Requirement of Ground Tie Points for
InSAR DEM Generation
Guoqing Sun, K. Jon Ranson, Jack Bufton, and Michael Roth
including baseline length and tilt. Successful implementation
Ground tie points have been used to improve the accuracy of of an interferometric topographic mapping instriment requires
that both the uncertainties in the baseline components and the
a DEM derived from interferometric SAR (I~SAR)data. The
number of tie points required for ensuring certain accuracy of phase noise be minimized. Phase noise comes &om instrument
thermal noise and from decorrelation due to the changes in
the I~SAR-derivedDEM was investigated in this study in two
ways. One is the least-squares estimate of the corrections to a viewing geometry and target characteristics during the imaging
process. According to Zebker and Villasenor (1992),the effects
DEM using tie points, and the other is using an optimization
procedure to estimate the uncertainties in estimations of I~SAR of decorrelation due to thermal noise can be easily evaluated
parameters, mainly the baseline length, tilt angle, and reference and removed, while those due to slight angular changes
between flight tracks are negligible for data acquired using
phase using tie points, and resultant DEM error. It was found
near-repeat orbits. Spatial baseline and rotation-induced
that, in terms of required tie points, both give comparable
decorrelation can be derived using the Fourier transform of the
results. The latter method, though, can be applied in more
impulse
response intensity, and increase linearly with baserealistic cases to design the tie point acquisition strategy for
line or rotation in an ideal system. As the effects of these three
a mission.
sources of decorrelation can be quantified, their contribution
to the observed overall correlation can be removed, yielding a
Introduction
measure of the temporal decorrelation due to change in the tarAccurate knowledge of the topography of the Earth's surface is
get itself. For repeat-pass InSAR data, temporal decorrelation
important for hydrology, ecology, geology, and military applications. Recently, satellite-based methods have been developed due to the changes of targets will reduce the DEM accuracy, or
Bven make it impossible to estimate the elevation.
that show promise for providing digital elevation models
For the error source (2) listed above, ground tie points have
[DEMS)
over large portions of the Earth's surface. Development
of DEMs with Interferometric Synthetic Aperture Radar ( I ~ S A R ) been used to improve the accuracy of interferometry SARbasehas been demonstrated using airborne (e.g., Zebker et al., 1992; line estimation (Zebker et al., 1994; Small et al., 1993). Use of
tie points with known elevation can improve the estimation of
Madsen et al., 1993) and satellite (e.g., Moreira et al., 1995;
these parameters and provide an evaluation of the DEM
Lanari et al., 1996)image data. Another technique being develaccuracv.
oped is the use of laser altimeters or lidars to determine surface
The number of tie points required for ensuring a certain
heights from airborne or spaceborne systems. Each type of sysaccuracy level of the InSAR derived DEM was investigated in
tem has inherent problems which limits the accuracy or extent
this study in two ways. One used the least-square estimate of
of coverage. For example, InSAR can produce DEMs over large
the corrections to DEM using tie points, and the other employed
areas, but requires ground control points to establish high
an optimization procedure to estimate the uncertainties in estiaccuracy. Laser based systems cannot provide contiguous covmations of I ~ S Mparameters, mainly the baseline length, tilt,
erage of the Earth's surface, but can provide the ground control
and reference phase, and the resultant DEM errors.
points required by Insfa. For example, it has been estimated
that the proposed Vegetation Canopy Lidar satellite can provide the -lo8 ground control points (GCPS) required to correct a The lnSAR
The phase difference q5 from a pair of I ~ S Uimages is
global Insfa DEM (Dubayah et al., 1997). Sun and Ranson
(1997) demonstrated that Shuttle Laser Altimeter (SLA)data
4 = 2k (h - p) = 2k(,/p2 - 2pB sin (6' - or) + B2 - p) + &
could be used to provide surface control points to produce a
DEM from Spaceborne Imaging Radar-C interferometric data.
