Air Borne GPS

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PRINCIPLES OF AIRBORNE GPS

INTRODUCTION

The utilization of the global positioning system (GPS) in photogrammetric mapping beganalmost from the inception of this technology. Initially, GPS offered a major improvement inthe control needed for mapping. It provided coordinate values that were of higher quality and

more reliable than those using conventional field surveying techniques. At the same time thecost and labor required for that control were lower than conventional surveying. Experiences

from using GPS-control showed several improvements [Salsig and Grissim, 1995]:

a)There was a better fit between the control and the aerotriangulation results, particularly for

large-area projects.b)Surveyors were not concerned with issues like intervisibility between control points,

therefore the photogrammetrist often received the control points in locations advantageous tothem instead of the location determined from the execution of a conventional field survey.c)Visibility of the ground control point to the aerial camera is always important. Fortunately,

those points that are visible using the GPS receivers are also free of major obstructions thatwould prevent the image from appearing in the photography. This led to a better recovery rate

for the control.

Unfortunately, the window from which GPS observations could be made was not always at

the most desirable time of day. This changed as the satellite constellation began to reach its

current operational status. Also, with these increasing windows came the idea of placing aGPS receiver within the mapping aircraft.

Airborne-GPS is now a practical and operational technology that can be used to enhance the

efficiency of photogrammetry, although Abdullah et al [2000] reports that only about 30% ofthe photogrammetry companies are using this technology at this time. But, this does account

for about 40% of the projects undertaken by photogrammetric firms. Airborne GPS can beused for: precise navigation during the photo flight, centered or pin-point photography,determination of the coordinates of the nodal point for aerial triangulation

To achieve the first two applications the user requires real-time differential GPS positioning

[Habib and Novak, 1994]. Because the accuracy of position for navigation and centeredphotography ranges from one to five meters, C/A-code1 or P-code2 pseudorange is all that isrequired. The important capability is the real-time processing. For aerotriangulation, a higher

1C/A Code: The standard (Clear/Acquisition) GPS PRN code, also known as the Civilian Code or S-Code.

Only modulated on the L1 carrier. Used by the GPS receiver to acquire and decode the L1 satellite signal,

and from which the L1 pseudo-range measurement is made.2P-Code: The Precise or Protected code. A very long sequence of PRN binary biphase modulations on the

GPS L1 and L2 carrier at a chip rate of 10.23MHz, which repeats about every 267 days. Each one week

segment of this code is unique to a GPS satellite and is reset each week. Only US military and other

authorised users are able to overcome AS using special receivers.


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accuracy is needed which means observing pseudorange and phase. Here, real-time

processing is not as important in terms of functionality.

Airborne GPS is used to measure the location of the camera at the instant of exposure. Thisgives the photogrammetrist XL, YL, and ZL. GPS can also be used to derive the orientation

angles by using multiple antennas. Unfortunately, the derived angular relationships only havea precision of about 1 of arc while photogrammetrists need to obtain these values to betterthan 10 of arc.

To compute the position of the camera during the project, two dual frequency geodetic GPSreceivers are commonly employed. One is placed over a point whose location is known and

the other is mounted on the aircraft. Carrier phase data are collected by both receivers duringthe flight with sampling rates generally at either 0.5 or 1 second. The integer ambiguity must

be taken into account and this will be discussed later. Generally, on-the-fly integer ambiguityresolution techniques are employed.

ADVANTAGES OF AIRBORNE GPS

The main limitation of photogrammetry is the need to obtain ground control to fix the exterior

orientation elements. The necessity of obtaining ground control is costly and time-consuming.In addition, there are many instances where the ability to gather control is not feasible.Corbett and Short [1995] identify situations where this exists:

a) Time. Because phenomena change with time, it is possible that the subject of themapping has either changed or disappeared when that the control has been collected.

Another limitation occurs when the results of the mapping need to be completed in avery short time period.

b) Location. The physical location of the survey site may restrict access because ofgeography or the logistics to complete a field survey may be such to make the survey

prohibitive.

c) Safety. The phenomena of interest may be hazardous or the subject may be located inan area that is dangerous for field surveys.

d) Cost. Tied to the other problems is that of cost. The necessity of obtaining control

under the conditions outlined above may make the cost of the project prohibitivebecause control surveys are a labor-intensive activity. Even under normal conditionsthe charge for procuring control is high and, if too much is needed, could negate theeconomic advantages that photogrammetry offers. GPS gives the photogrammetrist

the opportunity to minimize (or even eliminate) the amount of ground control and stillmaintain the accuracy needed for a mapping project. Lapine points out that almost all

of the National Oceanic and Atmospheric Administration (NOAA) aerial mappingprojects utilize airborne-GPS because they have found efficiencies due to a reductionin the amount of ground control required for their mapping.

While airborne GPS can be used to circumvent the necessity of ground control, it offers the


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photogrammetrist additional advantages. These include [Abdullah et al, 2000; Lucas, 1994]:

It has a stabilizing effect on the geometry. The attainable accuracy meets most mapping standards. Substantial cost reduction for medium and large-scale projects are possible. There is an increase in productivity by decreasing the amount of ground controlnecessary for a project. It reduces the hazards due to traffic, particularly for highway corridor mapping. Precise flight navigation and pin-point photography are possible with this

technology.

It is now possible, at least theoretically, to use GPS aerotriangulation without any groundcontrol. This requires [Lucas, 1996] a near perfect system, an unlikely scenario. Moreover, it

would be extremely prudent to have control, if for no other reason than to check the results.While airborne GPS is operational, there are special considerations that must be accounted forto ensure success for a project.

Airborne GPS is operational and being used for more mapping projects. There are some

concerns that need to be addressed for a successful project. These include [Abdullah et al,2000]:

Risk is greater if the project is not properly planned and executed. There is less ground control. As ground control gets smaller, datum transformation problems become

more important. There is some initial financial investment by the mapping organization. Requires non-traditional technical support.

ERROR SOURCES

The use of GPS in photogrammetry contains two sets of error sources and the introduction ofadditional errors inherent in the integration of these two technologies. For precise work, these

errors need to be accounted for.

Photogrammetric errors include the following:

a) Errors associated with the placement of targets. The Texas Department ofTransportation has determined that an error of 1 cm can be expected in centering thetarget over the point [Bains, 1995]. This is based on a 10 cm wide cross target. Themain problem is that the center of the target is not precisely defined.

b) Errors inherent in the pug device used to mark control on the diapositives. If the pug

is not properly adjusted then the point transfer may locate pass- and tie-pointserroneously. Regardless, the process of marking control introduces another source oferror into the photogrammetric process.

c) Camera calibration is crucial in determining the distortion parameters of the aerial


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camera used in photogrammetry. Bains [1995] has found that the current USGS

calibration certificate does not provide the information needed for GPS assistedphotogrammetry. Merchant [1992] states that a system calibration is more important

with airborne GPS.

d) The camera shutter can contain large random variability as to the time the shutter isopen. Most of the time, this error source is not that important but if this irregularity istoo great, contrast within the image could be lost. The major problem with this

non-uniformity is when trying to synchronize the time of exposure to the epoch inwhich the GPS signal collecting data.

