

FRINGE 96
Impact of Precise Orbits on SAR Interferometry
Christoph Reigber 
 GeoForschungsZentrum Potsdam
Telegrafenberg A17, D14473 Potsdam
reigber@gfzpotsdam.de

Ye Xia   GeoForschungsZentrum Potsdam
Telegrafenberg A17, D14473 Potsdam
xiaye@gfzpotsdam.de

Hermann Kaufmann 
 GeoForschungsZentrum Potsdam
Telegrafenberg A17, D14473 Potsdam

FranzHeinrich Massmann 
 GeoForschungsZentrum Potsdam, GFZ/DPAF
c/o DLR, D82230 Oberpfaffenhofen
fhm@dfd.dlr.de

Ludger Timmen 
 GeoForschungsZentrum Potsdam
Telegrafenberg A17, D14473 Potsdam
timmen@gfzpotsdam.de

Johann Bodechtel 
 Institute for General and Applied Geology
University of Munich
Luisenstr. 37, D803333 München

Michaela Frei  
Institute for General and Applied Geology
University of Munich
Luisenstr. 37, D803333 München

*   
Abstract

 For repeat pass SAR interferometry, two precision orbit
products from ESA (processed at GFZ/DPAF, Oberpfaffenhofen) are
available: ERS1/2.ORB.PRC's and ERS1/2.ORB.PRL's. The conversion
of interferogram phases to absolute surface heights require a
relative baseline accuracy of 5 cm or even better. In a case study,
the preliminary (PRL) and precise (PRC) orbits are used to derive
DEMs. The results are compared with existing DTMs. In the test
area in Thuringia (Germany), corner reflectors allow an additional
accuracy assessment. The impact of orbit uncertainties on DINSAR
deformation analysis is less critical and the PRC's already fulfil
the accuracy demands. This is demonstrated by an example from
the Dead Sea transform zone in Israel.

 Keywords: Precise Orbits, DEM accuracy, corner reflectors
 Introduction
 Repeatpass interferometric techniques are employed for generation
of topography models (DEMs) and, as a related application, for
monitoring temporal surface changes (deformations connected with
earthquakes or vulcanism, land sliding, soil erosion). The "state
of the art" radar sensors, such as those established on ERS2
and RADARSAT, acquire SAR image pairs from seperated orbit positions
at different epochs. Their accurate knowledge allows a fringe
pattern estimation of a reference surface and a conversion from
phase differences to surface heights or displacements. Actually,
there are uncertainties in the available orbit ephemerides which
may distort the imaging geometry significantly. This problem can
partly be overcome by using flat areas or sea shores as references.
After "flat earth" correction (reduction of ellipsoid
fringes), the interferogram fringe pattern must not show any height
changes in this parts of the image. The interferogram may be adjusted
and a conclusion for the relative orbit positions can be drawn.
A more sophisticated approach for baseline assessment is to deploy
a radar corner reflector array over the scene, e.g. one line of
reflectors in slant range and one in azimuth direction. Unfortunately
this can only be done in very few study areas because of the logistical,
financial and timing limitations. The most straightforward way
to solve the baseline problem is the determination of precision
orbits using geodetic satellite tracking techniques like laser
ranging and PRARE range and doppler observations. In this paper,
the accuracy of the ESA orbit products ERS1/2.ORB.PRC and ERS1/2.ORB.PRL
is investigated and compared with the SAR interferometry (INSAR)
requirements.
 ERS orbit accuracy demands
 In order to obtain an analytical estimation of the required
orbit accuracy for INSAR applications, the mathematical dependency
of the interferogram phase from the SAR sensor and the object
position have to be understood. In Fig. 1, the across track interferometer
geometry is shown with a plain reference surface (for simplification),
the sensor positions S_{1} and S_{2} at altitude
H, the object P with elevation h, the baseline components
B_{x} and B_{y}, the slange ranges
R_{1} and R_{2}, and the offnadir
angle (look direction). Because the height h as well as
the baseline length B are small compared with H
or R, the following equation is valid (Hartl and Xia 1993):

