BSc Thesis-Spatial Resolution Enhancement Using RA-2...LPF: Low Pass Filter MFT: Model Free Tracker...
Transcript of BSc Thesis-Spatial Resolution Enhancement Using RA-2...LPF: Low Pass Filter MFT: Model Free Tracker...
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ISTANBUL TECHNICAL UNIVERSITY
ELECTRICAL – ELECTRONICS ENGINEERING FACULTY
SPATIAL RESOLUTION ENHANCEMENT
USING RADAR ALTIMETER 2
BSc Thesis by
Batuhan OSMANOĞLU
040010250
Department: Electronics and Communication Engineering
Programme: Telecommunication Engineering
Supervisor: Assis. Prof. Dr. Mesut Kartal
May 2005
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Batuhan OSMANOĞLU
FOREWORD
I would like to thank Dr. Mesut Kartal for spending his precious time working on this project with me. I would also like to thank Dr. Shimon Wdowinski, and Dr. Tim Dixon at University of Miami, USA for their support, and providing ESA-ENVISAT data. James D. Garlick at De Montford University, UK, is another person that I have to thank for his guidance since the very early stages of this study.
9 May 2005
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CONTENTS
FOREWORD ............................................................................................................... ii CONTENTS ................................................................................................................iii ABBREVIATIONS .................................................................................................... iv TABLES ...................................................................................................................... v FIGURES .................................................................................................................... vi SYMBOLS ................................................................................................................. vii ÖZET ........................................................................................................................viii SUMMARY ................................................................................................................ ix 1 INTRODUCTION ............................................................................................. 10
1.1 Introduction ................................................................................................ 10 1.2 General Measurement Principle ................................................................. 11 1.3 Echo Waveform Characteristics................................................................. 12 1.4 Error Sources ............................................................................................. 14
2 ENVISAT RADAR ALTIMETER SYSTEM (RA-2)....................................... 15 2.1 Introduction ................................................................................................ 15 2.2 Technical Details........................................................................................ 16 2.3 Full Deramp Technique ............................................................................. 17 2.4 Model Free Tracker .................................................................................... 19 2.5 Data Format ............................................................................................... 20
3 RESOLUTION ENHANCEMENT ................................................................... 21 3.1 Introduction ................................................................................................ 21 3.2 Simulator .................................................................................................... 21 3.3 Annuluses ................................................................................................... 24 3.4 Crescents .................................................................................................... 26
4 CONCLUSION .................................................................................................. 28 4.1 Overview .................................................................................................... 28 4.2 Results ........................................................................................................ 28
4.2.1 Simulation Result for Annuluses ....................................................... 28 4.2.2 Simulation Result for Crescents ......................................................... 30 4.2.3 RA-2 Example for Crescents ............................................................. 32
REFERENCES .......................................................................................................... 35 APPENDIX A - DATA FORMATS .......................................................................... 36 APPENDIX B – ANNULUS ANNALYSIS RESULTS ........................................... 46 APPENDIX C – SIMULATOR CODES ................................................................... 50 APPENDIX D – PREVIOUS WORK ....................................................................... 55
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ABBREVIATIONS