Error sources for GPS are well identified. A loss or disruption of the GPS signal could causeproblems in resolving the integer ambiguities and could result in erroneous positioning of the

camera location thereby invalidating the project. The GPS error sources include:

a) Software problems can cause problems with a GPS mission, particularly in the

kinematic mode. Some software cannot resolve cycle slips in a robust fashion,although newer on-the-fly ambiguity resolution software will help. There is also a

limitation on the accuracy of different receivers used in the kinematic surveys.Geodetic quality receivers, with 1-2 cm relative accuracy, should be employed forprojects where high precision is required.

b) Datum problems. The GPS position is determined in the WGS 84 system whereas

the survey coordinates are in some local coordinate system or in NAD 27 coordinateswhere there is no exact mathematical relationship between systems.

c) Signal interruption. This is critical if continuous tracking is necessary in order to

process the GPS signal. Interruption may occur during sharp banking turns throughthe flight.

d) Geometry of the satellite constellation.

e) Receiver clock drift. Although this error is relatively small, this drift should be

accounted for in the processing of GPS observations.

f) Multipath. This is particularly problemsome on surfaces such as the fuselage or on

the wings. This error is due to reception of a reflected signal, which represents adelay in the reception time.

Errors that can be found in the integration of GPS with the aerial camera and photogrammetryare [Bains, 1995; Merchant, 1992; Lapine, nd]:

a) The configuration of airborne GPS implies that the two data collectors are not

physically in the same location. The GPS antenna must be located outside and on topof the aircraft to receive the satellite signals. The aerial camera is located within theaircraft and is situated on the bottom of the craft. The separation distance between the

antenna and camera (the nodal point) needs to be accurately determined. Thisdistance is found through a calibration process prior to the flight. This value can also


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be introduced in the adjustment by constraining the solution or by treating it in the

stochastic process.

b) Prior to beginning a GPS photogrammetric mission, the height between the groundcontrol point and the antenna needs to be measured. Experience has found that there

can be variability in this height based on the quantity of fuel in the aircraft. Thisproblem occurs only when the airborne-GPS system is based on an initializationprocess when solving for the integer ambiguities.

c) The camera shutter can cause problems as was identified above. The effect of thiserror creates a time bias. Of concern is the ability to trip the shutter on demand. In the

worst case, Merchant [1992] points out that the delay from making the demand for anexposure to the midpoint of the actual exposure could be several seconds. For large-

scale photography this could cause serious problems because of the turbulent air inthe lower atmosphere and the interpretation from the GPS signal to the effectiveexposure time. Early experiments with the Wild RC10 with an external pulse

generator showed wide variability in time between maximum aperture and shutterrelease [van der Vegt, 1989]. The values ranged from 10-100 msec. Traveling at 100

m/sec, positional errors from 1-10 m could be expected.

d) Interpolation algorithm used to compute the position of the phase center of the

antenna. Since the instant of exposure does not coincide with the sampling time in theGPS receiver, an interpolation of the position of the antenna at the instant of exposure

must be computed. Different algorithms have varying characteristics, which couldintroduce error in the position. Related to this uncertainty is the sampling rate used tocapture the GPS signal. Too low of a rate will increase the processing whereas too

high of a rate will degrade the accuracy of the interpolation model.

e) Radio frequency interference can cause problems, particularly onboard the airplane.A receiver that can filter out this noise should be used. One example receiver is theTrimble 4000 SSI with Super-Trak signal processing which has been used

successfully in airborne-GPS [Salsig and Grissim, 1995].

Camera Calibration

One of the weak links in airborne GPS involves the camera calibration. As was pointed out

earlier, the traditional camera calibration may not provide the information needed when GPSis used to locate the exposure station. What should be considered is a system calibrationwhereby the whole process is calibrated and exercised under normal operating conditions

[Lapine, 1991; Merchant, 1992]. Because of the complex nature of combining differentmeasurement systems within airborne GPS, two important drawbacks are identified with thetraditional component approach to camera calibration [Lapine, 1991]:

1. The environment is different. In the laboratory, calibration can be performed under

ideal and controlled conditions, situations that are not possible in practice. This leadsto different atmospheric conditions and variations in the noise found in photomeasurements.


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2. The effect of correlation between the different components of the total system are notconsidered.

Traditionally, survey control on the ground had the effect of compensating for residual

systematic errors in the photogrammetric process [Lapine, 1991; Merchant, 1992]. This is dueto the projective transformation where ground control is transformed into the photo coordinatesystem. The exposure station coordinates are free parameters that are allowed to float

during the adjustment thereby enforcing the collinearity condition. With GPS-observedexposure coordinates, the space position of the nodal point of the camera are fixed and groundcoordinates become extrapolated variables. Because of this, calibration of the

photogrammetric system under operating conditions becomes critical if high-level accuracy isto be maintained.

GPS Signal Measurements

There are many different methods of measuring with GPS: static, fast static, and kinematic.

Static surveying requires leaving the antennas over the points for an hour or more. It is themost accurate method of obtaining GPS surveying data. Fast static is a newer approach that

yields high accuracies while increasing the productivity since the roving antenna need only beleft over a point for 10-15 minutes. The high accuracies are possible because the receiver willrevisit each point after an elapsed time of about an hour. Of course, neither of these situations

are possible in airborne-GPS. Kinematic measures the position of a point at the instant of themeasurement. At the next epoch, the GPS antenna has moved, and continues to move.

Because of this measurement process, baseline accuracies determined from kinematic GPS

will be 1 cm 2 ppm of the baseline distance from the base station to the receiver [Curry andSchuckman, 1993].

Flight Planning for Airborne GPS

When planning for an airborne GPS project, special consideration must be taken into account

for the addition of the GPS receivers that will be used to record the location of the camera.The first issue is the form of initialization of the receiver to fix the integer ambiguities. Next,

when planning the flight lines, the potential loss of lock on the satellites has to be accountedfor. Depending on the location of the airborne receiver, wide banking turns by the pilot may

result is a loss of the GPS signal. Banking angles of 25 or less are recommended whichresults in longer flight lines [Abdullah et al, 2000].

The location of the base receiver must also be considered during the planning. Will it be atthe airport or near the job site? The longer the distance between the base receiver and the

rover on the plane the more uncertain will be the positioning results. It is assumed that therelative positioning of the rover will be based upon similar atmospheric conditions. Thelonger the distance, the less this assumption is valid. Deploying at the site requires additional

manpower to deploy the receiver and assurances that the person who is occupying the base iscollecting data when the rover is collecting the same data.


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When planning, try to find those times when the satellite coverage consists of 6 or more

satellites with minimum change in coverage [Abdullah et al, 2000]. Also plan for a PDOPthat is less than 3 to ensure optimal geometry. Additionally, one might have to arrive at a

compromise between favorable sun angle and favorable satellite availability.

