Direct Exterior Orientation of Airborne Imagery with GPSINS

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Direct Exterior Orientation of  Airborne Imagery with GPSINS Powered By Docstoc
					    Navigation, Vol. 46, No. 4, pp. 261-270, 1999


    Direct Exterior Orientation of Airborne Imagery with GPS/INS System:
                                          Performance Analysis

                                          Dorota A. Grejner-Brzezinska

                 Department of Civil and Environmental Engineering and Geodetic Science
                                        The Ohio State University
                                   470 Hitchcock Hall, 2070 Neil Ave.
                                Tel. (614) 292-8787, fax. (614) 292-2957
                                    e-mail: dorota@cfm.ohio-state.edu

ABSTRACT


Integrating the Global Positioning System (GPS) with an Inertial Navigation System (INS) allows for direct image
georeferencing, offering a possibility of relaxing the demand for aerial triangulation (AT) in airborne
surveying/mapping. The performance of the prototype of the Airborne Integrated Mapping System (AIMS™), based
on GPS/INS/CCD (charge-coupled device) integration, developed by The Ohio State University Center for
Mapping, is investigated in this paper. A brief description of the essential features of the integrated system and its
practical implementation is presented. The performance of AIMS™ is primarily assessed based on the
photogrammetric processing of 1:6,000 large-scale aerial imagery considered as a truth reference. An accuracy
analysis and discussion of the impact of direct orientation and the multi-sensor system calibration on the
photogrammetric data extraction process are also addressed.


INTRODUCTION


Recent technological developments have created a number of new systems for 3D data acquisition, processing and
visualization. On the spatial data acquisition side, one can find a variety of new sensors, whose direct orientation is
provided by the integrated GPS and INS. In fact, the GPS/INS platform orientation systems are rapidly emerging as
a core component of modern airborne mapping and remote sensing systems. Over the past few years, there has been
a growing interest of the airborne survey and remote sensing community in using the integrated GPS/INS systems
for direct georeferencing [1-9]. The application of GPS in determination of the camera perspective center location
has already become a commonly accepted procedure in aerial surveys. The most pronounced advantage of GPS-
supported aerotriangulation is the decrease of ground control, leading to a substantial cost reduction in aerial
mapping.


System augmentation by an inertial sensor offers a number of advantages over a stand-alone GPS, such as immunity
to GPS outages and reduced ambiguity search volume/time for the closed-loop systems, and more importantly,
continuous attitude solution. Conversely, GPS contributes its white error spectrum, high accuracy and stability over
time, enabling a continuous monitoring of inertial sensor errors. Implementation of a closed-loop error calibration



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allows continuous, on-the-fly (OTF) error update bounding INS errors, leading to increased estimation accuracy. A
GPS-calibrated, high-to medium-accuracy inertial system can provide attitude accuracy in the range of 10-30 arcsec
[10, 6, 11, 9].


Alternatively, a direct platform orientation (DPO) can also be achieved by means of an array of GPS antennas
mounted on a mobile platform with known relationship to the reference frame of an imaging sensor. For the most
demanding mapping applications, however, the stand-alone multi-antenna GPS, is currently not able to provide
acceptable Exterior Orientation Parameters (EOP, including the three position coordinates and the three attitude
angles of the camera). Assuming that some ambiguity resolution method was applied before the attitude components
are estimated by the interferometric method, the actual attitude accuracy can reach 1-2 arcmin for long baselines of
20-30 m [12, 13], depending primarily on the GPS antenna separation and orientation with respect to line-of-sight,
and multipath level. Moreover, attitude is available usually at 1-10 Hz rate, which may not be satisfactory for the
fast-moving airborne platforms, where frequency of 64-256 Hz is needed. In general, the stand-alone multi-antenna
GPS provides less accurate attitude information, and at much lower frequency, compared to integrated GPS/INS
solutions, where a high accuracy inertial system is supported by differential GPS (DGPS). For example, the Ashtech
GPS 3DF-ADU multi-antenna system is capable of providing 2 Hz attitude information, with accuracy estimated at
0.2 deg RMS (root mean square error) for heading, and 0.4 deg RMS for pitch and roll, based on a 1 m square
antenna array (3DF-ADU Manual), and the Trimble TANS Vector delivers 10 Hz attitude information with an
accuracy of 0.3 deg for 1m baseline (TANS Vector product description). As pointed out by Ward and Axelrad [13],
in order to achieve 0.1 deg pointing accuracy by the interferometric method, the baselines connecting the phase
centers of GPS antennas must be known to within 2 mm on a 1 m antenna separation, which is rather difficult to
achieve. Since the baseline separation can change from the pre-surveyed value during the airborne or space-borne
mission (due to varying conditions compared to the laboratory environment), the baseline estimation must often be
performed by the attitude determination filter, which naturally adds to the overall system’s algorithmic complexity.