AGC : Automatic Gain Controller CNES : Centre National d’Eutes Spatiales (French Space Agency) CoG : Centre of Gravity DORIS : Doppler Orbitography and Radio-positioning Integrated by Satellite ESA : European Space Agency, Avrupa Uzay Ajansı I : Inverse LADAR : Laser Detection and Ranging LFM : Linear Frequency Modulation LPF : Low Pass Filter MFT : Model Free Tracker MWR : Microwave Radiometer MSS : Mean Sea Surface NASA : National Aeronautics & Space Administration (USA) OCoG : Offset Center of Gravity PRF : Pulse Repetition Frequency Q : Quadrature RA : Radar Altimeter RA-2 : Envisat Radar Altimeter-2 System RWS : Range Window Size, Receive Window Size SWH : Significant Wave Height SSH : Sea Surface Height TEC : Total Electron Content
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TABLES
Table A.1 RA - 2 MDS .............................................................................................. 36 Table A.2 18 Hz Waveforms MDS ............................................................................ 44 Table B.1 Analysis results on annuluses .................................................................... 46
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FIGURES
Fig. 1.1 – Geometric Relations .................................................................................. 11 Fig. 1.2 – Reflected Echo Waveform, Hayne Model. [10] ........................................ 13 Fig. 2.1 – RA-2 Receiver Block Diagram (Ku Band) ................................................ 18 Fig. 2.2 – Illustration of OCoG Algorithm ................................................................ 19 Fig. 3.1 – Block Diagram of the simulator ................................................................ 22 Fig. 3.2 – Graphical Result of Annulus Radiuses ...................................................... 25 Fig. 3.3 – Relationship between Annuluses and Antenna Gain. ................................ 26 Fig. 3.4 – Forming of crescents in consecutive measurements .................................. 27 Fig. 4.1 – Simulator Generated Waveform for a Flat Surface and Its Corrected Form
against Antenna Gain Factor ..................................................................... 29 Fig. 4.2 – Tracking Surface Reflectivity using Annuluses ........................................ 30 Fig. 4.3 – Geometrical Analysis of Crescent Approach ............................................ 30 Fig. 4.4 – Difference of Echo 0 and Echo 1. .............................................................. 31 Fig. 4.5 – Difference of Echo 2 and Echo 1. .............................................................. 32 Fig. 4.6 – Envisat RA-2 Measurements ..................................................................... 33 Fig. 4.7 – Differences between Consecutive Measurements ..................................... 34
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SYMBOLS
B : Bandwidth c : Speed of light d : Displacement of the satellite D : Distance E : Elevation ft : Transmit frequency fr : Reference frequency H : Altitude n,N : Number of samples r : Radius of the footprint R : Range α : Incident angle ∆t : Time resolution ∆r : Range resolution µ : Compression ratio φ : Phase of signal ττττ : Pulse length ττττ’ : Uncompressed pulse length ∆ττττ : Two way time delay θ, θ3dB : 3 dB beam width
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ÖZET
Radar Altimetre (RA) ilk olarak 1973 yılında SKYLAB olarak adlandırılan bir aktif
uzaktan algılama uydusunda kullanıldı. O günden beri radar altimetre uzaktan
algılama uydularının bir çoğunda kullanılmıştır. Ana tasarım amacı okyanusun
dinamik özelliklerini çıkarmak olsa da, gelişen teknikler radar altimetrenin buz ve
suyun birlikte bulunduğu kutuplara yakın bölgelerde ya da tamamen buzlar ile kaplı
olan kutup bölgelerinde kullanılabileceğini göstermiştir. Öyle ki Avrupa Uzay
Ajansı (European Space Agency, ESA) tarafından hazırlanan ve temmuz ayında
fırlatılacak olan Cryosat kutup inceleme uydusu iki ayrı anten kullanılarak
hazırlanmış bir radar altimetre sistemi kullanmaktadır.
Bu ödevin giriş bölümünde ilk olarak radar altimetrenin kullanım alanları, önceden
kullanılan modellerdeki hatalar ve sorunlar ele alınmıştır. Daha sonra radar altimetre
sistemlerinin çalışma yöntemi genel olarak ele alınmıştır.
Đkinci bölümde çalışmanın temellendirildiği Envisat Radar Altimetre 2 sistemi
incelenmiştir. Sistem parametreleri aktarılmış ve Envisat radar altimetre sisteminin
önceki sistemlerden farkları, yararlı yönleri ortaya konmuştur.
Üçüncü bölüm çalışma çerçevesinde neden bir simulatör’e ihtiyaç duyulduğu ile
başlayıp, kullanılan simulatör ve uygulanan teknikleri tüm detayları ile
kapsamaktadır. Daha sonra çözünürlüğü artırmak için denenen iki yöntemi,
temelleriyle birlikte açıklamaktadır.
Son bölümde ise çalışma sonuçları aktarılmıştır. Kullanılan bu iki yönteme ait
sonuçlar ve bazı özel koşullar için simülatör’de uygulanan metotlar gerçek veri
üzerinde uygulanmış ve sonuçlar karşılaştırılmıştır.
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SUMMARY
Radar Altimeter (RA) was first installed on SKYLAB, an active remote sensing
satellite in 1973. Since then, radar altimeters have been installed on most of the
remote sensing satellites. Even though its main objective is to extract dynamic
information of the oceans, it has been shown that radar altimeters can be used over
sea-ice and Polar Regions. Moreover, European Space Agency (ESA) is preparing a
satellite called Cryosat which will inspect polar ice sheets using its “two antenna
radar altimeter system”. Cryosat is planned to be launched in July 2005.