Make sure that the GPS receiver has enough memory to store the satellite data. This isparticularly true when a static initialization is performed and satellite data is collected fromthe airport. There may also be some consideration on the amount of sidelap and overlap when

the camera is locked down during the flight. This will be important when a combined GPS-INS system is used. Finally, a flight management system should be used to precalculate theexposure station locations during the flight

The limitations attributed to the loss of lock on the satellite places additional demands on

proper planning. These problems can be alleviated to some degree if additional driftparameters are used in the photogrammetric block adjustment.

Antenna Placement

To achieve acceptable results using airborne GPS, it is essential that the offset between the

GPS antenna and the perspective center of the camera be accurately known in the imagecoordinate system (figure 1). The measurement of this offset distance is performed byleveling the aircraft using jack above the wheels. Then, either conventional surveying or

close range photogrammetry can be used to determine the actual offset.

Figure 1. GPS Offset

For simplicity, the camera can be locked in place during the flight. This helps maintain thegeometric relationship of the offset vector. But, the effect is that tilt and crab in the aircraft

could result in a loss of coverage on the ground unless more sidelap were accounted for in theplanning. If the camera is to be leveled during the flight then the amount of movement should

be measured in order to achieve higher accuracy.


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The location of the antenna on the aircraft should be carefully considered. Although any pointon the top side of the plane could be thought of as a candidate site, two locations can be

studied further because of their advantages over other sites. These are on the fuselage directlyabove the camera and the tip of the vertical stabilizer.

The location on the fuselage over the camera has the advantage of aligning the phase centeralong the optical axis of the camera thereby making the measurement of the offset as well as

the mathematical modeling easier [Curry and Schuckman, 1993]. Moreover, the crab angle ishardly affected and the tilt corrections are negligible for large image scale [Abdullah et al,2000]. The disadvantages are as follows. First, the fuselage location increases the probability

of multipath. Second, this location, coupled with the wing placement, may lead to a loss ofsignal because of shadowing. Antenna shadowing is the blockage of the GPS signal, which

could occur during sharp banking turns. Finally, mounting on the fuselage may require specialmodification of the aircraft by certified airplane mechanics.

Placing the antenna on the vertical stabilizer will require more work in determining the offsetvector between the antenna and the camera [Curry and Schuckman, 1993]. But once

determined, it should not have to be remeasured unless some changes would suggest aremeasurement be undertaken. The advantages are that both multipath and shadowing are lesslikely to occur. Moreover, the actual installation might be far simpler since many aircraft

already have a strobe light on the stabilizer, which could easily be adapted to accommodate anantenna.

Determining the Exposure Station Coordinates

The GPS receiver is preset to sample data at a certain rate, i.e., 1 second intervals. This

sample time may not coincide with the actual exposure time. Therefore, it is necessary tointerpolate the position of the exposure station between GPS observations. An error in timing

will result in a change in the coordinates of the exposure station. For example, if a plane istraveling at 200 km/hr (- 56 m/sec), then a one millisecond difference will result in 6 cm ofcoordinate error.

With the rotary shutters used in aerial cameras the time between when the shutter release

signal is sent (see figure 2) to the mid-point of the exposure station varies [Jacobsen, 1991].Therefore, a sensor must be installed to record the time of exposure. Then, through a

calibration process, the offset from the recorded time to the effective instant of exposure canbe determined and taken into account. Without calibration the photographer should notchange the exposure during the flight thereby maintaining a constant offset distance, which

can be accounted for in the processing. This, though, can only be done approximately.

Many of the cameras now in use for airborne-GPS will send a signal to the receiver when the

exposure was taken. The receiver then records the GPS time for this event marker within thedata. Merchant [1993] points out that some cameras can determine the mid-exposure pulse

time to 0.1 ms whereas some of the other cameras use a TTL pulse that can be calibrated toaccurately measure the mid-point of the exposure. Accuracies better than 1 msec have beenreported for time intervals by using a light sensitive device within the aerial camera [van der


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Vegt, 1989]. This device will create an electrical pulse when the shutter is at the maximum

aperture.

Prior to determining the exposure station coordinates, the location of the phase center of theantenna must be interpolated. Since the receiver clock contains a small drift of about 1

s/sec., Lapine [nd] suggests that the position of the antenna be time shifted so that thepositions are equally spaced. Several different interpolation models can be employed todetermine the trajectory of the aircraft. Some of them include the linear model, polynomial

approach, spline function, and quadratic time-dependent polynomial. Some field results foundvery little difference between these methods [Forlani and Pinto, 1994]. This may have beenbecause they used the GPS receiver PPS (pulse per second) signal to trip the shutter on the

aerial camera. This meant that the effective instant of exposure was very close to the GPStime signal.

Figure 2. Shutter release diagram for rotary shutters [from Jacobsen, 1991].

One of the most simplest interpolation models is the linear approach. The assumption is made

that the change in trajectory from one epoch to another is linear. Thus, one can write a simpleratio as:

where: i = time interval between GPS epochs

?(X,Y,Z) = changes in GPS coordinated between two epochsdi = time difference when the exposure was made within an epoch, and

d(X,Y,Z) = changes in GPS coordinates to the exposure time.

The advantage of this model is its simplicity. On the other hand, it assumes that the change in

position is linear which may not be true. Sudden changes in direction are very common atlower altitudes where large scale mapping missions are flown. For example, figure 3 shows asudden change in the Z-direction during the flight. Assuming a linear change, the location of

( ) ( )Z,Y,Xd

di

Z,Y,X

i=


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the receiver could be considerably different than the actual location during exposure. One

alternative would be to decrease the sample interval to, say, 0.5 seconds. This would reducethe effect of the error but increase the number of observations taken and the time to process

those data.

Figure 3. Effects of linear interpolation model when the aircraft experiences sudden changesin its trajectory between PG epochs

Because of the non- linear nature of the aircraft motion, Jacobsen [1993] suggests that a least-

squares polynomial fitting algorithm be used to determine the space position of theperspective center. By varying the degree of the polynomial and the number of neighbors to

be included in the interpolation process, a more realistic trajectory should be obtained. Thedegree and number of points will depend on the time interval between GPS epochs. Theadded advantage of this method is that if a cycle slip is experienced, it can be used to estimate

better the exposure station coordinates than a linear model.