Combining DGPS and inertial measurement unit (IMU) data bounds the gyro drifts, leading to high accuracy
attitude estimates even with a single roving GPS antenna. Furthermore, implementing the interferometric method to
the integrated systems based on low accuracy IMU may result in a more robust system. In this case, the gyros are
used to estimate the phase differences related to the airborne GPS baselines, which form a class of external updates
to the integrated filter. This solution, however, may lead to some parameter observability problems, and thus,
requires special care in proper parameterization and dynamic modeling of the filter states, since attitude and baseline
errors (that need to be added to the state vector) are closely coupled. Moreover, careful maneuvering of the platform
is required, since attitude motion is needed to separate baseline and attitude errors in the combined filter.


The Ohio State University Center for Mapping has developed a prototype of an integrated GPS/INS system to
support direct platform orientation for a fully digital airborne mapping system (AIMS™), designed primarily for
precise large-scale mapping. The AIMS™ positioning module is based on a tightly integrated differential, dual




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frequency GPS, and a strapdown inertial system. The tight integration, as implemented in AIMS™, is preferred as
opposed to the loose coupling approach, as it allows for continuous IMU error calibration and positioning even if the
number of satellites drops below four. Furthermore, the high accuracy of the well-calibrated inertial system over
short time periods allows correction of cycle-slips affecting GPS measurements, and supports more robust OTF
ambiguity resolution, even after a total loss of GPS lock. Although, the extended losses of GPS lock do not occur
very frequently in the airborne mapping scenario, since careful mission planning and avoiding steep banking will
usually assure a continuous lock on several satellites, the power of tight integration becomes more important for the
low-altitude missions (300-500 m), especially over urban areas. At this level, the radio interference (possibly from
commercial VHF radio, over-the-horizon military radar, broadcast television, mobile satellite system telephones,
etc.) causes signal reception problems, resulting in a very low signal-to-noise ratio, leading ultimately to extended
losses of GPS lock [14].


During the past 18 months, the AIMS™ technology has been tested over baselines ranging from 20 to 350 km, in
order to assess the accuracy of the positioning component. Extended discussion about the system’s architecture,
integrated Kalman filter design, and GPS/INS error sources and modeling, as well as initial test results were
presented in [11, 15, 7, 16, 17]. This paper discusses the results of the airborne tests performed in summer 1998 with
the prototype AIMS™ hardware configuration, and reviews the key aspects of multi-sensor system calibration and
their influence on the ground object coordinates.


DIRECT IMAGE GEOREFERENCING


Sensor orientation, also called image georeferencing, is defined by a transformation between the image coordinates
specified in the camera frame and the geodetic (mapping) reference frame. This process requires knowledge of the
camera interior and exterior orientation parameters. The interior orientation, i.e., principal point coordinates, focal
length and lens geometric distortion characteristics, are provided by the camera calibration procedure. The interior
orientation parameters are only concerned with the modeling of the camera projection system, whereas the exterior
orientation parameters directly define the position and the orientation of the camera at the moment of exposure. In
photogrammetry, the six exterior orientation parameters (three coordinates of the perspective center, and three
rotation angles known as ω, ϕ, and κ) are determined using a mathematical model for transformation between object
and image spaces, defining correlation between ground control points and their corresponding image
representations. This illustrates a traditional approach, where georeferencing is achieved indirectly by adjusting a
number of well-defined ground control points and their corresponding image coordinates. In the case of frame
imagery, only one set of exterior parameters per image must be determined. However, for sensors such as
push-broom line systems or panoramic scanners, perspective geometry varies with the swing angle (panoramic
scanners), and with each scan-line (push-broom systems). For these kinds of sensors, the direct georeferencing by
means of GPS/INS integrated systems becomes indispensable in order to achieve operationally effective high
volume production.




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Implementation of the DPO system to frame imagery can render a dramatic reduction in the number of control
points, and might eventually lead to the elimination of AT in the traditional sense (however, it is still needed for
system calibration). Eventually, the GPS base station might be the only ground control point applied in the aerial
mapping process, translating into substantial cost savings. Furthermore, the automatic aerial triangulation requires
image matching, which might be very difficult for large-scale images of urban areas, no texture images, steep slopes
or moving objects. These problems are naturally avoided if direct georeferencing is used.


