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ESTIMATION OF IMAGE GEOLOCATION USING PARAMETRIC MODEL FOR EARTH OBSERVATION SATELLITES

Authors:

Abstract

The aim of this study is to calculate the geolocation of an image acquired from an electro-optic earth observation satellite using the satellite external and internal orientation parameters. The main purpose of this study is to determine the intersecting coordinates of an ellipsoid model defined according to WGS84 and a looking vector. In the first phase, these calculations will be conducted without any Digital Terrain Model (DTM). In order to compare the results, in a second phase, the same calculations will be conducted with DTM. For demonstration purposes, a geolocation software will be developed using open-source libraries. This software will be tested with sample data from the SPOT-5 satellite. There are several plug-ins for certain open source and commercial Geographical Information Systems (GIS) software. One of the objectives of this study is to later develop an independent program which will be used to assist in the development of a satellite and a ground station image processing unit. This program is also intended to be used in the training of individuals with various areas of expertise.
AIAC-2021-000 Kahveci, Tuğcular, Daşer & Yiğit
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Ankara International Aerospace Conference
11th ANKARA INTERNATIONAL AEROSPACE CONFERENCE AIAC-2021-
048
Q08-10 September 2021 - METU, Ankara TURKEY
ESTIMATION OF IMAGE GEOLOCATION USING PARAMETRIC MODEL FOR
EARTH OBSERVATION SATELLITES
Almıla Kahveci1, Uzay Tuğcular2, Berkay Daşer3 and Renda Yiğit4
Turkish Aerospace Industry
Ankara, Turkey
ABSTRACT
The aim of this study is to calculate the geolocation of an image acquired from an electro-optic
earth observation satellite using the satellite external and internal orientation parameters. The
main purpose of this study is to determine the intersecting coordinates of an ellipsoid model
defined according to WGS84 and a looking vector. In the first phase, these calculations will be
conducted without any Digital Terrain Model (DTM). In order to compare the results, in a
second phase, the same calculations will be conducted with DTM. For demonstration
purposes, a geolocation software will be developed using open-source libraries. This software
will be tested with sample data from the SPOT-5 satellite. There are several plug-ins for certain
open source and commercial Geographical Information Systems (GIS) software. One of the
objectives of this study is to later develop an independent program which will be used to assist
in the development of a satellite and a ground station image processing unit. This program is
also intended to be used in the training of individuals with various areas of expertise.
INTRODUCTION
The latest satellite technologies allow us to capture images with a 30 cm ground sampling
distance. This leap in technology brings forth expectations of considerable increase in the
accuracy of geolocation of images. Therefore, geometric correction and geolocation processes
have become more important. There have been academic and industrial studies conducted for
this matter yet it is still necessary to develop independent studies towards revealing needs.
In geolocation estimations that are calculated by using parametric models, acquiring a
particular performance value is very important. It is very clear that this performance value
depends on working with several disciplines from satellite design to sensor test and
measurement methods, from ground station image processing to improving the satellite
external position parameters with related algorithms. Another purpose of this study is to
acquire all the necessary know-hows of rough geolocation, and the software planned to be
published as open source.
1
Satellite Ground Segment Design Engineer. Email: almila.kahveci@tai.com.tr
2
Satellite Ground Segment Design Engineer. Email: uzay.tugcular@tai.com.tr
3
Satellite Ground Segment Design Engineer. Email: berkay.daser@tai.com.tr
4
Space Systems Software Design Engineer. Email: renda.yigit@tai.com.tr
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METHOD
As a starting point, literature review has been done, conventional solutions has been
investigated and a roadmap has been identified. Accordingly, Geometry Handbook of the
SPOT-5 satellite has been taken as a reference [Riazanoff, 2004].
In this study, the sensor geometry, satellite orbit and attitude parameters were used as is,
however for the usage of more detailed models, it was decided to create certain necessary
modular structures [Riazanoff, 2004]. Primarily, the software to be developed was aimed to be
as clear and simple as possible and to only contain basic approaches to solutions rather than
complex ones.
The SPOT-5 satellite pursues a nadir-looking direction in orbit. Mirrors are used on the HRG-
A (High Resolution Geometry) and HRG-B telescopes to acquire images outside of the nadir-
looking angle. These telescopes have a single 12k-pixel sensor in the focal plane and provide
a ground sampling distance of 5 meters at an average altitude. The HRG-A and HRG-B
telescopes point towards earth with a difference of 17.5 meters in the along-track and 2.5
meters in the across-track direction. The difference in these angles and the adjustable line
sampling clock on the satellite gives the satellite an advantage, the PAN image from both
sensors can be resampled as if it were being taken from a single 2.5 meters 24k-pixel viewer
[Raizanoff, 2004]. In addition, the SPOT-5 Satellite provides a test image for uncommercial
users. This image is also provided with the satellite external orbit and attitude parameters. This
test image was taken in the nadir-looking state of the off-nadir imaging mirrors and therefore
was evaluated to be suitable for geolocation software development using a parametric model.
The look angles which are defined on the satellite reference coordinate system, for the HRG-
A and HRG-B telescopes are provided by the manufacturer. Using these angles, the
intersection of each pixel with the WGS84 ellipsoid at the line sampling time (line dating) can
be calculated.
Finally, Digital Terrain Model was introduced to the program to acquire more accurate
longitude and latitude values.
To achieve the steps determined above, the algorithms in the geometry handbook of SPOT-5
satellite were applied using the Java programming language.
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Frame Definitions
Navigation Reference Coordinate System:
The Navigation Reference Coordinate System (NRCS) is a body fixed coordinate system that
is used to maintain the nadir looking attitude by coinciding the auxiliary frames with itself. The
NRCS is centered at the satellite’s center of mass. The CCD geometry is defined with respect
to NRCS, therefore it is one of the most important frames of the SPOT-5 satellite. Furthermore,
the looking angles and are measured from the camera field of view and they are used
to represent the pixel orientation or so called the look direction.
Orbital Coordinate System:
The Orbital Coordinate System (OCS) is an orientation depended system that is centered on
the satellite’s center of mass. Even though it coincides with the center of the NRCS, the OCS
depends on the satellite position and velocity. Therefore, one needs to map the look vectors
that are initially defined in the NRCS to the OCS. This can be done by using the attitude
information that is provided by the Star-Trackers. The attitude measurements are done with
respect to the NRCS frame. Therefore, it provides the transformation matrix between the
NRCS and the OCS from the measured Euler angles. The definition of the OCS is given as
follows;