A second order polynomial is used by Lapine to determine the position offset, velocity andacceleration of the aircraft in all three axes. This is done by fitting a curve to a five epochperiod around the exposure time. The effect of this polynomial is to smooth the trajectory of

the aircraft over the five epochs. The following model is used:

Similar equation can be generated for Y and Z. Thus the three models look, in a general form,like:

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )235X35XX5

2

34X34XX4

2

33X33XX3

2

32X32XX2

2

31X31XX1

ttcttbaX

ttcttbaX

ttcttbaX

ttcttbaX

ttcttbaX

++=

++=

++=

++=

++=


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where: t = ti - t3 and i = 1, 2, ..., 5a = distance from the originb = velocity, andc = twice the acceleration

From this the observation equations can be written as

The design or coefficient matrix is found by differentiating the model with respect to theunknown parameters. All three models have the same coefficient matrix:

The observation vectors (f) are:

The normal equations can then be expressed as

where ? represent the parameters ( ? = [a b c]T ). The solution becomes

2

ZZZ

2

YYY

2

XXX

tctbaZ

tctbaY

tctbaX

++=

++=

++=

0Ztctbav

0Ytctbav

0Xtctbav

2

ZZZZ

2

YYYY

2

XXXX

=++=

=++=

=++=

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

=

=

2

2

2

2

2

2

3535

2

3434

2

3333

2

3232

2

3131

tt1

tt1

tt1

tt1

tt1

tttt1

tttt1

tttt1

tttt1

tttt1

B

=

=

=

5

4

3

2

1

Z

5

4

3

2

1

Y

5

4

3

2

1

X

Z

Z

Z

Z

Z

f

Y

Y

Y

Y

Y

f

X

X

X

X

X

f

ZZZ

YYY

XXX

fBv

fBv

fBv

+=

+=

+=


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where W is the weight matrix. Assuming a weight of 1, the weight matrix then becomes theidentity matrix and

For the X observed values, as an example,

The weighting scheme is important in the adjustment because an inappropriate choice of

weights may biased or unduly influence the results. Lapine looked at assigning equal weightsbut this choice was rejected because the trajectory of the aircraft may be non-uniform. The

final weighting scheme used a binomial expansion technique whereby times further from thecentral time epoch (t3) were weighted less than those closest to the middle. Using a variance

of 1.0 cm2 for the central time epoch, the variance scheme looks like

where the off-diagonal values are all zero (0). A basic assumption made in Lapine's studywas that the observations are independent therefore there is no covariance. Once the

( )

( )

( ) ZT1T

Z

Y

T1T

Y

X

T1T

x

WfBWBB

WfBWBB

WfBWBB

=

=

=

==432

32

2

TT

t5t5t5

t5t5t5

t5t55

IBBWBB

++++

++++

++++

==2

5

2

4

2

3

2

2

2

1

5321

54321

X

T

X

T

tXtXtXtXtX

tXtXtXtXtX

XXXXX

IfBWfB

=

2

2

2

2

2

22

22

22

22

22

cm4

cm4

cm4

cm4cm4

m01.02

m01.02

m01.02

m01.02

m01.02


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coefficients are solved for, the position of the antenna phase center can be computed using the

following expressions

Determination of Integer Ambiguity

The important error concern in airborne-GPS is the determination of the integer ambiguity1.

Unlike ground-based measurements, the whole photogrammetric mission could be lost if acycle slip occurs and the receiver cannot resolve the ambiguity problem. There are two

principal methods of solving for this integer ambiguity: static initialization over a know

reference point or using a dual-frequency receiver with on-the-fly ambiguity resolutiontechniques [Habib and Novak, 1994].

Static initialization can be performed in two basic modes [Abdullah et al, 2000]. The first

method of resolving the integer ambiguities is to place the aircraft over a point on a baselinewith know coordinates. Only a few observations are required because the vector from thereference receiver to the aircraft is known. The accuracy of the baseline must be better than

6-7 cm. The second approach is a static determination of the vector over a know baseline orfrom the reference station to the antenna on the aircraft. The integer ambiguities are solved

for in a conventional static solution. This method may require a longer time period tocomplete, varying from 5 minutes to one hour, due to the length of the vector, type of GPS

receiver, post-processing software, satellite geometry, and ionospheric stability. When static

initialization is performed it does require that the receiver on-board the aircraft maintain aconstant lock on at least 4 and preferable 5 GPS satellites.

Abdullah et al [2000] identify several weaknesses to static initialization:

The methods add time to the project and are cumbersome to perform. GPS data collection begins at the airport during this initialization. Since the data are collected for so long, large amounts of data are collected and need

to be processed about 7 Mbytes per hour.

The receiver is susceptable to cycle slips or loss of lock. It is possible that the initial solution of the integers was incorrect thereby invalidatingthe entire photo mission.

The use of on-the-fly (OTF) ambiguity integer resolution makes the process much easier. Thenew GPS receiver and post-processing software are much more robust and easy to use whilethe receiver is in flight. OTF requires P-code receivers where carrier phase data are collected

using both the L1 and L2 frequencies. The solution requires about 10-15 minutes of

1 The unknown number of whole wavelengths of the carrier signal contained in an unbroken set of measurements

from a single satellite at a single receiver.

( ) ( )

( ) ( )( ) ( )23expZ3expZZexp

2

3expY3expYYexp

2

3expX3expXXexp

ttcttbaZttcttbaY

ttcttbaX

++=++=

++=


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measurements before entering the project area.

Component integration can also create problems. For example, a test conducted by the

National Land Survey, Sweden, experienced cycle slips when using the aircraftcommunication transmitter [Jonsson and Jivall, 1990]. Receiving information was not a

problem, just transmissions. This test involved pre-flight initialization with the goal ofre-observation over the reference station at the end of the mission. This was not possible.

GPS-Aided Navigation

One of the exciting applications of airborne-GPS is its utilization of in flight navigation. Theability to precisely locate the exposure station and activate the shutter at a predetermined

interval along the flight line is beneficial for centering the photography over a geographicregion, such as in quad-centered photography for orthophoto production.

An early test by the Swedish National Land Survey [Jonsson and Jivall, 1990] showed earlyprogress in this endeavor. The system configuration is shown in figure 4. Two personal

computers (PCs) where used in the early test - one for navigation and the other fordetermination of the exposure time.

Figure 4. Configuration of navigation-mode GPS equipment [from Jonsson and Jivall, 1990].

The test consisted of orientation of the receiver on the plane prior to the mission over aground reference mark. This initialization is performed to solve for the integer ambiguity.

This method of fixing the ambiguity requires no loss of lock during the flight thusnecessitating long banking turns, which adds to the amount of data collected.

A flight plan was computed with the location of each exposure station identified. The PC usedfor the navigation activated a pulse that was sent to the aerial camera to trip the shutter. The

test showed that this approach yielded about a 0.5 second delay. Thus, the exposure station


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locations were 20-40 meters too late. An accuracy of about 6 meters was found at the

preselected position along the strip. When compared to the photogrammetrically derivedexposure station coordinates, the relative carrier phase measurements were within about 0.15

meters in agreement.

The Texas Department of Transportation (TDOT) had a different problem [Bains, 1992].Using airborne-GPS gave TDOT the ability to reduce the amount of ground control for theirdesign mapping. With GPS one paneled control point was placed at the beginning of the

project and a second at the end. If the site was greater than 10 km in length then a thirdpaneled control point was placed near the center. For their low altitude flights (photo scale of1 cm = 30 m), the desire was to control the side-lap to 50 m. Using real-time differential GPS,

accuracies of better than 10 m, at that time, were realistic. Using this 10 m error value, thisamount of error would only cause a variation in side-lap of 7%. TDOT uses 60% side- lap for

their large scale mapping.

For the high altitude mapping (photo scale of 1 cm = 300 m) and 30% side-lap, it was

determined that the "50 m was not really necessary. This 50 m value would cause a variationof only about 2%.

