recognizing that this represented aunique solution, the program automaticallytruncated the two cubic terms, leaving onlysix transformation constants to be solved for.Nevertheless, the "fit" to all three distancesand azimuths was essentially perfect (i.e.,zero residuals).

The above step normally would be the lastperformed in production inasmuch as it pro­duces the final X-Y ground coordinates. Forcomparison purposes, though, these resultswere further translated and rotated to theresults from the conventionally controlledstrip adjustment. RMS differences betweenthe two sets of data now amounted to 0.52and 0.30 ft in X and Y with maximum differ­ences of 1.32 and 0.68 ft.

BLOCK ADJUSTMENTS

The entire block was also computed intwo ways. In the first calculation the blockwas bridged in the usual fashion using theX-Y horizontal control points about theperimeter of the block (Figure 1). The resul­tant RMS "fit" to the control was 0.37, 0.28,and 0.31 ft in X, Y, and Z, with maximumdifferences of 0.89, 0.71, and 0.70 ft. At tiepoints between the strips the RMS of the"half residuals" was 0.30, 0.23, and 0.29 ft,with maximum half-values of 0.68, 0.67, and0.66 ft.

In the second calculation the block wasrebridged and initially adjusted to six"approximate" X-Y horizontal control points.Three of these were across the top of theblock and three were across the bottom suchthat each strip contained two such approxi­mate control points. All of these points werephoto identities in the sense that they couldbe located on the 1:24000 USGS quadranglesheets, from which the X- Y coordinates werescaled. Hence, the designation "approxi­mate" horizontal control.

It is well to mention here that this proce­dure of using approximate horizontal controlis deemed desirable for bridging blocks with

programs which use polynomial smoothingfunctions. In order to obtain a good fit at tiepoints between longer strips it is necessaryto allow the polynomial functions to go intothe second and third degree. If only two X-Yhorizontal control points are used to initiallycontrol the block (as is done with singlestrips) it is conceivable that the block maybe very severly deformed in the absence ofX-Y horizontal control within each or, atleast, within every other strip.

As expected, the "fit" at the approximatehorizontal control was poor by ordinary stan­dards. RMS misfits amounted to 27 and 14 ftin X and Y, respectively. But, bear in mindthat this is only what was referred to earlieras the "first-step adjustment." The goal upto this point was to obtain a provisional solu­tion with remaining errors of such systemat­ic nature that they may be removed in thesecond-step adjustment to the independenthorizontal control.

Before proceeding with the second-stepadjustment, results of the provisional solu­tion was translated and rotated to the resultsobtained from the conventionally controlledaerial triangulation. RMS differences be­tween the two sets of data were found to be5.83 and 9.01 ft, respectively, in X and Y.But, by rescaling the provisional solutionbased on the 12 independent distances, theRMS values were reduced to 1.15 and 1.01ft in X and Y, respectively, with maximumdifferences of 3.15 and 2.72 ft. This wasactually an unexpected result. Other experi­ments have indicated that such small valuescannot always be expected after a simplescaling.

The next step was to perform the second­step adjustment using the 12 azimuths and12 distances (Figure 2) as the independenthorizontal control. One endpoint of onehorizontal distance was also assigned altifi­cial X-Y coordinates to prevent the blockfrom "floating" in the X-Y plane. Together,these control data generated 26 conditionequations which allowed all eight transfor­mation constants of Equations 1 to be deter­mined. Upon conclusion of this adjustment,the residuals at the control were as shown inFigure 3. However, the large residual at azi­muth 127-126 is misleading. Because ablunder occurred in this palticular azimuth,its assigned accuracy (standard deviation)was set at 9 999 sec of arc whereas all otherazimuths were assigned accuracies of 3 secof arc. In essence, then, azimuth 127-126contributed nothing to the solution (i.e., hadno effect on the solution) but its residual wasnonetheless computed.

BRIDGING WITH INDEPENDENT HORIZONTAL CONTROL 693

FIN;lL RESIOUt'lLS

;185. CONTROL PTS. (ADJUSTED Vt'lLUES)POINT ii \' Vii UI'

363 734617.68 1876311.57 8.&8 B.8e

HORIZ. DIST;lNCES (t'lD_~STED Vt'lLUES)PT. TO PT. DIST. VD

111..1 189 2874.138 -ti.361(16 1e5 1922, 22 -0. 15182 181 2881.78 ,,54127 126 3216.43 8.8?124 154 2818.14 8.82155 122 2864.8J 8.4612" 119 28J8.61 -8.43113 J12 1972.82 9.253633362245.29 -8.47334 368 1774.59 -8.85333 343 2459.96 -8.23115 116 2407.83 -;).59

U;lZ& 0 -5.42l~ 8 27.89Ii ;)-37 4813 -2-52.68 1<

8 8 25.188 8 -7.198 8 -4.268 8 -8.568 8-49.418 ;) 1513tI e 17.75;) ;) 27.16

PLt'lNE t'lZINUTHS (;lDJUSTED VALUES)PT. TO PT. t'lZlnUTH

118 J@9 152 16 34. 42106 105 152 5 2J .911;)2 181 1533716.48127 126 91 1511.68124 154 8 2 12.82155 122 336 4 113.19128 119 337 14 42. 26113 112 224 11 11.56363 336 1794425.41334 368 53 947.87333 343 182 45 18.25115 116 155 33 38. 84

* azimuth relaxed

FIG.3. Computer output of final residuals at inde­pendent horizontal control.