Eq 1


Eq 2
Eq 3
.
Earth Surface
Figure 2: Navigation Reference Frame
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International Terrestrial Coordinate System:
The International Terrestrial Coordinate System (ITRF) is a non-inertial reference frame, which
is crucial for the geolocation algorithm [Wolf Et all, 2014]. The ITRF is defined with respect to
the International Earth Orientation Service (IERS). Normally, an inertial frame to ITRF
conversion requires complex set of rotations by using the earth orientation parameters. The
satellite orbit is already provided with respect to the ITRF, which results to no necessary
conversion.
Attitude Measurements Definition
The attitude data of the SPOT-5 is provided by the Star-Trackers and the gyroscopes with 8
Hz of frequency [Riazanoff, 2004]. The raw data from the sensors are downloaded and stored
in the form of Satellite Auxiliary Data. The acquired satellite attitude values are going to be
used without applying any filters. The attitude values are not directly represented in NRCS but
its inverted system, which are labeled as (



). The definition of the inverted system
is given as follows;


Eq 4


Eq 5


Eq 6
Roll and pitch components of the rotation matrix from NRCS to OCS is need to be multiplied
by -1, yet the yaw component needs to be kept untouched.
Orbit Measurements Definition
The orbit data of the SPOT-5 satellite is provided by a DORIS (Doppler Orbitography and
Radiopositioning Integrated by Satellite) sensor, which has a measuring rate of 30 seconds
[Riazanoff, 2004]. In order to calculate the geolocation, at least four ephemeris points before
and after the acquisition must be provided by DORIS. The DORIS sensor has a high accuracy
thus the provided ephemeris can be used directly without applying any filters. In the process
of geolocation calculation, one must interpolate the state vectors to the required time of each
line with the use of provided ephemeris. The state vectors are calculated directly with respect
to the ITRF. Therefore, one can transform the looking vector that is defined in OCS by using
the position and velocity components
Definition of Look Direction
The look direction is a vector, which defines the sensor’s pixel orientation with respect to
NRCS. As seen in Figure 2, the looking vector can be defined by and angles. These
angles are called look angles. They are defined for every individual pixel of the sensor with
respect to the NRCS. Even though these angles do not depend on the satellite position or the
orientation, they are provided within the metadata since it is mandatory to use these angles to
perform a geolocation.
The look angles can be written with respect to the pixel number as follows;
Eq 7
Eq 8
represents the pixel number (p = 1...12000),
represents the along-track look angle for the pixel number p,
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represents the across-track look angle for the pixel number p.
The Look direction can be written in NRCS as follows:



 
Eq 9
Note that the NRCS is a body fixed frame and is only used for the definition of the look
vector.
APPLICATIONS
A Java program was developed with the algorithms mentioned in the Methods section. This
program performs geolocation estimation using the parametric model. The algorithms and their
explanations are given below:
Figure 1: Scheme of Algorithm
Line Dating
This algorithm represents the relation between any pixel of the image (l,p) and acquisition time.
One can calculate the corresponding acquisition time of a particular pixel by just knowing the
line sampling period of the sensor.
Figure 2: Line Dating
25.11.2020 T 10:44:10.025
25.11.2020 T 10:44:10.100
25.11.2020 T 10:44:10.075
25.11.2020 T 10:44:10.050
25.11.2020 T 10:44:10.125
25.11.2020 T 10:44:10.150
25.11.2020 T 10:44:10.175
CCD Linear
Sensor
Line Period
Line Dating
Ephemeris
and
Attitude
Interpolation
Look
Direction in
the
Navigation
Referance
Coordinate
System
Look
Direction in
the Orbital
Coordinate
System
Look
Direction in
the Terrestrial
Coordinate
System
Geodetic
point on Earth
Model
(WGS84)
Apply DTM
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
Eq. 10
scene center time,
scene center line,
 line sampling period.
Ephemeris Interpolation
This algorithm determines the position P(t) and velocity V(t) vectors at the time t. The Lagrange
interpolation technique is used for the interpolation of ephemeris points, since the variation is
nonlinear.








Eq. 11







Eq. 12
Satellite position components,
Satellite velocity components.
To achieve this algorithm, four points before and four points after the target time t are acquired.
The acquisition time (9 seconds) is not included to these points. Here, it is not needed to apply
any attitude interpolation.
The points which
will be interpolated.
Orbit
Measurements
Acquisition Start Time
Acquisition End Time
Figure 3: Ephemeris Interpolation
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Attitude Interpolation
Attitude variations are too small and several samples are taken during the acquisition. The
samples that are given in the metadata are in the form of Euler angles. Linear interpolation is
the best choice for the nadir looking instance. Thus, three linear interpolation functions are
defined as follows;


Eq 13


Eq 14


Eq 15
; is the index of valid attitude measurement whose time is just before t ,
; is the rotation angle around the pitch axis at time t,
; is the rotation angle around the roll axis at time t,
; is the rotation angle around the yaw axis at time t,
is the rotation angle around the pitch axis at time found in auxiliary data,
is the rotation angle around the roll axis at time found in auxiliary data,
is the rotation angle around the yaw axis at time  found in auxiliary data.
Look Direction Transformation to Orbital Coordinate System
The origin of the OCS is placed in the center of mass of the satellite. The Z-direction always
represents the vector from the Earth center of mass to the satellite’s center of mass. The X-
direction is the dot product of the Z and Y-directions. In order to define the transformation
between OCS and NRCS, one needs to interpolate the satellite attitude to the corresponding
line date. The OCS frame is unique since the Euler angles are defined in this frame, and hence
it differs from NRCS.
The OCS is used to map the NRCS using the Euler angles. The Spot-5 Satellite tries to
maintain its nadir looking attitude during the imaging phase. Therefore, one needs to use the
Euler angles to map NRCS to OCS.
The transformation matrix between NCRS and OCS frames can be written as follows;


Eq 16
 
 
 
Eq 17
  
  
  
Eq 18
  
 
 
Eq 19
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Note that because of the attitude measurement definition, the rotation around and axes
are needed to be inverse signed.
Look Direction Transformation to Terrestrial Coordinate System
This algorithm represents the rotation between the OCS and ITRF. Since the position vector,
P(t) and the velocity vector, V(t) are already on the ITRF and the definition of OCS depends
on P(t) and V(t), one can use these basis vectors for the rotation.