(1)
As described by Zebker et al. (1994),the significant error
sources of interferometric SAR-deriveddigital elevation are (1) where k = 2?r/A,B is the length of baseline, $is radar look (inciphase n d s e and (2) uncertainties in baseline components,
dence) angle, p and pz are the slant ranges of antennae 1(reference) and 2, respectively, or is the baseline orientation (tilt)
angle as shown in Figure 1,and & is a reference phase.
The radar incidence angle 0 is related to radar height H,
G. Sun is with the Department of Geography, University
slant
range p, Earth radius r, and elevation h by (Figure 2)
of Maryland, College Park, h4D 20742
[[email protected]).
K. J. Ranson is with NASA's GSFC, Biospheric Sciences Branch,
Code 923, Greenbelt, MD 20771 ([email protected]).
Photogrammetric Engineering & Remote Sensing
J. Bufton is with NASA's GSFC, Laboratory for Terrestrial
Vol. 66, No. 1,January 2000, pp. 81-85.
Physics, Code 920, Greenbelt, MD 20771
([email protected])
0099-1112/00/6601-000$3.00/0
O 2000 American Society for Photogrammetry
M. Roth is with the Applied Physics Laboratory, The Johns
and Remote Sensing
Hopkins University, Laurel, MD 20723 USA
-
J
January 2000
81
-
- -
+e
s.d.(p) =
2
B
u
- .--
. - ..r..
T-
=- u
4
(6)
-hux
where d is the variance of E ~ .
This equation implies that the variance of the slope estimate (p) will be small when: (1) the error variance d is small,
(2) the sample size n is large, and (3) the variance of the independent variable x i s large (Fox, 1997). In order to minimize
the variance of the estimated baseline tilt, the position of the tie
points should be located in such a way that the standard deviation of ground range x is maximized (i.e., tie points should be
evenly located at the extremes, the near and far ranges). If xis a
uniform distribution between a and b, its variance can be
shown to be (b - a)2/12. When the width (b-a) of the patch in
the range direction is R, and the required elevation error should
be less than E , the number of tie points (n) can be estimated by
1
8
TO Ground
Figure 1. lnterferometric
SAR geometry.
Figure 2. The geome
try of SAR looking at a
Point with elevation h
on the Earth.
dh =
xu
R J Z E < ~then
~ n>
4:) ):(
2
2
.
(7)
$ + (r + H)2 - (r + h)2
2p (r + H)
The key assumption of the simple regression are that the
error 4is normally distributed with mean 0 , and variance u2.u
is never known in practice and the variance of the residual of
the regression provides an unbiased estimator of u. If all errors
~h~ sources for InsAR elevation error are the
except the random errors of the tie point height measurements
of baseline length, baseline tilt, and phase.
were i ~ o r e dthen
* ucan be replaced by the error of the tie
The derivative of height h with respect to baseline length,
tilt, and interferometric phase will give a measure of the ~ S A R points.
Note that the error considered above is absolute error. If the
height error. If both radar height Hand slant range pare much
relative elevation error is to be considered, as in most cases, the
smaller than the ~~~~h
radius r, ~~~~~i~~~ and 2 can be
number of tie points may be estimated as follows. As shown in
bined and approximated as
Figure 3, the ground range x = x, + XI,where x,, is the ground
range of the center of the patch, which is the reference point,
4 = -2kB sin (0 - a)+ &,
(3) then we have
cose =
uncertainties
=
(
- 2 k B sin cos-I
("ah)-&)+&
-
dh
and the following derivative equation can be obtained:
dh
a4 sin(0 a)aB
={-=BI
-
+
1
aa
(4)
where B, = B cos(8 - a) is the perpendicular component of
baseline and x = p sin eis the ground range of the pixel.
The elevation error from InsAR consists of three components as shown in Equation 4, which we refer to as error budgets from uncertainties of baseline length, tilt angle, and InsAR
phase, respectively. The requirement on tie points was investigated in terms of these three error budgets in this study.
