KINEMATIC GPS
The GPS consists of 24 satellites orbiting about 20,000 kilometers
above the earth. The satellites transmit information in two carrier
frequencies L, and L, and modulated by two codes P and C/A code.
Differential GPS tracks the same satellites from two stations. Using
the carrier phase frequency, the base line vector can be computed
accurately. The accuracy depends on the accuracy of the phase
measurement, error due to multipath and the ionospheric error
depending on the distance between the two stations. The use of P
and C/A code may eliminate the multipath and use of L, and L, may
eliminate the ionospheric error. The receivers, such as the Z12
Ashtech receiver, measures the phase to an accuracy of 0.2
millimeters or better and has the capability of tracking L, and L,
frequencies.
In Kinematic GPS one of the receivers is fixed at the base station
and the other is free to move. The phase angle from each satellite
is measured continuously. However, only portions of the phase
angle less than 2x are measured at one time; hence the receiver has
to keep track of the total phase angle, and the integer number of 27.
When a receiver moves, there is a possibility that it may loose track
of a satellite and loose the integer number of 2x. Knowing the
position of the base receiver and the position of the rover, using the
other satellites, it is possible to calculate the lost integer count. The
PNAV software is capable of resolving the integer ambiguity on the
fly, provided there are more than 7 satellites at a time.
APPLICATION OF KINEMATIC GPS IN
PHOTOGRAMMETRY
If a GPS antenna is fixed above the camera nodal point in an
aircraft (camera antenna), then its position, (see Fig. 1) determined
in real time by kinematic mode, can be used to take aerial photos at
predetermined locations. Thus Kinematic GPS is used in pin-point
navigation for photogrammetric mapping.
Using differential Kinematic GPS, the camera's location (x,, y,, Z,)
can be determined precisely. Thus, in a stereo pair, of the 12
exterior orientation elements, six can be determined by Kinematic
GPS methods. Five of the exterior elements can be determined by
relative orientation and 12th element, à, has to be determined by
external ground control.
In a triplet with two photos in the y direction and two photos in the
x direction (see Fig. 2), the kinematic GPS can be used to determine
9 exterior orientation elements and the relative orientation to
determine the other nine exterior orientation elements.
In an aircraft, if 4 antennas are mounted as shown in Fig. 1 such that
the left wing antenna and the right wing antenna is along the y axis
of the aircraft, the camera antenna C and the forward antenna F is
along the x axis, then the Kinematic GPS can be used to determine
the locations of these antennas at the time of the exposure. From
the location of the antennas, the rotation angles of the aircraft with
respect to the ground system (x5, ys,Za) can be obtained from:
Sin às 7 (Z, - ZULR
Sin $ - (Z,- Z./ FC
Sin K * (Y;- Y. FC (2)
If R is the rotation matrix which makes the camera axis (Xe.YesZe)
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
parallel to the aircraft axis (x4,y4.Z4), then the rotation angles of the
camera is given by:
A-RA'R! (3)
where
A’ =RK; * Rd; * Rog and A=RK, * Ro, * Ru,
A’ = rotation of the aircraft obtained by GPS
A = rotation of the camera
R( ) = Rotation matrix about z, y or x axis
Thus in an aerial photo all the exterior orientation can be determined
by kinematic GPS provided the parameters of the matrix R are
determined by calibration. This means that no ground control is
required for rectification, stereo plotting, and orthophoto production.
RESULTS OF SELF CALIBRATION
On June 20, 1994, the Cessna aircraft fitted with four L,/L,
antennas and a I, antenna for navigation, was used to test the
airborne GPS concepts (see Fig. 3).
The aircraft was taxied over the Taxi point; the four GPS Z12
receivers were connected to the L,/L, antennas and arranged to
collect the data on flight. Two Z12 GPS receivers were set on the
nearby reference points Basel and Base 2.
The flight plan consists of one flight in the East - West direction at
a flying height of 3000 feet over the ISU campus, and another over
the ISU campus and continuing over the Highway 30 test site at a
flying height of 1500 feet (see Fig. 4). The campus site is 3 to 5
kilometers from the airport and the Highway 30 site is about 17 to
30 kilometers from the airport.
The results were smooth and the positions of the antennas with
respect to all three references agreed within acceptable limits. Fig.3
shows the location of the left wing, right wing and camera antennas
with respect to the Taxi point. The difference between the camera
antenna coordinates determined by PNAV when the aircraft is over
the Taxi point and the coordinates from control survey is 0.06
meters in x and 0.13 meters in y indicating that the PNAV position
determination is accurate and the small difference shows the ability
of the pilot to taxi the plane exactly over the Taxi point. The height
of the camera antenna above the camera's nodal point given by
PNAV and the tape measurement is 1.541 meters which compares
with the previous calibrated value of 1.464 meters; the difference
is due to the use of a cloth tape for measurement and the lack of
knowledge of the exact location of the nodal point.
Using the time, antenna locations, and angles at all times of flight;
the angles at camera exposure times are prepared by utilizing a
spreadsheet.
For this study, it was sufficient to accept the data with Base 2 as a
reference and the interpolated antenna positions given by the PNAV
software. Photos 1-3 from flight 1; and photos 4,5,6, and 7 are from
flight 2 campus site and photos 8 & 9 are from flight 2 Highway 30
site are used in the analysis .
Table 5 shows that the difference in orientation angles between the
photogrammetry and GPS methods were consistent for the campus
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