 (1) 

 By differentiating with respect to B_{x}, B_{y}
and H, we obtain:

 (2) 



 Fig. 1: Imaging geometry of a SAR SLC image pair
(S_{1}, S_{2}: sensor position at epoch 1 and
2; R_{1}, R_{2}: slant ranges to object P; B_{x},
B_{y}: baseline components; h: topographic height)

 For INSAR the impact of orbit uncertainties on areas with
limited extension in ground range are of interest. Therefore,
the maximum relative error d = d_{far}  d_{near}
has been calculated. The extension of the test areas are assumed
to be 5 km (local) and 50 km (regional), and the baseline seperation
is considered with 50 m (differential INSAR applications) and
200 m (DEM generation). Approximate parameters of ERS1 SAR system
( = 0.057 m, H = 785000 m, R_{mid swath}_{
}= 853000 m) are introduced in the error equations.
The interferogram phase shows a very low sensitivity to errors
in sensor altitude. With dH = 10 m, the effect on topography or
displacement is in the order of 1 m or 1 mm. For baseline errors
of 0.05 m and 1.00 m, systematic phase errors will be obtained
as compiled in Tab. 1. They are converted to surface displacement
or topography errors using the equations:

 (3) 
 To assess the results in Tab. 1, they have to be related to
the phase noise which is typically inherent in an interferogram
of ERS1/2 SAR data. The noise is caused by temporal decorrelation
(e.g. vegetation, moisture), atmospheric perturbations, geometric
baseline decorrelation, as well as data acquisition and processing
defects. The validation of radar topography maps yielded errors
of 5 to 10 m rms, (e.g. Prati et al. 1993, Small et al. 1993,
Schwäbisch 1995, Zebker et al. 1994). This corresponds to
a phase uncertainty of about one tenth of the wavelength or 0.6
rad. The phase noise acts mainly locally on a DEM and not systematically
over the whole image. The effect of local noise may be a few times
larger than the rms values. Therefore, the impact of orbit uncertainties
is allowed to be in the order of 0.6 rad or even larger for local
displacement analyses.

 Tab. 1: Systematic errors for surface heights and
displacements due to baseline errors of 0.05 m and 1.00 m. The
derived values are related to areas with 5 km (local) or 50 km
(regional) spartial extension, and to baseline length of 50 m
(for change detection) or 200 m (for topography modelling).

 dB_{x}=0.05 m

 dB_{y}=0.05 m

 dB_{x}=1.00 m

 dB_{y}=1.00 m

 Interferogram Phase
 Error
   

 d(5 km) [rad]

 0.06

 0.02

 1.1

 0.5

 d (50 km) [rad]

 0.5

 0.2

 10.2

 4.6

 Displacement Error
 (Slant Range)
   

 d(5 km) [mm]

 0.3

 0.1

 4.9

 2.2

 d (50 km) [mm]

 2.2

 0.9

 45.5

 20.5

 Topography Error,
 B_{x}=50 m
   

 dh(5 km) [m]

 2.0

 0.7

 36.4

 16.6

 dh(50 km) [m]

 16.6

 6.6

 337.8

 152.3

 Topography Error,
 B_{x}=200 m
   

 dh(5 km) [m]

 0.5

 0.2

 9.1

 4.1

 dh(50 km) [m]

 4.1

 1.7

 84.4

 38.1

 From Tab. 1 the following conclusions can be drawn:
 as expected, the across track baseline component B_{x}
is dominant, but the radial component must not be neglected;
 to avoid significant systematic errors in topography mapping
(e.g. a tilt in ground range direction) a baseline precision of
5 cm has to be striven for;
 for the detection of surface uplift or subsidence in areas
with local extension, the baseline precision should be better
than 1 m; for areas with larger extensions, the baseline should
be accurate up to 0.1 m.
 At GFZ/DPAF, the quality of the generated orbit products
ERS1/2.ORB.PRC and ERS1/2.ORB.PRL is controlled internally by
examining the fits of the laser ranges and the altimeter crossovers
to the adjusted orbits and by comparing overlapping arc segments
(Massmann et al. 1994, Gruber et al. 1996). Results (mean differences)
of orbit investigations over a time interval of 6 month are given
in Tab. 2.