Magnitudes of the distance residualsshown in Figure 3 are in line with thosewhich should be expected from aerial tri­angulation with 1 in. = 500 ft photographs.For production work with the RABATSaerial triangulation programs it is usuallyestimated that the passpoints will be deter­mined with an RMS accuracy (standard de­viation) of 1 part in 1,850 of the negative~cale, as expressed in feet per inch, in X andin Y, provided, ofcourse, that the ground con­trol is of good quality and well distributed.For 1 in. = 500 ft negatives, then, the ex­pected RMS passpoint accuracy (standarddeviation) is 0.27 ft in X and in Y. Statistical­ly it can be shown that the distance calcu­lated between any two passpoints, regard­less of their distance a~t, should have astandard deviation of V 2 x 0.27 or 0.38 ft.As a practical matter the maximum expectederror would be approximately 2.5 times thestandard deviation or 0.95 ft. These valuescompare very nicely to the distance residuals"VD" shown in Figure 3.

'vVith regard to the azimuth residuals,these too are within expectations. Statistical­ly it can be shown that the standard devia­tion of an azimuth computed between twopasspoints is equal to the standard deviationof the distance divided by the distance itself.It was shown in the preceding paragraph

that the expected standard deviation be­tween any two passpoints is 0.38 ft. Sincethe lengths of the lines over which azimuthswere observed range between 2,000 and3,000 ft, it should be expected that the stan­dard deviations of the azimuths will lie inthe range of 26 to 39 sec of arc with maxi­mum expected errors on the order of65 to 98sec of arc. From Figure 3 it can be seen thatthe results were actually better than statisti­cal estimates would indicate.

Two practical points should be mentionedhere. The first is that misfits on the horizon­tal distances and on the azimuths are attrib­utable almost entire ly to error in the aerialtriangulation. Survey errors in measuringthe distances and azimuths are small relativeto the errors in the aerial triangulation. Thisis the basis for the earlier statement thatcareful solar observations can be employedin lieu of observations on Polaris.

The second point is relative to elevationscomputed in the aerial triangulation. Inas­much as the pilot project covered rather flatterrain, elevations computed in the first­step adjustment were correct and were usedfor the mapping. If a project is in rough ter­rain, however, these elevations will sufferfrom incorrect scaling at this stage. To obtaincorrect elevations it is necessary, therefore,to repeat the aerial triangulation in a con-

694 PHOTOGRAMMETRIC ENGI lEERING & REMOTE SENSI G, 1978

TABLE 1. DIFFERENCES BETWEEN BRIDGING WITH CONVENTIONAL CONTROL

AND INDEPENDENT HORIZONTAL CONTROL

STRIP BLOCKRMS-X RMS-Y MAX-X MAX-Y RMS-X RMS-Y MAX-X MAX-Y

After First-StepAdjustment 1.04 1.72 2.79 4.54 5.83 9.01 14.12 17.40

After Rescaling' 0.89 1.40 2.14 3.20 1.15 1.01 3.15 2.72

After Adjustmentto IndependentControl 0.52 0.30 1.32 0.68 0.58 0.60 1.74 1.66

! Step not done in practice. The adjustrnent to independent horizontal control immediately follows the first-step adjustment.

ventional sense using a few pass points ashorizontal control points, X-Y values forwhich would be taken from the results of theadjustment to independent horizontal con­trol.

In order to further evaluate results ob­tained with the block adjustment to inde­pendent horizontal control, the final X-Ycoordinates were translated and rotated (butnot scaled) to the corresponding values fromthe block adjustment with perimeter X-Yhorizontal control. RMS differences were0.58 and 0.60 ft in X and Y, with maximumdifferences of 1.74 and 1.66 ft.

SUMMARY OF DATA A 'A LYSIS

Inasmuch as the preceding discussionswere necessarily complicated by numerousexplanations, it is well to summarize theresults before proceeding. It must be bornein mind, however, that all of the compari­sons described earlier were against the re­sult of the conventionally controlled aerialtriangulation. Hence, all differences re­ported really reflect differences betweendata produced by conventional aerial trian­gulation and data produced by the adjustmentto independent horizontal control method,

both of which contain errors of their own.Table 1 summarizes only relative accuracysince the adjustments to independent hori­zontal control were not done on the Stateplane coordinate system (but, the programcan do so if State plane coordinates areknown for one or more points).