=
(x,
x1
+ x,) s.d. (P) = (dh), + RJJE
(8)
where -R/2 Ix, IR/2. The second term is the relative error. If
this error is to be less than E for the worst case lxll = R/2, then n
can be characterized by
dh
Error dh
-x
da
Methods and Results
LeastSquares Method
From Equation 4 and considering only the baseline tilt, if elevation height h, and ground range x, for i = 1,..., n define n tie
points, then a least-squares fit can be performed to estimate d a
(the slope Pin Equation 5) and E,, (the intercept) of the regression equation: i.e.,
dh=Px+~~+e,
(5)
where (dh),= z, - h,, i = 1,...,n. z is the elevation derived from
the InSAR. The error E,is the random error of the dependent
variable dh. The corrected elevation should be z, = z - xp. The
standard deviation, or the error of estimated P, can be written
as (Draper and Smith, 1982)
82
January 2000
Ralativa
xo
X
SAR ground range
Figure 3. Illustration of absolute and relative elevation
errors due to the uncertainty of baseline tilt angle a as
a function of radar ground range.
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
Figure 4 is the plot of Equation 9. When 1000 tie points
were used, the error budget ofbaseline tilt €would be ~118.3.If
the required error budget is 0.1 m and 1000 tie points were
used, the tie points error ushould be less than 1.83 m.
In Table 1, the percentage of pixels with various local
slopes in a DEM map (to be used for simulation in this study)
were listed. The tie point height errors were listed in Table 2 as
a function of local slope. The average error of tie points randomly located in this map can be estimated from these two
tables, and was 1.11meters.
SAR Parameters
DEM Data
Height 250 krn
Incidence angle 45" (image
center)
Wavelength 0.235 m
Baseline length 120 m and tilt
angle 10"
Elevation: 212 m to 2580 m
644 lines by 312 pixels
Pixel size 50 m
Local Earth radius 6380 Km
set to be 1.If the error distribution is not random but known,
we can assign a statistical weight to each data point. There are
many ways to fit the non-linear functions (e.g., Adby and
Dempster, 1974). Most of these general-purpose, non-linear,
Estimate Baseline Length, Tilt angle, and rnsAR Reference Phase by Optlmbation curve-fitting algorithms are recursive, and the parameters
Given n tie points of (hi,
pi), and +i,the problem of finding the
must be adjusted in an iterative way with no idea of how many
best values of B, a, and & is to minimize the error of the prerepetitions are needed to achieve convergence, or even if condicted phase angle, i.e., to minimize
vergence is possible (Caceci and Cacheris, 1984).The simplex
method used here was first proposed by Nedler and Mead
(1965),and the codes were translated into C from the Pascal
code list in the paper by Caceci and Cacheris (1984).As
described by Caceci and Cacheris, there are many advantages of
For random errors randomly distributed, the weight w's are the simplex method. It always converges, and it is fast, accurate, and simple.
Computer simulation was used to investigate the requirements
of tie points. From a DEM of a mountainous region and the
2 6 0 O r " " ~ ' " ' 1 " " ~ ' " ' ~ " " ~ " "
radar flight parameters (Table 3), the data set needed in Equation 10 can be simulated. For a uniformly distributed tie point
scheme, these points were randomly picked from the DEM. For
each of these points, the ground range pi and I ~ ~ A
phase
R +iwere
calculated using the DEM height ("true height") and the parameters of the radar flight (Table 3). Because the tie points to be
used represent the measurements from a laser altimeter, the
instrument error needs to be introduced. Table 2 shows that the
tie point accuracy is a function of local slope. We assume that
the tie point errors are normally distributed with zero mean and
standard deviations u (the error listed in Table 2). For each of
the
randomly selected tie points, the local slope was calcu500 lated. An error was generated from the distribution NO, a),and
then added to the "true height." Figure 5 illustrates the height
errors introduced to 1000 points using this method.
A total of n tie points were simulated and then the Simplex
0
5
10
15
20
25
30
Ratio of tiepoint error to required DEM error ( o l e )
method was used to find the best values for baseline length B,
Figure 4. A plot of Equation 9, which shows
the number of tie points required a s a function
of the ratio of the tie point height error to the
. E here is
required InsAR DEM error ( u / ~ )The
the DEM error budget of baseline tilt angle a.