It should be emphasized, however, that special attention must be paid to the accuracy and reliability of the mapping
products generated by direct-orientation aerial systems. The requirements of position and attitude accuracy are
application dependent, defined primarily by the scale of the resulting maps. For example, cadastral or precise
construction engineering projects require sub-decimeter and at least 3-arcminute accuracy in position and
orientation, respectively [5]. However, the most demanding applications such as precise large-scale airborne
mapping with required mapping accuracy at 10-30 cm level may need higher precision for the exterior orientation,
depending on the imaging sensor and flight altitude. As an example, Table 1 presents the results of the simulations
of the impact of the errors in the camera exterior orientation on the positioning accuracy of the ground points
extracted from the imagery. A representative sample of 2000 sets of Von Gruber points (six evenly distributed
points in the image) was generated for every set of assumed errors in attitude and projection center location, and the
resulting mean error, median and RMS for the ground point location were computed, as shown in Table 1. Focal
length of 0.05 m and flight altitude of 300 m were assumed, which represents typical scenario of the low-altitude
mission with the medium format digital frame camera. For comparison, the focal length of 0.153 m and altitude of
1000 m, typical for large format analog aerial cameras, are also considered in Table 1. In addition, Figures 1 and 2
illustrate the dependence of the ground position error on the amount of error in the exposure center position and
image attitude at 300 m altitude. It can be observed in Figure 1 that for the fixed error in the exposure center
coordinates, the increase in the attitude error (to the extent considered here) does not significantly change the ground
position error. Consequently, an increasing error in the exposure center coordinates shows increase in ground
coordinate errors comparable for all the levels of errors in attitude analyzed here (Figure 2). This can be explained
by the fact that the assumed errors in attitude are relatively small, compared to the assumed errors in exposure center
coordinates, and their projection to the ground level from 300 m amounts to about 7 mm for 5 arcsec error, 1.4 cm
for 10 arcsec, 3 cm for 20 arcsec, 4.3 cm for 30 arcsec, and 8.7 cm for 60 arcsec. They become more important for
higher altitude flights and in situations where the exposure centers are estimated with high accuracy (below 10 cm),
which is currently achievable with quality GPS/INS systems.




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        Errors in                                              50 mm focal length                              153 mm focal length
        Xo,Yo,Zo                                                 300 m altitude                                  1000 m altitude
         ωo,ϕo,κo                                     Mean           RMS            Median             Mean           RMS          Median
                                                       [m]            [m]             [m]               [m]            [m]           [m]
         5 cm, 5”                                     0.142          0.088           0.119             0.134          0.076         0.117
        5 cm, 10”                                     0.147          0.091           0.128             0.173          0.103         0.149
        5 cm, 20”                                     0.168          0.106           0.142             0.275          0.165         0.236
        5 cm, 30”                                     0.192          0.119           0.163             0.393          0.236         0.338
        5 cm, 60”                                     0.303          0.193           0.254             0.775          0.467         0.671
       10 cm, 10”                                     0.287          0.182           0.239             0.266          0.155         0.232
       10 cm, 20”                                     0.297          0.190           0.248             0.348          0.209         0.301
       10 cm, 30”                                     0.307          0.194           0.260             0.436          0.265         0.373
       10 cm, 60”                                     0.396          0.245           0.346             0.791          0.473         0.681
       20 cm, 10”                                     0.569          0.345           0.488             0.491          0.288         0.425
       20 cm, 20”                                     0.576          0.362           0.488             0.535          0.311         0.466
       20 cm, 30”                                     0.587          0.364           0.502             0.611          0.359         0.533
       20 cm, 60”                                     0.603          0.382           0.504             0.893          0.536         0.768
       30 cm, 20”                                     0. 833         0.528           0.700             0.752          0.433         0.661
       30 cm, 30”                                     0. 858         0.533           0.737             0.805          0.470         0.694
       30 cm, 60”                                     0.879          0.547           0.740             1.036          0.612         0.901

Table 1. 3D ground point positioning error resulting from the errors in exterior orientation: simulation results.



                                             0.9

                                             0.8                                                Xo, Yo, Zo error 0 cm
                                                                                                Xo, Yo, Zo error 5 cm
                                                                                                Xo, Yo, Zo error 10 cm
                                             0.7                                                Xo, Yo, Zo error 20 cm
                                                                                                Xo, Yo, Zo error 30 cm
                    Ground point error [m]




                                             0.6

                                             0.5

                                             0.4

                                             0.3

                                             0.2

                                             0.1

                                              0
                                                  0            10       20          30         40              50        60
                                                                          Error in attitude [arcsec]



Figure 1. 3D ground point error as a function of increasing errors in attitude for variable error levels in exposure
     center location.




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                                              0.9
                                                       attitude error 0”
                                              0.8      attitude error 5”
                                                       attitude error 10”
                                                       attitude error 20”
                                              0.7      attitude error 30”
                                                       attitude error 60”
                     Ground point error [m]
                                              0.6

                                              0.5

                                              0.4

                                              0.3

                                              0.2

                                              0.1

                                               0
                                                   0       5           10         15          20   25   30
                                                                        Error in Xo, Yo, Zo [cm]



Figure 2. 3D ground point error as a function of increasing errors in exposure center location for variable error
     levels in attitude.