PROCESSING AIRBORNE GPS OBSERVATIONS

The mathematical model utilized in analytical photogrammetry is the collinearity model,

which simply states that the line from object space through the lens cone to the negative planeis a straight line. The functional representation of this model is shown as:

where: xij, yij are the observed photo coordinates, i, for photo j

xo, yo are the coordinates of the principal pointc is the camera constant

? Xi, ? Yi, ? Zi are the transformed ground coordinates

This mathematical model is often presented in the following form:

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )Li33Li32Li31

Li23Li22Li21

oyij

Li33Li32Li31

Li13Li12Li11

oxij

ZZmYYmXXm

ZZmYYmXXmcyvy

ZZmYYmXXm

ZZmYYmXXmcxvx

ij

ij

++

++=+

++

++=+

( ) ( )

( ) ( ) 0Z

YcyyyF

0ZXcxxxF

i

i

oij

i

ioij

=

=

==


16/32

where: vx, vy are the residuals in x and y respectively for point i on photo jX, Y, Z are the ground coordinates of point i

XL,YL,ZL are the space rectangular coordinates of the exposure station forphoto j

m11 ... m33 is the 3x3 rotation matrix that transforms the ground coordinates toa photo parallel system.

The model implies that the difference between the observed photo coordinates, corrected forthe location of the principal point, should equal the predicted values of the photo coordinatesbased upon the current estimates of the parameters. These parameters include the location of

the exposure station and the orientation of the photo at the instant of exposure. The formervalues could be observed quantities from onboard GPS. These central projective equations

form the basis for the aerotriangulation.

It is common to treat observations as stochastic variables. This is done by expanding the

mathematical model. For example, Merchant [1973] gives the additional mathematical modelwhen observations are made on the exterior orientation elements as:

The mathematical model for observation on survey control can be similarly.

( )

( )

( )

( )

( )

( ) 0ZZZF

0YYYF

0XXXF

0F

0F

0F

aL

oLL

a

L

o

LL

aL

oLL

ao

ao

ao

==

==

==

==

==

==


17/32

Figure 5. Position ambiguity for a single photo resection [from Lucas, 1996, p.125].

Using GPS to determine the exposure station coordinates without ground control is not

applicable to all photogrammetric problems. Ground control is needed for a single photoresection and orientation [Lucas, 1996]. If the exposure station coordinates are preciselyknown then the only thing known is that the camera lies in some sphere with a radius equal to

the offset distance from the GPS antenna to the cameras nodal point, figure 5. The antenna islocated at the center of the circle. All positions on the sphere are theoretically possible but

from a practical viewpoint, one knows that the camera, being located below the aircraft andpointing to the ground, is below the antenna. The antenna, naturally, is located on top of theaircraft to receive the satellite signals.

Adding a second photo reduces some of the uncertainty. This is due to the additional

constraint of the collinearity condition that is placed on the rays from the control to the imageposition. The collinearity theory will provide the relative orientation between the two photos[Lucas, 1996]. Without ground control, the camera is then free to rotate about a line that

passes through the two antenna locations (see figure 6). Without ground control, or someother mechanism to constrain the roll angle along the single strip, this situation could be

found throughout a single strip of photography.


18/32

Figure 6. Ambiguity of the camera position for a pair of aerial photos [from Lucas, 1996,p.125].

While independent model triangulation continues to be employed in practice, the usual

iterative adjustment cannot be used with the recommended 4 corner control points [Jacobsen,

1993]. Moreover, the 7-parameter solution to independent model triangulation results in a lossof accuracy in the solution.

Determining the coordinates of the exposure stations can be easily visualized in the following

model [Merchant, 1992]. Assume that the photo coordinate system (x,y,z) are aligned with thecoordinate system (U, V, W). Further, assume that the survey control (X, Y, Z) is reported in

the WGS 84 system. Then, it remains to transform the offset between the receivers phasecenter and the nodal point of the aerial camera (DU, DV, DW) into the corresponding surveycoordinate system. This is shown as

where: DU, DV, DW are the offset distances

MM is the camera mount orientationME is the exterior orientation elements of the camera

The camera mount orientation is necessary to ensure that the camera is heading correctly

+

=

DW

DV

DU

MM

Z

Y

X

Z

Y

X

ME

A

a

a

L

L

L


19/32

down the flight path.

In the normal acquisition of aerial photos, the camera is leveled prior to each exposure. This is

done so that the photography can be nearly vertical at the instant of exposure even though theaircraft is experiencing pitch, roll and swing (crab or drift). When the coordinate offsets

between the antenna and camera were surveyed, the orientation angles on the mount areleveled. A problem occurs if there is an offset between the location of the nodal point and thegimbals rotational center on the mount. When the camera is rotated, the relationship between

the two points should be considered.

The simplest way to ensure that the relationship between the receiver and the camera are

consistent would be to forgo any rotation of the camera during the flight. With this rigidrelationship fixed, the antenna coordinates can be rotated into a parallel system with respect to

the ground by using the tilts experienced during the flight.

Alternatively, Lapine [nd] points out that the transformation of the offsets to the local

coordinate system can easily be performed using the standard gimbal form. In this situation,pitch and swing angles between the aircraft and the camera are measured. Then, one can

simply algebraically sum the camera mount angles with the appropriate measured pitch andswing angles. Here, ? and swing are added to form one rotational element and f and pitch aresimilarly combined. Since roll was not measured during the test, ? is treated independently.

Using the Wild RC-10 camera mount, Lapine found that the optical axis of the camera

coincided with the vertical axis of the mount. That meant that the combination of ? and swingwould not produce any eccentricity. Testing revealed that the gimbal center was locatedapproximately 27 mm from the nodal points. Thus, an eccentricity error could be introduced.

During the flight, a 1.5o maximum pitch angle between the aircraft and the camera mount was

found. Thus the error in neglecting this effect in the flight direction would be

maximum pitch error = 0.027m * sin 1.5o = 0.0007 meters

Experiences from tests in Europe [Jacobsen, 1991] indicate that the GPS positions of theprojection centers differ from the coordinates obtained from a bundle adjustment. Moreover,

many of the data sets have shown a time dependent drift pattern in the GPS values. When thissystematic tendency is accounted for in the adjustment, excellent results are possible. Forrelative positioning, 4 cm can be reached whereas 60 cm are possible using absolute

positioning.

A second approach to perform airborne GPS aerial triangulation is sometimes referred to asthe Stuttgart method. In this technique, certain physical conditions are assumed or accepted[Ackermann, 1993]. First, it is accepted that loss of lock will occur. This means that low

banking angles onboard the aircraft will not be used as in those methods where a loss of lockmeans a thwarted mission. Because loss of lock, it is also unnecessary to perform a stationary

observation prior to take-off to resolve the integer ambiguities. These ambiguities are solvedon-the-fly and can be determined for each strip if loss of lock occurs during the banking (or atother times during the photo mission). Seldom will loss of lock happen along the strip though.

Second, it will be assumed that single frequency receivers will be used on the aircraft. Finally,the ground or base receiver will probably be located at a great distance from the photo


20/32

mission.