 


Eq 20


Eq 21


Eq 22
Eq 23
Figure 4: Abstraction of Coordinate Transformation
Intersecting to an Ellipsoid
After mapping the look direction into the ITRF frame, the intersection must be evaluated with
the WGS84 Earth ellipsoid. Firstly, the look direction must be written with respect to the
ellipsoid center. Afterwards, one needs to find the scale factor of the look direction which can
cut through the WGS84 model. The elevation h is important for the intersection algorithm.
Initially it is assumed to be 0. For the first case, geolocation is performed without Digital Terrain
Model (DTM). For the second case, DTM is taken into account.
Looking Vector
x
y
z
X
Y
Z
Sensor Coordinate
System
Satellite Coordinate
System
Earth Centered Coordinate
System
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Figure 5: Intersection Geometry
From the relative vector analysis, and the equation of the ellipsoid one can write the following
equations:





Eq 24


Eq 25
To solve second degree equation:
Calling:


Eq26
.
Intersection
Point
w/o DTM
.
Intersection
Point
with DTM
b
h
a
h
h
O
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This equation has two different solutions (). The greater root value is omitted and the
smaller one is taken into account. When the results are re-introduced into Eq. 17, it gives the
point M. Note that this M point is written with respect to Cartesian Coordinates. For proper
analysis, one must convert Cartesian Coordinates into Geodetic Coordinates. This can be
done using the algorithm provided by [Boucher, 1995].
DTM Iteration Algorithm
In this algorithm, an iterative approach was used. The intersection between the looking vector
and the ellipsoid highly depends on the terrain of the intersection point. In order to determine
the true height of the intersection point, it is mandatory to find it with an iterative method. The
iteration scheme given in Figure 8 is used for the determination of the accurate elevation of
the terrain.
Figure 6: DEM Iteration Algorithm [Riazanoff, 2004]
Polynomial Function Model
A polynomial function is created as an improvement over the brute force method of storing all
576000000 pixels. This polynomial function takes the line number (l) and the pixel number (p)
as parameters, and returns the geodetic latitude and longitude. The polynomial degree of this
function is suggested to be three.
One can define a polynomial function as follows;