CURRENT HARDWARE CONFIGURATION


The prototype of the integrated GPS/INS system used in tests presented here comprises two dual-frequency Trimble
4000SSI GPS receivers, and a medium-accuracy and high-reliability strapdown Litton LN-100 inertial navigation
system, based on Zero-lockTM Laser Gyro (ZLGTM) and A-4 accelerometer triad (0.8 nmi/h CEP, gyro bias –
0.003°/h, accelerometer bias – 25µg). The LN100 firmware, modified for the AIMSTM project, allows for access to
the raw IMU data, updated at 256Hz [18]. Estimation of errors in position, velocity, and attitude, as well as errors in
inertial and GPS measurements, is accomplished by a centralized Kalman filter that processes GPS L1/L2 phase
observable in double-differenced mode together with the INS strapdown navigation solution.


The AIMS™ imaging component in the current configuration consists of a digital camera based on a 4,096 by 4,096
CCD with 60 by 60 mm imaging area (15 micron pixel size), manufactured by Lockheed Martin Fairchild
Semiconductors. The imaging sensor is integrated into a camera-back (BigShot™) of a regular Hasselblad 553 ELX
camera body, and the camera is installed on a rigid mount together with the INS. The current 6 s image acquisition
cycling rate is limited mainly by the CCD read-out rate. This acquisition time is too long to achieve the required
60% forward overlap for the fast moving airborne platforms at low altitude. Thus, for these missions a special flight
pattern has to be applied, where the flight lines are flown several times, and the required overlap is achieved by
combining images from the repeated passes.




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MULTI-SENSOR SYSTEM CALIBRATION


In traditional airborne surveying, angular components of EOP are related to the camera body reference frame. The
DPO rotational components are, however, naturally related to the INS body frame. In order to relate the GPS/INS-
derived positions and attitude components to the image point coordinates, a multi-sensor system calibration is
required. This procedure must be able to resolve the misalignments between the INS body frame and the imaging
sensor frame with sufficient accuracy. In addition, the imaging sensor has to be calibrated to determine the camera
interior orientation and the lens distortion parameters. The calibration parameters should stay constant for the entire
mission duration. Moreover, since the crucial part of the DPO concept is the rigidity of the common mount of the
imaging and the georeferencing sensors, no flex or rotation can occur during the airborne mission.


Camera calibration


Traditionally, the photogrammetric analog cameras have been periodically laboratory-calibrated for actual
estimation of the location of the principal point, focal length and lens distortion. CCD-based frame cameras
currently enjoy increasing interest among the remote sensing and aerial surveying communities. However, they are
not manufactured metric devices, therefore, their calibration has to be performed repeatedly by using a suitable test
range. Consequently, the AIMS prototype camera is not a metric device. Moreover, the connection between the
camera body and the sensor assembly is rather loose, therefore, significant changes in the location of the principal
point can be observed during the camera calibration after the CCD has been removed and re-attached to the camera
body (see Table 2). Hence, it is crucial that these type of digital cameras are frequently re-calibrated to recover the
current interior orientation parameters, if they are to be used in precision mapping applications.

                                            Calibration 1 -         Calibration 1 -         Calibration 1-
Parameter           Calibration 1           Calibration 2           Calibration 3           Calibration 4

  Xo [mm]                0.314                  -0.355                   0.389                   0.464
  Yo [mm]                0.112                  -0.115                   -0.264                  0.039

Table 2. Difference in principal point location between subsequent CCD frame camera calibration. Calibration 1 is
     used here as a reference.


For the airborne test described in this paper, the calibration of the AIMS camera equipped with 50-mm lens was
performed at the indoor test range, containing over a hundred high-accuracy survey points. A total of 610 image
coordinate pairs were measured on eight images acquired from four exposure stations and subsequently processed
with the OSU Bundle-Adjustment with Self-Calibration (BSC) software, providing estimates of the focal length,
principle point, and lens distortions. The additional parameters for decentering distortion and the affine
transformation for scale differences between axes were constrained to zero for compatibility with the used softcopy
system’s (Autometric SoftPlotter ) distortion model. This, however, introduces an error in the image coordinates at



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the order of 2-3 microns (equivalent to less than 0.2 of a pixel), and therefore is negligible. The calibration results
are shown in Table 3 and Figure 3. Clearly, this camera exhibits significant distortions (at the order of 450 microns
or ~30 pixels) towards the edges of the image. These distortions are typical to a camera that is not specifically
designed for photogrammetric applications.