6
SiA range error
4
TABLE1. PERCENTAGE
OF PIXELSFOR GIVENSLOPE
CATEGORIES
IN DEM DATA
Slope (")
0
1
2
5
%
4.18
0.00
0.00
20.31
Slope (")
10
15
20
25
%
26.87
18.82
14.34
6.80
%
Slope (")
30
35
40
45
4.30
2.20
1.24
0.94
E
U
2
C
,O
0
."
r
0,
.-
0
r
2 -2
-4
TABLE2. SLOPE
DEPENDENCE
OF SLA-02 HEIGHTERRORS
Slope (")
Error [m]
Slope ("1
Error (m)
Slope ("1
Error (m)
0
1
2
5
0.11
0.13
0.18
0.37
10
15
20
25
0.72
1.00
1.52
2.02
30
35
40
45
2.61
3.34
4.28
5.52
--
-
PHOTOGRAMMETRIC ENGINEERING 81REMOTE SENSING
-6
0
10
20
30
40
Slope (degree)
Figure 5. Errors of 1000 simulated tie points.
50
tilt a,and reference phase &,. The Simplex method does not
provide an estimate of the errors of B, a,and 6.In order to estimate the errors, a Monte Carlo analysis, i.e., repeating the above
process for a sufficiently large number of times (e.g., loo), was
performed. The standard deviations of the estimated B, a,and
are the reasonable estimates of their errors.
To summarize, the simulation procedure used to determine the requirement for the number of tie points was as
follows:
.
--
0.020
-&
0.015
-
0.010
-
-
0.005 -
-
'
'
.
.
E
5m
I
.
.
.
.
I
.
.
.
.
I
.
,
.
-
Using SLA height error table
...............
Height error fixed ot 0.1 l m
-
.--e
C
On
1)
r,
C
0
(1)Randomly select n tie points from the DEM image (hiand pi,
i = 1, n). n was varied in range, e.g., from 50 to 2000.
(2) Calculate ~ S A R
phases for these points (4,, i = 1, n).
5
n
(3) Calculate local slope.
ti
....
....
(4)Add errors to local height (hJto simulate SLA measurement
using error model N(0,cr), where u is listed in the slope-error
table (Table 2).
(5) Estimate baseline length B, tilt angle a,and reference phase
6 by minimizing the sum shown in Equation 10.
(6) Repeat Steps (4)and (5)for m times (Bi,
a,,and hii = 1,....
0
P
......
0.000
....
.............................................
;
r
0
500
1000
Number of Tie Points
1500
2000
Figure 7. Error of estimated baseline length a s a function
of the number of tie points.
m) to estimate the means and standard deviations of estimated
B, a,and &. Note that m was 100 in this simulation.
Simulations were performed both for a flat area (no slope,
so SLA height error was fixed at 0.11 m) and for the mountainous area selected for this study. The discussions below were for
the mountainous area. For a flat area, where the height error of
tie points are smaller, the numbers of tie points required are
much less than those needed for a sloped area. The dotted lines
in all figures were for a flat area.
It can be seen from the simulation results (Figure 6) that the
error of baseline tilt was reduced as the number of tie points n
increases, but reached a level (0.002") when the number of tie
points is greater than about 1000. For a patch with a width of
10 km, the 0.002" error ofbaseline tilt angle causes the relative
elevation error of 0.17 m in this simulated case. Two-thousand
tie points reduces the error to 0.13 m.
Figure 7 shows the mean and standard deviation of estimated baseline length B. When the number of tie points
exceeds 300, the baseline length error is less than 0.005m,
which leads to an InSARDEM error of 0.09 m for the same patch
and at the SAR flight conditions specified in Table 3.