ECONOMIC ANALYSES

Costs involved in perfolwing both types ofhorizontal surveys were carefully monitored.Final costs to produce the mapping controlfor the block are given in Table 2.

From Table 2 it is clear that savings infield work alone amounted to 50 percent.Overall savings, however, amounted to 33percent owing to the increased cost of theaerial triangulation work. Of course, thesepercentages apply only to this particularproject. It is the opinion of the authors,however, that this pilot project is actually apoor example insofar as savings are con­cerned. This is because it was possible torun the perimeter traverse on hard surfacesalong three sides of the project with only thefourth side (and one of the shortest) beingcross-country. Also, access to the interior ofthe project was difficult owing to the

TABLE 2. COSTS TO PRODUCE MAPPING CONTROL FOR THE BLOCK

CONVENTIONAL BRIDGING1. Perimeter horizontal

survey' .420 hI'S. @ $15.00 $ 6,3002. Elevation survey' 180 hI'S. @ $15.00 2,7003. Aerial triangulation 67 frames @ $37.00...................................................... 2,479

$11,479

BRIDGING WITH INDEPENDENT HORIZONTAL CONTROL1. Measure distances

and azimuths' 120 hI'S. @ $15.00 $2. Elevation survey' 180 hI'S. @ $15.00 ..3. Aerial triangulation 67 frames @ $47.00 ..

$

I Includes targetting and computations.

1,8002,7003,1497,649

BRIDGING WITH INDEPENDENT HORIZONTAL CONTROL 695

swampy nature of the land. Finally, the job­site was so close to home base that transpor­tation and per diem expenses were notexperienced. Surely all of these conditionswill be just the reverse on many projects,thereby making the use of independent hor­izontal control even more attractive.

REFERENCES

Brandenberger, A. J., 1959. Strip TriangulationWith Independent Geodetic Controls; Tri­angulation of Strip Quadrangles, PublicationNo.9 of The Ohio State University Instituteof Geodesy, Photogrammetry and Cartog­raphy.

Colcord, J. E., 1961. Aerial Triangulation StripAdjustment With Independent Geodetic

Control, Photogrammetric Engineering,March, 1961.

Ghosh, S. K., 1962. Strip Triangulation With Inde­pendent Geodetic Control; PhotogrammetricEngineering, November 1962.

Gyer, M. S., and J. F. Kenefick, 1970. The Propa­gation of Random Error in Block AnalyticalAerotriangulation, Photogrammetric Engi­neering, September 1970.

Kunji, B., 1968. "The Accuracy of Spatially Adjust­ed Blocks", presented at the Eleventh Con­gress of the International Society of Photo­grammetry, Lusanne, Switzerland.

Wong, K. W., and G. Elphingstone, 1972. Aerotri­angulation by SAPGO, PhotogrammetricEngineering, August 1972.

(Received December 8, 1977; revised and ac­cepted February 27, 1978)

A Major Reorganization!! Do You Get The Picture?The fonner Photography Division of the ASP is now the

PRIMARY DATA ACQUISITION DIVISION

with responsibilities and functions expanded to more clearly recognize and give a firmerhome base to the many ASP members whose work, interests, and expertise are in these fields:

• Electro-Optical Sensors. Scanning and framing; vidicons; MSS, CCD's, MLA's; you name it.• SAR and SLAR. Enough said.• Thermal and Passive Microwave. Imaging or otherwise.• Holographic Image Acquisition and Processes.• X-Ray and Neutrographic Image Acquisition.• Aerospace Photographic Systems. Close range, orbital, and extra terrestrial image acquisition.• Environmental Factors. The atmosphere, the hydrosphere, the platform.• Navigational and Positional Data. Inertial, Doppler, laser altimetry, navigational satellites.

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If your interests are in theory, systems design, practice, computer technology, or the nuts­and-bolts of hardware for acquiring and producing the highest quality of deliverable FirstGeneration data for analysis and application, let us know of your support:

DON ROSS (613) 224-90601210 Major StreetOttawa, Ontario K2C 2S2(Director, PDAD)

RONALD J. ONDREJKA (617) 276-2502Itek Corporation10 Maguire RoadLexington, Massachusetts 02173(First Deputy, PDAD)

DR. PHILIP SLATER (602) 296-26278415 E. SpeedwayTucson, Arizona 85710(Second Deputy Director, PDAD)

P.S. How about papers for Albuquerque, Oct 15-21, 1978? Deadlines, 15 June for abstracts, 30July for manuscripts. Call Dr. Stan Morain, (505) 277-4000