                                        Parameter                 Value               Sigma
                                         C (mm)                   51.762              0.008
                                        Xo (mm)                   0.669               0.005
                                        Yo (mm)                   0.227               0.005
                                          Rad1                   -2.71E-05        3.40E-07
                                          Rad2                   1.38E-08         2.50E-10


Table 3. Calibration parameters of 50-mm lens equipped 4K by 4K CCD frame (C is the focal length, Xo and Yo
         are the principal point coordinates, Rad1 and Rad2 are the SoftPlotter lens radial distortion model
         parameters).




                              0
                        ]
                        s
                        n   -100
                        o
                        r
                        c
                        i
                        m
                        [   -200
                        s
                        n
                        o
                        i
                        t   -300
                        r
                        o
                        t
                        s
                        i
                        d   -400
                        l
                        a
                        i
                        d   -500
                        a
                        r     40
                                   20                                                   40
                                          0                                      20
                                                                             0
                                               -20                  -20
                                        [mm]         -40   -40            [mm]




Figure 3. Radial distortion surface for Carl Zeiss Distagon 4/50 lens.

Boresight calibration

Since DPO rotational components are naturally related to the INS body frame, they must be transformed to the
imaging sensor frame. The angular and linear misalignments between the INS body frame and the imaging sensor
frame are known as boresight components. The boresight transformation must be determined with sufficiently high
accuracy, and is usually resolved by comparing the GPS/INS positioning/orientation results with the independent



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aerotriangulation solution, or as a part of bundle adjustment with constraints. Naturally, the boresight parameters can
only stay constant for the entire mission duration if no flex or rotation of the common mount of the imaging and the
georeferencing sensors occurs during the airborne mission.


The quality of the boresight estimation is limited by the quality of the AT adjustment and the quality of the direct
orientation components that are used in the boresight estimation process. Consequently, the availability of a high
quality test range with very well signalized points that should be used for the calibration process becomes an
important issue. Our practical experiences indicate that even if the control points are surveyed with cm-level
accuracy on the ground, their poor signalization (non-symmetric marks, natural targets) may propagate to the
projection centers’ positioning quality (in the aerotriangulation process), immediately compromising the boresight
performance. As an example, Table 4 presents the effects of the image measurement error on the ground point
location error. This table was compiled for a sample of 2000 Von Gruber point sets, under the assumption that only
image measurements were erratic. Camera and flight parameters are similar to those presented in the second column
of Table 1.


              Image measurement             Mean [m]             Median [m]              RMS [m]
                 error [micron]
                3.75 (0.25 pixel)              0.06                   0.05                  0.04
                  7.5 (0.5 pixel)              0.12                   0.10                  0.07
                   15 (1 pixel)                0.24                   0.20                  0.15
                   30 (2 pixels)               0.47                   0.40                  0.29

Table 4. 3D ground point positioning error resulting from the errors in image measurement: simulation results.

Another important aspect that determines the quality and reliability of the direct platform orientation methods is a
reliable ambiguity resolution/cycle slip fixing procedure. Inability to restore the ambiguities after the loss of GPS
lock, especially over the long baseline, limits the systems’ operability. This is especially important for the real-time
applications where the positioning results cannot be rectified by the benefits of post-processing.


The effects of the boresight quality on the final object coordinates in the mapping frame can be shown based on the
analysis of Equation 1, which is the well-known georeferencing formula [1]. Under the simplified assumptions that
all the components, except for the boresight rotations and offsets, are error-free and uncorrelated, the covariance
matrix of the object ground coordinates can be obtained by the error propagation formula, as shown in Equation 2.
Table 5 illustrates an example of the effects of the errors in the boresight components on the object ground
coordinates. The rcj vector was selected as [0.015 0.015 0.05], the latitude and longitude were chosen as 40 deg and
–81 deg, heading, pitch and roll were selected at 100 deg, 3 deg and 3 deg, respectively for this example.



                                            M
                                                (
                        rM ,i = rM , INS + RBINS s ⋅ RC ⋅ rC , j + bBINS
                                                      BINS
                                                                           )                              (1)



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        MrM ,i = s 2 ⋅ RBINS ⋅ dRC ⋅ M ω ⋅ dRC
                        M        BINS
                                              (
                                             BINS
                                                       ) ⋅ (R )
                                                        T     M
                                                              BINS
                                                                   T
                                                                       + RBINS ⋅ M offset ⋅ RBINS
                                                                          M
                                                                                          (  M
                                                                                                    )
                                                                                                    T
                                                                                                             (2)



     where :
     rM ,i − 3D object coordinates in mapping frame
     rM , INS − 3D INS coordinates in mapping frame
     rC , j   − image coordinates of the object in camera frame C
      BINS
     RC        − boresight matrix between INS body and camera frame C
     R BINS − rotation matrix between body and mapping frames
       M