The next plot (Figure 8) shows the error of estimated reference phase (&, in Equation 1)&omthe simulation. In the simulation, this reference phase was set to be zero. The error budget
of the InsAR DEM from the uncertainty of the InsAR phase can
be estimated fromEquation 3. The phase error of 0.008 radians
-%
10.0004
3
10.0000
......
u
0
Ermr f l d ot O.1lm
0
10.0002
e
-.-
"
0.020
"
~
'
"
'
~
'
"
'
~
"
"
0
...............
g
-
Using SLA height error toble
Height error fixed at 0.1 1m
-
0.005
...-.
v
0
3i
. . . .
0.000
0
I
500
. . . .
I
. . . .
1000
Number of Tie Points
I
1500
. . . .
2000
Figure 8. Error of estimated reference phase a s a function
of the number of tie points.
leads to a height error of 0.0076 meters. In fact, for this simulated case, 0.1 m in the height error budget will require an I ~ S A R
phase error of 0.105 radians, i.e., about 6".
R
Compared to the effect of baseline tilt on ~ S A elevation
accuracy, the effect of this phase offset (or reference phase) is
small. The error of phase shown in Figure 8, i.e., about 0.005 to
0.01 radians, will only lead to a 0.8- to 1.7-cm error of elevation
in this simulated case. In real I ~ S A R
data, many factors cause
R
c$~ by reducing the
the uncertainty (error) of the I ~ S A phase
R
as we
correlation (coherence) between the two ~ S A images
mentioned before. Therefore, only those tie points that show
high correlation between two InSAR data may be used.
0
9
0
Summary
C
P
9.9998
0
500 1000 1500 2000
Number of Tie Points
0
500 1000 1500 2000
Number of Tie Points
Figure 6. Estimated baseline tilt angle and its error a s functions of the number of tie points.
84
lanuary 2000
(1)Both analyses (the regression and simulation) show
that, for a given InSAR DEM accuracy requirement, the number
of tie points required for reducing height errors caused by baseline length, tilt angle, and reference phase errors is dependent
on the tie point accuracy. Because the tie point accuracy is a
function of local slope as shown in Table 2, the number of tie
points is thus dependent on the average slope of the mapped
patch.
(2) The regression study shows that, in order to reduce the
baseline-tilt component of the elevation error budget to a range
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
of 0.05 to 0.10 meters over a patch size of 10km by lokm, 1000
tie points with an average accuracy of 0.92 to 1.83 m were
required.
(3) The simulation study shows that, at a mountainous area
such as the one selected for this study, 1000 tie points with the
accuracy of the current SLAelevation data can reduce the elevation error budget of baseline length to about 0.05 m and the
error budget of baseline-tilt to about 0.17 m. Two-thousand tie
points reduces the latter error budget to 0.13 m.
(4) The number of tie points will also be limited by the total
number of sample points available in a patch, which is determined by the sampling frequency and the size of sample points.
The Vegetation Canopy Lidar (VCL)will collect 2000 samples
with a circular foot print of 25 m in a 10-by 10-krn patch at ideal
elevaatmosphere conditions. The accuracy of V~L-measured
tion is expected to be much better than the SLA data used in this
study, VCL and future Laser Altimeters can provide adequate
tie points for a two-antenna InSAR to generate DEM at high
accuracy.
References
Adby, P.R., and M.A.H. Dempster, 1974. Introduction to Optimization
Methods, A Helsted Press Book, John Wiley & Sons, New York,
706 p.
Caceci, M.S., and W.P. Cacheris, 1984. Fitting curves to data, Byte,
pp. 340-361.
Draper, N.R., and H. Smith, 1982.Applied Regression Analysis, Second
Edition, Wiley Series in Probability and Mathematical Statistics,
John Wiley & Sons, New York.
Dubayah, R., J.B. Blair, J.L. Bufton, D.B. Clark, J. Jaja, R.G. Knox, S.B.
Lathcke, S. Prince, and J.F. Weishampel, 1997. The Vegetation
Canopy Lidar Mission, Proc. American Societyfor Photogrammetry and Remote Sensing, Land Satellite Information in the Next
Decade II: Sources &Applications,Washington D.C., 02-05 December, pp. 100-112.