The solution of the integer ambiguities is performed using C/A-code pseudorange positioning.

These positions can be affected by selective availability (SA). Because of this, there will bebias in the solution. These drift errors, which can include other effects such as datum effects,

are systematic in nature and consist of a linear and time dependent component. The blockadjustment is used to solve for these biases.

Early test results added confusion to the drift error biases. In a test by the Survey Departmentof Rijkswaterstaat, Netherlands, a systematic effect was not noticeable on all photo strips [vander Vegt, 1989]. Evaluation of the results indicated that this was probably due to the GPS

processing of the cycle slips. The accuracy of the position in the differential mode ispredicated on the accuracy of solving these integer ambiguities at both the base receiver and

the rover. This test used a technique where the differences between the observedpseudoranges and the phase measurements were averaged. The accuracy of this approach willbe dependent upon the accuracy of the measurements, the satellite geometry and how many

uncorrelated observations are used in the averaging approach.

If no loss of lock occurs during the photo mission, the aircraft trajectories will be continuousand, therefore, only one set of drift parameters need to be carried in the bundle adjustment.Unfortunately, banking turns could have an adverse effect by blocking the signal to some of

the satellites causing cycle slips. Hghlen [1993] states that an alternative to the strip-wiseapplication of the biases, the block may be able to be split into parts where the aircraft

trajectories are continuous thereby decreasing the number of unknown parameters within theadjustment.

The advantage of modeling these drift parameters is that the ground receiver does not have to

be situated near the site. It could be 500 km or farther away [Ackermann, 1993]. This isimportant because it can decrease the costs associated with photo missions. Logisticalconcerns include not only the deployment of the aircraft but also the ground personnel on thesite to operate the base. When projects are located at great distances from the airplanes home

base, uncertainty in weather could mean field crews already on the site but the photo missioncanceled. It also is an asset to flight planning in that on-site GPS ground receivers will require

fixing the flight lines at least one day before the mission. During the flying season this couldbe a problem [Jacobsen, 1994]. In Germany, the problem is solved because of the existence ofpermanent reference stations throughout the country that could be occupied by the ground

receiver.

Using the mathematical model for additional stochastic observations within the adjustment asoutlined earlier [Merchant, 1973], a new set of observations can be written for the perspectivecenter coordinates as [Blankenberg, 1992].

iL

L

L

iZ

Y

X

iL

L

L

Z

Y

X

v

v

v

Z

Y

X

GPS

GPS

GPS

=

+


21/32

where: (XL, YL, ZL)GPS = the perspective center coordinates observed with GPS

vX, vY, vZ = residuals on the observed principal center coordinatesXL, YL, ZL = the adjusted perspective center coordinates used within the

bundle adjustment

As it was discussed earlier, the antenna does not occupy the same location as the camera

nodal point. The geometry is shown in figure 7. Relating the antenna offset to the ground isdependent upon the rotation of the camera with respect to the aircraft and the orientation of

the aircraft to the ground. The bundle adjustment can be used to correct the camera offset ifthe camera remains fixed to the aircraft during the photo mission. If this condition is met then

the orientation of the camera offset will only be dependent upon the orientation elements (,, ).

The new additional observation equations to the collinear model are given as [Ackermann,1993; Hghlen, 1993]:

( )

jZ

Y

X

jZ

Y

X

APC

A

PC

A

PC

i

iL

L

L

iZ

Y

X

iA

A

A

b

b

b

dt

a

a

a

z

y

x

,,R

Z

Y

X

v

v

v

Z

Y

X

GPS

GPS

GPS

+

+

+

=

+

where: (XA, YA, ZA)GPS = ground coordinates of the GPS antenna for photo i

vX, vY, vZ = residuals for the GPS antenna coordinates (XA, YA, ZA)GPS forphoto i

XL, YL, ZL = exposure station coordinates of photo ixAPC, y

APC, z

APC = eccentricity components to the GPS antenna

aX, aY, aZ = GPS drift parameters for strip j representing the constant term

dt = difference between the exposure time for photo I and the timeat the start of strip j

Figure 7. Geometry of the GPS antenna with respect to the aerial camera (zeroxcopy, source unknown)


22/32

bX, bY, bZ = GPS drift parameters for strip j representing the linear time-

dependent terms

R(, , ) = orthogonal rotation matrix.

It is recognized in analytical photogrammetry that adding parameters to the adjustment

weakens the solution. To strengthen the problem, one can introduce more ground control, butthis defeats one of the advantages of airborne GPS. Introducing the stepwise drift parametersand using four ground control points located at the corners of the project, there are three

approaches to reducing the instability of the block [Ackermann, 1993]. These are shown infigure 8 and are:

i) using both 60% end- and 60% side-lapii) using 60% end- lap and 20% side-lap and adding an additional vertical control point

at both ends of each strip, andiii) using the conventional amount of overlap as indicated in (ii) and flying at least two

cross-strips of photography.

The block schemes shown in figure 8 are idealized depictions. The figure 8(i) scheme can be

used for airborne GPS when no drift parameters are employed in the block adjustment. It is

important that the receiver maintains lock during the flight which necessitates flat turnsbetween flights. Maintaining lock ensures that the phase history is recorded from take-off tolanding. Abdullah et al [2000] points out that this is the most accurate type of configuration

in a production environment. The same control scheme can also be used when block driftparameters are used in the bundle adjustment.

If strip drift parameters are used then a control configuration as shown in figure 8(ii) shouldbe used. Here, drift parameters are developed for each flight line strip which requires

additional height control at the ends of each strip. The control configuration in figure 8(iii)incorporates two cross strips of photography. This model increases the geometry andprovides a check against any gross errors in the ground control. But it does add to the cost of

Figure 8. Idealized block schemes.


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the project because more photography is required to be taken and measured. For that reason,

it is not frequently utilized in a production environment.

More often the area is not rectangular but rather irregular. In this situation it is advisable toadd additional cross-strips or provide more ground control. Figure 9 is an example.

Figure 9. GPS block control configuration.

Theoretically, it is possible to perform the block adjustment without any ground control. Thiscan easily be visualized if one considers supplanting the ground control by control located atthe exposure stations. Nonetheless, it is prudent to include control on every job, if nothing

more than providing a check to the aerotriangulation. Using the four control point scheme asjust presented has the advantage of using the GPS position for interpolation only within the

strip.

As is known, conventional aerotriangulation requires ground control. As an example, for

planimetric mapping, control is required at an interval of approximately every seventh photoon the edge of the block. Topographic mapping requires vertical control within the block at

about the same spacing. Using this background and simulated data, Lucas [1996] was able to


24/32

develop error ellipses from a bundle adjustment showing the accumulation of error along the

edges of the block (figure 10). The is commonly referred to as the edge effect and stems froma weakened geometric configuration that exists because of a loss in redundancy. Under

normal circumstances, a point in the middle of a block should be visible on at least ninephotos. But on the edge, the photos are taken only from one side of view.

Figure 10. Error ellipses with ground points positioned by conventional aerotriangulationadjustment of a photo block [Lucasm 1994].