     MrM ,i − ground position covariance matrix
     M ω , M offset − diagonal covariance matrices of boresight angles and offsets, respectively
     dRC − partial derivative of RC ⋅ rC , j with respect to the boresight angles
       BINS                       BINS


     s - scaling factor
     bBINS - boresight offset vector



                                    Error in          Error in boresight angles
                                   boresight          10          20         60
                                   offset [m]       arcsec      arcsec     arcsec
                                   X       0.05      0.05        0.05       0.06
                                   Y       0.05      0.05        0.06       0.10
                                   Z       0.05      0.05        0.06       0.10


                                   X      0.10       0.10        0.10         0.11
                                   Y      0.10       0.10        0.10         0.14
                                   Z      0.10       0.10        0.11         0.13

                                   X      0.20       0.20        0.20         0.20
                                   Y      0.20       0.20        0.21         0.23
                                   Z      0.20       0.20        0.21         0.23

Table 5. Error in object’s ground coordinate due to boresight error [m].


MULTI-SENSOR SYSTEM: PERFORMANCE ANALYSIS


The airborne test analyzed here was conducted in cooperation with the University of Florida and the Florida
Department of Transportation. The major goals of the mission were to evaluate the georeferencing performance of
AIMS in the production environment, and delivery of a digital elevation model (DEM) of the transportation
corridor in the Callahan area. Due to the low altitude requirement, a special flying pattern had to be used to resolve
the conflict between the required high image acquisition rate (1.5 s) and the limited camera cycling time (6 s).




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Therefore, the project area was divided into smaller segments, which were flown in several passes with phased
image capture, as shown in Figure 4. To provide sufficient overlap margin, six passes were organized with 1 s
delayed image acquisition. The data processing focused mainly on the central segment of the Callahan area.


GPS/INS Processing Results


To analyze the system’s mapping performance, the GPS and the inertial data collected over the transportation
corridor were processed by the integrated filter. The resulting estimated standard deviations per coordinate for the
IMU center averaged around 2 cm. The estimated standard deviations for the attitude components were at the level
of about 5 arcsec during the portion of the flight where the image data were collected.




                                 30.6



                                30.58
               latitude [deg]




                                30.56



                                30.54


                                                                            * - control points
                                30.52


                                   -81.9   -81.88   -81.86        -81.84       -81.82            -81.8
                                                          longitude [deg]



Figure 4. Aircraft trajectory over the Callahan area, June 2, 1998.

Aerial Triangulation Solution


A block of 18 images was aerotriangulated by the standard bundle adjustment method. The effective photo scale was
1:6,000, since a 50 mm lens was used at an average altitude of ~300 m. Control points with accuracy estimated at
the 2 cm level were available from a static GPS survey. The image measurements were collected using the
Autometric SoftPlotter digital photogrammetric workstation configured with the appropriate camera calibration
parameters, determined during the camera calibration, as described earlier. The accuracy of the image coordinate
measurement was at the level of 7 microns. Table 6 below summarizes the aerotriangulation results.




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     Exterior             Image point               Perspective               Control
    orientation           measurement                  center                  point
                             RMS                        RMS                    RMS
         Xo                7 microns                   0.12 m                 0.02 m
         Yo                7 microns                   0.14 m                 0.02 m
         Zo                   N/A                      0.04 m                 0.02 m
         ωo                   N/A                    1.5 arcmin                N/A
         ϕo                   N/A                   1.27arcmin                 N/A
         κo                   N/A                    0.3 arcmin                N/A


                                    Table 6. Photogrammetric adjustment results.



GPS/INS and Aerotriangulation: Comparison of the Results


The boresight estimation was performed by comparing AT and GPS/INS positioning and attitude estimates. The
resulting boresight standard deviations were 0.29, 0.17 and 0.15 m for the linear displacements, and 3.7, 2.7 and 1.7
arcmin for the rotation angles, respectively (for the estimates based on the six centrally located images, containing
the majority of the control points, the respective standard deviations were: 0.22, 0.08 and 0.06 m for the offsets, and
1.8, 2.4 and 0.6 arcmin for the rotation angles). These accuracy measures were not as good as expected. Some
possible reasons are photogrammetric processing accuracy, mechanical problems with the camera body/mount, and
anomalies in the image time tagging. It should be emphasized, that although the photogrammetric adjustment results
were relatively good (see Table 6), the photogrammetric solution is composed of internal and external constraints
such as tie points and control points. These constraints, intensified by image resolution and geometric modeling
inefficiencies, imply limitations on the image measurement accuracy. For example, even though the control points
were surveyed at cm-level accuracy on the ground, due to their poor signalization their image representation
measuring accuracy was not even close to the otherwise sub-pixel image measurement performance. This poor
localization was subsequently propagated to the projection centers’ positioning quality. Therefore, the boresighting
performance was immediately compromised and never reached the accuracy range of the GPS/INS data.