 Tab. 2: Accuracy of ESA orbit products ERS1/2.ORB.PRC
and ERS1/2.ORB.PRL, derived form internal quality checks (fit
of tracking observations to adjusted orbit, comparison of overlapping
arc segments)
 Orbit Product

 radial

 across

 along

 .PRC

 7 cm

 33 cm

 31 cm

 .PRL

 8 cm

 35 cm

 35 cm

 As shown in Tab. 2 the accuracy of .PRC and .PRL products
is very similar. The demanded accuracy of 5 cm for DEM generation
is not achieved, which makes a baseline estimation during the
interferometric SAR processing still necessary. Such an estimation
can serve as an external test of the orbit quality and will help
to find out, whether there are advantages of .PRC orbits compared
to .PRL orbits.
Application of ESA ERS1/2 orbit products
In this section we provide two INSAR products generated with the
ESA orbit products (humid climate in Germany, arid climate along
the Dead Sea Rift). It is demonstrated how the orbit is used to
generate the fringe pattern of a reference flat surface and what
the orbit accuracy is.
In the first example a digital elevation model (DEM) is generated
for the test area Ronneburg in Thuringia/Germany (50.8° N
and 12.2° E). The single look image data pair was acquired
during a tandem operation on the 8th of Feb. 1996 by ERS1 and
on the 9th. of Feb. 1996 by ERS2. Fig. 2 shows the intensity
of the SAR image over an area of 30 km in azimuth and 40 km in
ground range. As reference the ellipsoid surface of WGS84 is applied.
The following equation models the fringe pattern of the ellipsoid
surface for a slant range line in the interferogram:

 (4) 
Here, is the phase of the pixel i (i is normalized
by image pixel number N1 from 0 to 1), _{0
}is the initial phase of the considered line, c_{0},
c_{1}, and c_{2} are the polynomial
coefficients. The instantaneous fringe frequency derived from
Eq. 4 is:

 (5) 
In order to calculate the polynomial coefficients c_{0},
c_{1}, and c_{2} the following linear
equation system has to be solved:

 (6) 
Here f_{0}, f_{1/2} and f_{1}
are the instantaneous fringe frequencies by i=0,
1/2 and 1, respectively.
The mathematical representation of the orbit (position and velocity)
for the primary and the secondary satellite is identical, but
with different coefficients:

 (7) 
The coefficients are derived from the precision orbit ephemerides
as determined by GFZ /DPAF in accordance with the image acquisition
time. By means of the orbital state (position vector and
velocity vector )
and using equations from Curlander (1982), the pixel coordinate
P_{(Xp, Yp, Zp)} for i=0, 1/2,
and 1 can be determined for each slant range line:

 (8) 
The position of the secondary satellite according to object P
is obtained by solving the following equation:

 (9) 
As soon as the satellite positions and pixel position for i=0,
1/2, and 1 are known, the instantaneous fringe frequency
is obtained from equation