Using the same simulated data, Lucas [1996] also showed the error ellipses one would expect

to find using 60% end- and side-lap photography along with airborne GPS and no control.The results show that for planimetry, the results are similar. Larger error ellipses were foundat the control points but at every other point they were either smaller or nearly equivalent.

Elevation errors were much different within the two simulations. Using just aerotriangulation

without control, error ellipses grew larger towards the center of the block. Using kinematicGPS, on the other hand, kept the error from getting larger. Compared with the originalsimulation with vertical control within the block, each point had improvements, except the

control points that were fixed in the conventional adjustment. Lucas [1996] states that thereason for the improvement lies in the fact that each exposure station is now a control point

and the distance between the control is less than one would find conventionally. It would notbe practical to have the same density of control as one would have in the air. These results arebased on simulations therefore reflect what is possible and not necessarily what one would

find in real data.

Accuracy considerations are important in determining the viability of using GPS observationswithin a combined bundle adjustment. Results of projects conducted with combined GPSbundle adjustment show that this approach is not only feasible but also desirable. In

conventional aerotriangulation, ground control points helped suppress the effects of block


25/32

deformation. GPS observed perspective center coordinates stabilize the adjustment thus

negating the necessity for extensive control. In fact, their main function now becomes one ofassisting in the datum transformation problem [Ackermann, 1993].

If the position of exposure station can be ascertained to an accuracy of 10 cm or better, then

the accuracy of the adjustment becomes primarily dependent upon the precision of themeasurement of the photo coordinates [Ackermann, 1993]. Designating the standard error of

the photo observations as s 0, the projected values expressed in ground units are O . Then as

long as OGPS , Ackermann indicates that the following rule could apply. The expected

horizontal accuracy (X, Y) will be approximately O5.1 and the vertical accuracy (Z) would

be around O0.2 . This assumes using the six drift parameters for each strip, four controlpoints and cross-strips.

Strip Airborne GPS

For route surveys, such as transportation systems, there is a problem with airborne GPS when

the GPS measurements are exclusively used to control the flight. Theoretically, a solution ispossible if the exposure stations are distributed along a block and are non-collinear. In the

case of strip photography, the exposure station coordinates will nearly lie on a line making itan ill-conditioned or singular system. Therefore, some kind of control needs to be provided onthe ground to eliminate the weak solution that would otherwise exist. As an example, Lucas

[1996] shows the error ellipses one would expect with only ground control and then withkinematic GPS. These are shown in figure 11 for horizontal values and figure 12 for vertical

control.

Merchant [1994] states that to solve this adjustment problem, existing ground control could be

utilized in the adjustment. Most transportation projects have monumented points throughoutthe project and intervisible control should be reasonably expected.

A test was performed to evaluate the idea of using control for strip photography [Merchant,1994]. A strip of three photos was taken from a Wild RC-20 aerial camera in a Cessna

Citation over the Transportation Research Center test site in Ohio. The aircraft waspressurized and the flying height above the ground was approximately 1800 m. A TrimbleSSE receiver was used with a distance to the ground-based receiver being approximately 35

km. The photography was acquired with 60% end-lap. Corrections applied to the measuredphoto coordinates included lens distortion compensation (both Seidel's aberration radial

distortion and decentering distortion using the Brown/Conrady model), atmospheric refraction(also accounting for the refraction due to the pressurized cabin), and film deformation(USC&GS 8-parameter model).


26/32

Figure 11

Figure 12.

The middle photo had 30 targeted image points. For this test, only one or two were used whilethe remaining control values were withheld. The results are shown in the following table. The

full field method utilized all of the checkpoints within the photography. The corridor methodonly used a narrow band of points along the route, which is typical of the area of interest formany transportation departments [Merchant, 1994]. The results are expressed in terms of the

root mean square error (rmse) defined as the measure of variability of the observed and "true"(or withheld) values for the checkpoints. The method is shown as:

where n is the number of test points.

( )n

observedtruermse

2

=


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rmse (meters)Number of TestPoints

X Y Z

Using 2 targeted ground controlpoints

Full Field 28 0.079 0.057 0.087

Corridor 10 0.031 0.026 0.073

Using 1 targeted ground control

point

Full Field 29 0.084 0.050 0.086

Corridor 11 0.034 0.033 0.082

The results indicate that accuracies in elevation are better than 1:20,000 of the flying height,which are comparable to results found from conventional block adjustments. It should also be

noted that pass points were targeted therefore errors that may occur due to the marking ofconjugate imagery is not present. Moreover, the adjustment also included calibration of the

system. Nonetheless, good results can be expected by using ground control to alleviate the illconditioning of the normal equations. A minimum of one point is needed with additional

points being used as a check.

Another approach, other than including additional control, would be to fly a cross strip

perpendicular to the strip of photography. This will have the effect of anchoring the stripthereby preventing it from accumulating large amounts of error. If the strip was only a singlestrip, then it is recommended that a cross strip be obtained at both ends of the strip [Lucas,

1996].

Combined INS and GPS Surveying

The combination of a combined inertial navigation system (INS) with GPS gives the surveyorthe ability to exploit the advantages of both systems. INS has a very high short-term accuracy,which can be used to eliminate multipath effects and aid in the solution of the ambiguity

problem. The long-term accuracy of the GPS can be used to correct for the time-dependentdrift found within the inertial systems. Used together will give the surveyor not only goodrelative accuracies but also good absolute accuracies as well. Moreover, within the bundle

adjustment, only the shift parameters need to be included within the adjustment model[Jacobsen, 1993], thereby increasing, at least theoretically, the accuracy of the

aerotriangulation.


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Texas DOT Accuracy Assessment Project

The Texas Department of Transportation undertook a project to assess the accuracy level that

is achievable using GPS and photogrammetry. Bains [1995] describes the project in length.Three considerations were addressed in this project: system description, airborne GPS

kinematic processing and statistical analysis.

The system description can be summarized as follows:

The site selected was an abandoned U.S. Air Force base located near Bryan, Texas. This

site was selected because the targets could be permanently set and there would be minimalobstructions due to traffic. Being an abandoned facility, expansion of the test facility waspossible. In addition, the facility could handle the King Air airplane.

Target design is important for the aerial triangulation. A 60 x 60 cm cross target with a pin

in the center was selected (based on a photo scale of 1:3000). The location of the center of

the target allowed for the precise centering of the ground receiver over the point. In areaswhere there was no hard surface to paint the target, a prefabricated painter wafer board

target was employed.

All of the targets were measured using static GPS measurements. Each target wasobserved at least once. Using 8 receivers, two occupied master control points while theremaining six simultaneously observed the satellites over the photo control points. The

goal was to achieve Order B accuracy in 3-D of 1:1,000,000. In addition, differentiallevels were run over all targets to test the accuracy of the GPS-derived heights.

The offset between the antenna and the camera was measured four times and the meanvalues determined. Prior to the measurement, the aircraft was jacked up and leveled. The

aerial camera was then leveled and locked into place. The offset distances were thenmeasured.