Additional problems that could explain the rather moderate quality of the boresight estimation are possible
variations in the mechanical structure of the camera body/mount/INS assembly during the flight, and the image time
tagging. The light body of the Hasselblad camera is subject to flex. A single point connection between the camera
body and the steel plate (limited by the camera design) of the mount is another likely source of some deformations
that map as random errors to the boresight components. It cannot also be ruled out that there was some discrepancy
in the timing of image captures. Table 7 presents the differences between the bundle adjustment-determined and
GPS/INS-derived exterior orientation data sets, after the boresight transformation was applied to the DOPs.




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    Navigation, Vol. 46, No. 4, pp. 261-270, 1999

                                    Image        Dx[m]       Dy[m]         Dz[m]
                                    38274         0.03        0.12          0.05
                                    37425         0.04       -0.02         -0.03
                                    37419         0.13        0.26         -0.02
                                    37026        -0.10       -0.37         -0.11
                                    37020        -0.09        0.03          0.00
                                    36620         0.00       -0.02          0.10
                                     Mean         0.00        0.00         -0.00
                                     RMS          0.09        0.21          0.07

                                    Image          κ
                                                 Dκ[deg]      φ
                                                            Dφ[deg]         ω
                                                                          Dω[deg]
                                    38274         -0.014     0.025         0.023
                                    37425         -0.041     0.024         -0.015
                                    37419         -0.010     0.023         -0.033
                                    37026         -0.024     0.022         0.020
                                    37020         -0.025     -0.014        -0.052
                                    36620         -0.015     -0.058        -0.066
                                     Mean         -0.021     0.004         -0.020
                                     RMS          0.010      0.033         0.043

Table 7. The differences between the boresighted GPS/INS and AT-derived exterior orientation parameters.


An additional quality check was performed by a manual measurement of 3D coordinates of the control points in four
stereo models oriented by DPO, each one containing two to five control points. The comparison of these results with
the reference ground coordinates is presented in Table 8, which clearly indicates that the quality of positions derived
from directly oriented imagery was compromised by a moderate quality of the boresight parameters, as explained
above.


             Stereo Pair                    dX                       dY                        dZ
                                 Average         Sigma     Average        Sigma     Average         Sigma
          37425     37026          -0.132        0.193      -0.154        0.185       0.230         0.206
          37026     36620          0.154         0.294      -0.189        0.188       0.442         0.158
          36620     38274          0.159         0.095      -0.083        0.170       0.298         0.219
          38274     37419          -0.271        0.514      0.292         0.140       -0.255        0.065
           Total Average           0.034         0.311      -0.066        0.237       0.298         0.219
                RMS                0.187                    0.195                     0.317

Table 8. Average differences between nominal and manually measured control point coordinates.


Final DEM and Orthophoto Generation


Final DEM of the highway intersection in the Callahan area was generated by the Autometric SoftPlotter DEM-
collection tools using GPS/INS-oriented images. Due to high image resolution over relatively featureless areas,
which cannot be properly handled by the correlation process implemented in SoftPlotter, and somewhat moderate
accuracy of DPO components, the system was unable to properly determine the elevation everyplace at the desired



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spacing, which forced some regions to be filled with values interpolated from neighboring regions. Thus, a large
fraction of the surface model was interpolated, leading eventually to manual editing of the roads and paved lots
around the buildings. The final DEM was compiled from the edited stereo pairs oriented with boresighted GPS/INS
DPO. The overall quality of the DEM is approximately 20 cm for the manually edited parts, and can reach a meter
or more for the unedited parts, due to the problems listed above. Figure 5 illustrates the orho-mosaic derived from
the images rectified by the DEM obtained from the DPO oriented stereo pairs.




Figure 5. Ortho-mosaic of the Callaghan intersection area.


LAND VEHICLE-BASED TEST


The integrated GPS/INS/CCD system was also tested in terrestrial applications. The sensor assembly was mounted
on the top of a van for acquiring data for a topographic survey of transportation corridors. The imagery was
collected along the surveyed road, and the subsequent stereo-pairs (formed by the time-offset succeeding images)
were formed with the directly acquired orientation parameters. The resulting GPS/INS positioning standard
deviation stayed at the level of 1-2 cm; pitch and roll standard deviations were at ~5 arcsec level, while for heading




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    Navigation, Vol. 46, No. 4, pp. 261-270, 1999

it reached 7 arcsec. Boresight calibration was established based on well-signalized points, with object distance of 8-
20 m.