 (10) 
Removing the fringe pattern of the reference surface, the residual
phase (or socalled relative phase) remains, which is shown in
Fig. 3. After phase unwrapping and conversion from phase to height
(Fig. 4), a comparison between the INSAR elevation model using
.PRC orbits and the DEM derived from aerial photogrammetry (Fig.
5) can be carried out. Fig. 6 shows a systematic slope error of
65 m in across direction from near range to far range (40 km).
In this case (baseline=142 m) the systematic slope error of 65
m is equivalent to a fringe frequency error of 0.89 or a baseline
error of 62 cm. Fig. 7 compares the corrected height model derived
from INSAR with the DGM. In the test area of 30 km * 40 km the
standard deviation is 8.5 m (or in phase 40°) and the mean
difference is 0.06 m. The maximum differences occur in the area
of the opencast mining where large mass movements (depositing
of slagheap material in the open pit) are taking place since several
years.
To compare the accuracy of the ESA orbit products ERS1/2.ORB.PRC
and ERS1/2.ORB.PRL, the Ronneburg data set is evaluated with
each of them. In Tab. 3, the fringe frequencies are calculated
for the first slant range line as an example, the baseline is
estimated in the middle of this line. The improvement of fringe
frequency and baseline estimation by using of the .PRC orbit instead
of the .PRL orbit is only 0.05 and 4 cm, respectively. This result
confirms the assessment from the internal quality checks of the
GFZ/DPAF [Tab. 2].
Tab. 3: Comparison of the fringe frequencies and the
corresponding baseline after applying the ESA orbit products ERS1/2.ORB.PRC
and ERS1/2.ORB.PRL: the improvement for fringe frequency
and baseline is 0.05 and 4 cm, respectively
 fringe f_{0} 
fringe f_{1/2}  fringe f_{1}
 baseline (m) 
derived from PRC  223.09 
204.06  188.03  141.92

derived from PRL  223.04 
204.01  188.98  141.88

During the SAR data acquisition in Feb. 1996, 5 passive corner
reflectors (CRs) were available in the test area, all positioned
by GPS (5 mm accuracy). Tab. 4 compares the heights derived from
INSAR and GPS for all CRs.
Tab. 4: Comparison of CR heights derived from INSAR
and from GPS: CR 2 was chosen as reference point, as level
ellipsoid the parameters of WGS84 are used .
Corner No.  Height (GPS)
 Height (INSAR)  Height Difference

1  306.25m  305.42m
 0.83m 
2  295.50m  295.50m
 0.00m 
3  335.75m  333.45m
 2.30m 
4  328.32m  324.96m
 3.36m 
9  379.67m  369.40m
 10.27m 
The CR 2 was chosen as the reference point. The maximum difference
occurs for CR 9 and amounts to 10.27 m. A big metaled light, fixed
to a wooden post in about 5 m altitude, and not removed at that
time was just in the direction from CR 9 to the satellite. This
would explain the large discrepancy. Considering the first 4 CRs,
the result is very good. The differences correspond to a radar
wave resolution of 1 mm.
In order to check the impact of the ERS PRC orbits on geocoding
of INSAR images, a positioning procedure for all CRs were accomplished
by use of the Eq. (7), (8) and the CR heights as derived from
GPS. The result is shown in Tab. 5, the global geocentric coordinate
system of ITRF is used and the all differences were transformed
into a local astronomical coordinate system. The positioning accuracy
for all CRs is in the order of several meters. It must be noted
that the resolution of the sampling in slant range is 7.9 m, in
azimuth direction about 4 m, or the pixel spacing of ERS1 and
ERS2 is 20 m*4 m related to the Earth's surface.
Tab. 5: Comparison of the positioning results:
the global coordinate system of ITRF is used and all differences
are transformed into a local astronomical coordinate system
Corner  X (m) 
x (m)  Y (m)  y (m)
 Z (m)  z (m) 
Number  GPS  INSAR
  GPS  INSAR
  GPS  INSAR
 