Fox, J., 1997. Applied Regression Analysis, Linear Models, and Related
Methods, Sage Publications, Inc., 597 p.
Lanari, R., G. Fornaro, D. Riccio, M. Migliaccio, K.P. Papathanassiou,
J.R. Moreira, M. Schwabisch,L. Dutra, G. Puglisi, G. Franceschetti,
and M. Coltelli, 1996. Generation of digital elevation models by
using SIR-CIX-SAR multifrequency two-pass interferometry: the
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Madsen, S.N., H.A. Zebker, and J. Martin, 1993. Topographic mapping
using radar interferometry: processing techniques, IEEE Transactions on Geoscience and Remote Sensing, 31(1):246-256.
Moreira, J., M. Schwabisch, G. Fornaro, R. Lanari, R. Bamler, D. Just,
U. Steinbrecher,H. Breit, M. Eineder, G. Franceschetti, D. Geudtner, and H. Rinkel, 1995. X-sar interferometry - First results, EEE
'Ikansactions on Geoscience and Remote Sensing, 33(4):950-956.
Neldler, J.A.,and R. Mead, 1965. A Simplex method for function minimization, Computer Journal, 7:308.
Small, D., C. Werner, and D. Neusch, 1993. Baseline modeling for ERS1SAR interferometry, Proceedings of IGARSS'93, -pp.
- 1204-1206.
Sun, G. and K.J. Ranson, 1997. Digital elevation models fkom SIR-C
interferometric and Shuttle Laser Altimeter (SLA) data, Proceedings of IGARSS'97, Singapore, August, pp. 460-462.
Zebker, H.A., S.N. Madsen, J. Martin, K.B. Sheeler, T. Miller, Y. Lou,
G. Alberti, S. Vetrella, and A. Cucci, 1992. The TOPSAR interferometric radar topographic mapping instrument, IEEE 7'ransactions
on Geoscience and Remote Sensing, 30:933-940.
Zebker, H.A., and J. Villasenor, 1992. Decorrelation in interferometric
radar echoes, IEEE 'Ikansactions on Geoscience and Remote Sensing, 30:950-959.
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(Received 23 June 1998;accepted 04 September 1998;revised 1 5 February 1999)
Correction
Due to some typesetting problems, there were errors
i n the article entitled "Application of Multi-Temporal
Landsat 5 TM Imagery for Wetland Identification," in
the November 1999 issue of PEbRS. The errors occurred on page 1304 of the article i n the section
subheaded "Methods." The affected paragraphs
should have read:
A three-step approach produced a land-cover map
for both upland and wetland land cover types. First,
an initial land-cover map was developed using late
spring, leaf-on imagery. Second, the distribution and
extent of upland (non-hydric) a n d wetland (hydric)
categories were established using early spring, leafoff imagery. The non-hydric versus hydric data coverage was generated from analysis of TM band 5 (1.55
pm to 1.75 pm) which i s sensitive to differential
moisture i n surficial soils and plant tissues
(Thenkabail et al., 1994). Lastly, both coverages were
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
analyzed using a GIs rule-based classification model
i n a n attempt to improve the classification accuracies
of the wetland classes. The hypothesis was that classification accuracies of wetlands extracted from
single-data imagery could be significantly improved
by revision with information derived from the second
date of TM imagery that was selected to coincide with
the seasonal period of wet soils.
The 11 June 1988 imagery was selected to allow
maximum discrimination of wetland vegetation.
Jensen et al. (1986) found that multispectral satellite
imagery acquired i n spring and early summer best
distinguished palustrine persistent inland wetland
types such as herbaceous, forest, and agricultural wetland categories. The 11 June image was subset to produce a data set of the study area that included TM
band 2 (0.7 pm to 0.8 pm), band 3 (0.8 pm to 0.9 pm),
band 4 (0.9 pm to 1.0 pm), and band 5 (1.55 pm to
1.75 pm) (Plate l a ) .
lanuary 2000
85