Eq 27

Eq 28
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 and  coefficients can be found by using the linear least square method. These
polynomials are the most efficient way to represent every pixel coordinate that is mapped on
Earth.
Results
The program was integrated with the above algorithms and the OREKIT library [Maisonobe,
2010] was used for the time and frame handlings. Furthermore, the results are compared with
the metadata of the provided image. Also note that, the first calculation is done omitting any
DTM data, while the second one includes this data. In addition, a polynomial function is created
as an improvement over the brute force method of storing all 576000000 pixels.
The acquired results after performing the above algorithm are compared with the values
provided by the SPOT-5 satellite in the metadata file. The values have been rounded to the
sixth decimal place.
Table 1: Computed Latitude Values without DEM
Line x Pixel
Latitude (Output)
Latitude (Metadata File)
Difference
( 1 x 1 )
41.765629
41.765629
4e-07
(1 x 24000)
41.600993
41.600993
4e-08
(24000 x 1)
41.244229
41.244229
4e-07
(24000 x 24000)
41.080596
41.080596
5e-07
(12001 x 12001)
41.424417
41.424417
2e-07
Table 2: Computed Longitude Values without DEM
Line x Pixel
Longitude (Output)
Longitude (Metadata File)
Difference
( 1 x 1 )
1.833191
1.833191
3e-07
( 1 x 24000 )
2.579140
2.579140
1e-07
( 24000 x 1 )
1.633764
1.633764
8e-08
( 24000 x 24000 )
2.374067
2.374067
1e-07
( 12001 x 12001 )
2.100964
2.100964
1e-07
Table 3: Computed Longitude Values with DEM
Line x Pixel
Longitude
(Output)
Longitude
(Metadata File)
Difference
( 1 x 1 )
1.832370
1.833191
8e-4
( 1 x 24000 )
2.578760
2.579140
4e-4
( 24000 x 1 )
1.633202
1.633764
6e-4
( 24000 x 24000 )
2.374067
2.374067
1e-8
( 12001 x 12001 )
2.099823
2.100964
1e-3
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Table 4: Computed Latitude Values with DEM
Line x Pixel
Latitude (Output)
Latitude (Metadata
File)
Difference
( 1 x 1 )
41.765826
41.765629
2e-4
( 1 x 24000 )
41.601085
41.600993
9e-5
( 24000 x 1 )
41.244365
41.244229
1e-4
( 24000 x 24000 )
41.080595
41.080596
9e-7
( 12001 x 12001 )
41.424692
41.424417
2e-4
Table 5: Polynomail Coefficinets for Rough Geolocation without DTM
Coefficient
Name
Compute Value
Meta Data Value
Latitude
A0
41.765672
41.765706
A1
-2.172283E-5
-2.172031E-5
A2
-6.604886E-6
-6.603697E-6
A3
-1.800358E-13
1.738931E-12
A4
1.789684E-12
-2.444078E-13
A5
-1.061819E-11
-1.066590E-11
Longitude
B0
1.833202
1.833216
B1
-8.368662E-6
-8.368747E-6
B2
3.045743E-5
3.045914E-5
B3
2.466332E-12
-9.803291E-12
B4
-9.800935E-12
2.467793E-12
B5
2.590250E-11
2.592081E-11
As illustrated in the tables above, the results were recorded for the corner pixels and the center
pixel of the image. In total, 576000000 results were acquired which contains 24000 lines and
24000 columns for a scene. The output that is calculated with direct model without DTM, and
the metadata values are nearly equal which means that the metadata contains geolocation
values calculated without DTM. Hence, one can say that the metadata values need to be
improved in order to find the precise geolocation values. In addition to this, one can say that
the polynomial coefficients for the rough geolocation without DTM is close enough to the
metadata values. Accordingly, the results of polynomial coefficients with DTM are not
recorded, since the case without DTM is more precise with respect to the metadata. Yet, in
reality, one needs to consider the DTM for rough geolocation.
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CONCLUSION
According to the calculations without considering DTM, the latitude and longitude at the corner
and center points of the test image from the SPOT-5 satellite were found with an error margin
of less than 1e-8. In contrast, the results that are calculated with inclusion of DTM differs from
the metadata values in the order of 1e-3. Hence, the results that are provided in the metadata
is clearly considered to be calculated without any DTM. Even though the results with DTM is
not close to the metadata, it is required to add DTM to the geolocation analysis in order to
increase the precision.
The software was developed according to a generic geolocation model that is provided by the
SPOT-5 Handbook. In further studies, the software is planned to be improved to allow users
to define their own frames, sensor geometry and satellite dependent values.
At this point, the algorithm can handle the rough geolocation, which is mentioned in STANAG
7194 NATO Imagery Interpretability Rating Scale as a Level-0. For future studies, the algorithm
is planned to be improved to handle precise geolocation analysis. That kind of analysis requires
precise orbit and attitude determination rather than just a simple interpolation.
As a conclusion, a rough geolocation calculation software is developed with the help of the
SPOT-5 Handbook. Thus, it can provide the know-how of geolocation to beginners as well as
photogrammetry enthusiasts.
References
Boucher, C. (1995) Formulaire Pour Transformations De Coordonnées Trıdımensıonnelles
Cartésiennes Ou Géographiques Entre 2 Systémes Géodésiques, Institut Géographique
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Maisonobe, L., Fernandez-Martin, C., (2010) Sharing the Knowledge: An Open-Source Vision
for Flight Dynamics, SpaceOps Conference, Alabama, Apr 25-30 2010.
Riazanoff, S. (2004) Spot 123-4-5 Geometry Handbook, Gael Consultant, Issue. 1, Aug 2004.
Wolf, P. R., Dewitt, B. A., & Wilkinson, B. E., (2014) Elements of Photogrammetry with
Application in GIS, New York: McGraw Hill Education.
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Formulaire Pour Transformations De Coordonnées Trıdımensıonnelles Cartésiennes Ou Géographiques Entre 2 Systémes Géodésiques
  • C Boucher
Boucher, C. (1995) Formulaire Pour Transformations De Coordonnées Trıdımensıonnelles Cartésiennes Ou Géographiques Entre 2 Systémes Géodésiques, Institut Géographique National, Jan 1995.
Spot 123-4-5 Geometry Handbook, Gael Consultant
  • S Riazanoff
Riazanoff, S. (2004) Spot 123-4-5 Geometry Handbook, Gael Consultant, Issue. 1, Aug 2004.
Elements of Photogrammetry with Application in GIS
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Wolf, P. R., Dewitt, B. A., & Wilkinson, B. E., (2014) Elements of Photogrammetry with Application in GIS, New York: McGraw Hill Education.