Examination of the repeatability of the solution obtained for the checkpoints measured in different directly oriented
stereo pairs provides an overall accuracy indication of the system. The statistics of such a comparison, based on 44
stereo pairs, is presented in Table 9, and indicate that the direct orientation parameters were indeed estimated with
high quality. Another repeatability test was performed by comparing the ground coordinates of 15 check points
measured on the directly oriented stereo pairs from two different passes, as shown in Table 10. The GPS/INS/image
data for those passes were collected with slightly different GPS constellation; the first pass observed six to seven
satellites, whereas the second pass was able to collect GPS data from no more than five satellites. This is reflected in
the differences listed in Table 10 that are slightly higher than their counterparts from Table 9.


                           Statistics       Easting       Northing        Height
                                              [m]           [m]            [m]
                           Mean              0.015         0.004          0.008
                           Median            0.006         0.003          0.006
                          Maximum            0.050         0.025          0.035
                            RMS              0.019         0.007          0.010

Table 9. Ground coordinate difference for the control points measured from different stereo pairs.


                           Statistics       Easting       Northing        Height
                                              [m]           [m]            [m]
                           Mean              0.015         0.014          0.044
                           Median            0.013         0.011          0.045
                          Maximum            0.050         0.034          0.130
                            RMS              0.020         0.018          0.052

Table 10. Ground coordinate difference for 15 control points measured on stereo pairs from different passes.


The ultimate accuracy test for the direct orientation derived from GPS/INS after the boresight was applied, is the
comparison of the ground coordinates obtained by the photogrammetric methods based on the directly oriented
imagery, and the ground coordinates of the GPS-determined control points. The control points used in this test were
estimated with accuracy of ~1.5 cm per coordinate. They were located ~20 m from the perspective center of the
camera when the imagery was collected. The comparison performed on 4 control points is presented in Table 11.




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    Navigation, Vol. 46, No. 4, pp. 261-270, 1999


                             Point      Easting        Northing       Height [m]
                                          [m]            [m]
                               1         0.002          0.029            0.008
                               2         0.009          0.015            0.000
                               3        -0.019          0.029            0.010
                               4        -0.059          0.018            0.009

Table 11. Coordinate difference between control points measured in the imagery and the ground truth.


SUMMARY


The study presented here was conducted primarily to assess the quality of direct georeferencing of the medium size
digital frame imagery with differential GPS integrated with a medium/high quality IMU. The importance of the
proper system calibration, with special emphasis on the non-metric digital camera calibration and boresight
calibration, as well as the significance of using a special calibration range was discussed. In particular, the effects of
the errors in the exterior orientation on the accuracy of the ground point location were analyzed. The impact of the
errors in boresight components and image coordinates on the ground coordinates was also presented. The analysis of
the results indicates that the major limitations of the GPS/INS/CCD system performance of the AIMS prototype,
in the airborne mission presented here, are due to insufficient quality of boresight estimation. This, in turn, is a
consequence of the lack of properly signalized targets of geodetic control quality, and the lack of rigidity of the
camera body and camera/mount/INS assembly of the current prototype. Both have seriously impacted the
photogrammetric data reduction. The total error introduced by point misidentification (due to lack of proper
signalization on the ground) during the image measurement of the control points has propagated into the
triangulation results, and limited the projection center accuracy far above the level of control point measurement
accuracy. Consequently, the boresight computation, which is single most critical item connecting the positioning and
imaging components, has inherited this poor accuracy. Therefore, a better control of the boresight errors might be
achieved by the embedded system architecture, where IMU is permanently attached to the camera body. Moreover,
in any precise mapping applications with DPO, special attention has to be paid to the multi-sensor system calibration
that should be performed with a quality test range of the ground targets.


Additional tests performed with the land-based vehicle, where the object distance to the well-signalized control
points was 8-20 m, indicated that the integrated system is capable of delivering a high quality georeferencing.
Naturally, for shorter object distances any possible inaccuracy in boresight components or flex of the camera/IMU
mount has much less visible effects as compared to 300 m altitude for the airborne test discussed here.




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     Navigation, Vol. 46, No. 4, pp. 261-270, 1999



ACKNOWLEDGEMENTS


The AIMS™ project was supported by the NASA Stennis Space Center, MS, Commercial Remote Sensing Program
grant #NAG13-42, and grants from Litton Guidance and Control Systems, Inc. and Lockheed-Martin Fairchild
Semiconductors. The test flight discussed here was supported by the University of Florida and Florida Department
of Transportation. This support is gratefully acknowledged. The author wishes to thank Dr. Charles Toth for his
helpful comments and suggestions, and Mr. Edward Oshel for providing the photogrammetric data processing.


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