The flight specifications were designed to optimize the accuracy of the test. They are:

Photo Scale: 1:3000Flying Height: 500 metersFlight Direction: North-South

Forward Overlap: 60% minimum

Side-lap: 60%Number of Strips: 3Exposures per Strip: 12Focal Length: 152 mm

Format: 230 x 230 mmCamera: Wild RC 20

Film Type: Kodak Panatomic 2412 Black/WhiteSun Angle: 30o minimumCloud Cover: None

GDOP: #4


29/32

The mission began by measuring the height of the antenna when the aircraft was parked.

The ground receiver was turned on and a sample rate of 1 second was used. The roverreceiver in the aircraft was then turned on and tracked the satellites for five minutes with

the same one-second sampling rate. Then the aircraft took off and flew its mission.

The processing steps involved the kinematic solution of the GPS observations. The PNAVsoftware was used for on-the-fly ambiguity resolution. The software vendor recommendedthat the processing be done both forward and backward for better accuracy but the test

indicated that, at least for this project, there was no increase in the accuracy when performingthat kind of processing.

The photogrammetry was processed using soft-copy photogrammetry. A 15Fm pixel size wasused. The aerial triangulation was then performed with the GAPP software using only four

ground control stations; two at the start and two at the end. The results were then statisticallyprocessed using the SAS (Statistical Analysis System).

The results of this study showed that the accuracy achieved fell within specifications. In fact,the GPS results were either equal to or better than the accuracy of conventional positioning

systems. The results also indicated that there was a need to have a reference point within thesite to aid in the transformation to State Plane Coordinates. As an example, Table 1 shows thecomparison between the GPS-derived control and the values from the ground truth. These

results show that airborne GPS can meet the accuracy specifications for photogrammetricmapping.


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Number of

Observations

Variable Minimum Maximum Mean Standard

Deviation

95 Easting -0.100 0.057 -0.021 0.031

95 Northing -0.075 0.089 -0.003 0.026

95 Elevation -0.068 0.105 -0.008 0.027

Table 1. Comparison of airborne GPS assisted triangulation with ground truth on day 279,

1993 over a long strip [from Bains, 1995, p.40].

ECONOMICS OF AIRBORNE-GPS

While no studies have been conducted that describe the economic advantages of airborne-GPS, some general findings are available [Ackermann, 1993]. Utilization of airborne-GPS

does increase the aerotriangulation costs by about 25% over the conventional approach. Thisincrease includes:

flying additional cross-strips film GPS equipment GPS base observations processing the GPS data and computation of aircraft trajectories aerotriangulation point transfer and photo observations, and combined block adjustment

The real savings accrue in the control where the costs are 10% or less than those requiredusing conventional aerotriangulation. The overall net savings will be about 40% when lookingat the total project costs.

If higher order accuracy is required (Ackermann uses the example of cadastralphotogrammetry which needs 1-2 cm accuracy) then the savings will decrease becauseadditional ground control are necessary.

REFERENCES

Abdullah, Q., M. Hussain and R. Munjy, 2000. Airborne GPS-Controlled Aerial-Triangulation: Theory & Practical Concepts, Workshop notes.

Ackermann, F., 1993. "GPS for Photogrammetry", The Photogrammetric Journal of Finland,


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13(20):7-15.

Bains, H.S., 1992. "Photogrammetric Surveying by GPS Navigation", Proceedings of the 6th

International geodetic Symposium on Satellite Positioning, Vol. II, Columbus, OH, March 17-20, pp 731-738.

Bains, H.S., 1995. "Airborne GPS Performance on a Texas Project", ACSM/ASPRS AnnualConvention and Exposition Technical Papers, Vol. 2, February 27 - March 2, pp 31-42.

Corbett, S.J. and T.M. Short, 1995. "Development of an Airborne Positioning System",Photogrammetric Record, 15(85):3-15.

Curry, S. and K. Schuckman, 1993. Practical Guidelines for the Use of GPS

Photogrammetry, ACSM/ASPRS Annual Convention and Exposition Technical Papers, Vol.3, New Orleans, LA, pp 79-88.

Forlani, G. and L. Pinto, 1994. "Experiences of Combined Block Adjustment with GPS Data",International Archives of Photogrammetry and Remote Sensing, Vol. 30, Part 3, Munich,

Germany, September 5-9, pp 219-226.

Habib, A. and K. Novak, 1994. "GPS Controlled Aerial Triangulation of Single Flight Lines",

Proceedings of ASPRS/ACSM Annual Convention and Exposition, Vol 1, Reno, NV, April25-28, pp 225-235; also, International Archives of Photogrammetry and Remote Sensing, Vol.

30, Part 2, Ottawa, Canada, June 6-10, pp 203-210.

Hghlen, A., 1993. "GPS-Supported Aerotriangulation in Finland - The Eura Block", The

Photogrammetric Journal of Finland, 13(2):68-77.

Jacobsen, K., 1991. "Trends in GPS Photogrammetry", Proceedings of ACSM-ASPRSAnnual Convention, Vol. 5, Baltimore, MD pp 208-217.

Jacobsen, K., 1993. Correction of GPS Antenna Position for Combined Block Adjustment,ACSM/ASPRS Annual Convention and Exposition Technical Papes, Vol. 3, New Orleans,

LA pp 152-158.

Jacobsen, K., 1994. Combined Block Adjustment with Precise Differential GPS-Data,

International Archives of Photogrammetry and Remote Sensing, Vol. 30, Part 3, Munich,Germany, September 5-9, pp 422-426.

Jonsson, B. and A. Jivall, 1990. Experiences from Kinematic GPS Measurements, Paperpresented at the Nordic Geodetic Commission 11th General Meeting, Copenhagen, 12p.

Lapine, L.A., 1991. Analytical Calibration of the Airborne Photogrammetric System Using

A Priori Knowledge of the Exposure Station Obtained from Kinematic Global PositioningSystem Techniques, Department of Geodetic Science and Survey Report No. 411, The OhioState University, Columbus, OH, 188p.

Lapine, L.A., nd. "Airborne Kinematic GPS Positioning for Photogrammetry - The


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Determination of the Camera Exposure Station", Xerox copy, source unknown.

Lucas, J.R., 1996. Covariance Propagation in Kinematic GPS Photogrammetry in Digital

Photogrammetry: An Addendum to the Manual of Photogrammetry, ASPRS, pp 124-129.

Merchant, D.C., 1992. "GPS-Controlled Aerial Photogrammetry", ASPRS/ACSM/RT92Technical Papers, Col. 2, Washington, D.D., August 3-8, pp 76-85.

Merchant, D.C., 1994. "Airborne GPS-Photogrammetry for Transportation Systems",Proceedings of ASPRS/ACSM Annual Convention and Exposition, Vol. 1, Reno, NV, April25-28, pp 392-395.

Salsig, G. and T. Grissim, 1995. GPS in Aerial Mapping, Proceedings of Trimble

Surveying and Mapping Users Conference, Santa Clara, CA, August 9-11, pp 48-53.

van der Vegt, 1989. Differential GPS: Efficient Tool in Photogrammetry, Surveying

Engineering, 115(3):285-296.

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