1  3939304.5  3939312.5
 6.1  855789.4  855793.3
 0.5  4926507.9  4926509.5
 6.8 
2  3939234.6  3939243.2
 2.9  856216.2  856213.7
 6.0  4926476.4  4926478.5
 6.8 
3  3940137.9  3940145.2
 3.1  854230.7  854234.1
 0.1  4926152.6  4926155.0
 7.0 
4  3940583.2  3940590.5
 4.0  855904.6  855905.3
 2.6  4925500.6  4925503.5
 6.9 
9  3945132.2  3945147.0
 1.3  851565.0  851564.5
 6.3  4922695.9  4922693.0
 7.0 
The second example concerns the detection of subtle surface changes
along the Dead Sea Rift, the natural border between Israel and
Jordan. The zone is well known as an active plate boundary, marked
by e.g. 32 earthquakes with magnitude > Ms. 4.5 in 1993. Using
the differential SAR interferometry technique the area has been
investigated because an earthquake occured on November 22, 1995,
near the transform zone in the Gulf of Elat/Aqaba to the south.
In 1995 three single look complex image sets were acquired: on
August 16 (21373/585) and on November 29 (22878/585) by ERS1,
and on September 21 (2201/585) by ERS2, respectively. Fig. 8
shows the intensity image of the test area (29.24° N / 34.55
° E, 40 km*40 km). First we have calculated two interferograms
from the three data sets. The one pair (21373/585 and 2201/585)
with a baseline of 308 m spans 35 days, the other one (21373/585
and 22878/585) with a baseline of 76 m spans 105 days. In each
case the fringe pattern of the reference surface was removed using
the precise orbits. After phase unwrapping the first interferogram
was normalized with the baseline rate, and was subtracted from
the corresponding second interferogram. The result focussing on
the transform zone is shown in Fig. 9, where no distinct changes
due to coseismic displacements can be observed. This is mainly
due to the fact that the epicenter of the earthquake is located
about 100 km to the south in the Gulf of Aqaba/Elat. Nevertheless,
observable subtle changes in the data are various. There is an
increasing level (blue) of a surface muddump to the north caused
by mining activities at the Timma Complex to the southwest. Decreasing
values (red) are displayed by partly harvested vegetation areas
(south) covering the northern rim of the Gulf, and by pediments
and alluvial fans at the western part of the rift. Most of the
phenomena can also be attributed to heavy rains within the given
recording frame. Assuming that the accuracy of the baseline estimation
by use of the precise orbits is in the range of 1 m, and that
the standard deviation of the relative phase is not more than
40°, the accuracy of the detected mass movements is approximate
0.3 cm.
 Conclusions
 The accuracy requirement of the satellite orbits for SAR interferometry
is discussed in this paper. To avoid significant systematic errors,
a baseline accuracy of 5 cm for DGM generation and of better than
1 m for subtle change or mass movement detection has to be striven
for. The comparison of an elevation model derived from INSAR by
use of ESA precise orbits with the existing DEM demonstrates that
ESA precise orbits provides a baseline accuracy of better than
one meter. This satisfies the DINSAR needs in most cases. A positioning
example of CRs shows that an accuracy of 1 resolution cell may
be achievable. For the goal of DEM generation, the employment
of CRs and their GPS survey is still essential.

Fig. 2 Intensity image of the test area Ronneburg

Fig. 3 Relative phase image by use of .PRC orbits

 Fig 4. Elevation model derived from INSAR

 105 m 393 m

Fig. 5 Existing DEM derived from photogrammetry
 148 m 386 m


 Fig. 6 Height difference between DEM derived from
INSAR and existing DEM: a systematic slope error of 65
m in across direction (40 km) corresponds to a fringe frequency
error of 0.89 or to a baseline error of 62 cm.

 45 m 40 m

 Fig. 7 Height difference between corrected DEM
derived from INSAR and existing DEM: mean=0.06 m, standard
deviation=8.5 m, the maximum differences occur in the area of
the opencast mining.

 112 m 106 m

 Fig. 8 Intensity image of an area north of the
Gulf of Elat/Aqaba (Israel/Jordan): the scene site is 29.24°
N / 34.55° E, the area is 40 km * 40 km.

 Fig. 9 Result of DINSAR for the Dead Sea Rift
area in the transform zone near Elat/Aqaba: the data sets
were acquired at 16.08.95, 21.09.95 and 29.11.95. IHScolor merge
of optical (Landsat TM band 4) and differential INSAR result (I=TM,
H,S =DINSAR).

 1.4 cm 0 1.4 cm
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Keywords: ESA European
Space Agency  Agence spatiale europeenne,
observation de la terre, earth observation,
satellite remote sensing,
teledetection, geophysique, altimetrie, radar,
chimique atmospherique, geophysics, altimetry, radar,
atmospheric chemistry