The first part of this work will cover areas where RA’s used, previous systems and
their problematic sides. After that, general principles of a radar altimeter system
have been addressed.
Second part is dedicated to Envisat Radar Altimeter-2 System on which the whole
study is based on. System parameters have been clarified and different aspects of
Envisat Radar Altimeter System from its ancestors have been described.
Third part starts with explaining the need of a simulator for this study and continues
by working out the simulation parameters and clarifying its design. Following these,
techniques that have been implemented to increase efficiency of RA-2 have been
analyzed.
Last part consists of results for both simulator and RA-2 measurements. It contains
simulation and real world examples of how these two techniques can be used.
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1 INTRODUCTION
1.1 Introduction
Radar Altimeter is an important instrument to obtain vital information about oceans.
It performs by measuring the two way delay of a radar signal to a very high
resolution. Shape and total power of the returned echo reveals significant
information about the surface.
Over the oceans, it observes effects of tides, climate change, hot streams like El
Nino, and ocean topography [1]. Even thought its main purpose is to collect ocean
information there are several other applications that RA are proven to be useful.
Monitoring of sea ice, polar ice sheets and some land surfaces is possible.
Radar Altimeters are in duty since the launch of very first space-borne active
microwave remote sensing satellite, namely Skylab, in 1973. Orbited at 435 km
Skylab’s radar altimetry mission was to inspect ocean state effects on the echo
waveform. With its 0.1 µs pulse length, leading a 15 m range resolution it was able
to show coarse features of ocean geoid such as trenches. After Skylab, radar
altimeters continued to assist scientific community on other satellites. Pulse
compression technique came on to the stage with GEOS-3 launched in 1974 to
compensate for its higher altitude (840 km). It provided better coverage and
resolution than Skylab; however, it was still not good enough to extract useful
science out of it. Four years later, NASA launched SeaSat-1 which employed “Full
Deramp Technique” making compression filters in the receiver pointless. Beyond
SeaSat-1 all radar altimeters use this technique which extensively improves the range
resolution. In 1985, US Navy launched Geosat in order to obtain information on
marine geoid, sea-state and wind conditions which are important for Navy
operations. Geosat provided the first long term high quality altimeter data to
scientific community. Two major families of radar altimeters occurred after Geosat.
Topex/Poseidon (NASA/CNES) and Jason (CNES) form the first family, which are
designed to perform over the oceans. ERS-1 and ERS-2 together with Envisat form
the second family, which are designed to work on any surface [2].
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××=2
tan22θ
Hr
1.2 General Measurement Principle
Radars are used to detect a target and reveal its position and speed using the
information extracted from returning pulse. Similarly, radar altimeters measure the
time delay of radar pulse and calculate the range regarding to it. Recent technology
provides better than 2.5 cm of accuracy over the oceans [2]. Sea surface conditions
and surface backscatter coefficient can be estimated looking at the echo waveform.
Radar Altimeter is a nadir looking active microwave instrument. To reduce the size
of the footprint, antennas with narrow beam angles are used. For instance, using an
antenna with 1.2 m diameter, ERS-1 has a 3dB beam width of 1.3 degrees. Using
simple geometric relations, at an altitude of 800 km, these figures lead to 18 km for
the diameter of footprint. Fig. 1.1 and eqn. 1.1 illustrates this relation, where H is
altitude, L is maximum range, θ is 3dB beam angle and r denotes the radius of the
footprint.
Fig. 1.1 – Geometric Relations
(1.1)
There are two limits on the footprint. The first one is due to the antenna 3 dB beam
angle which is described above and depicted in fig. 1.1. The other constraint comes
from the pulse length. As shown in eqn. 1.2, where ∆t is time resolution, ∆r is the
range resolution and c is the speed of light, in order to achieve 5 cm resolution from
800 km a pulse length of 0.3 ns is required. On the other hand, due to the pulse
length-bandwidth relation given in eqn. 1.3 such a pulse requires bandwidth of
around 3 GHz. In eqn. 1.3 τ denotes the pulse length in time domain and B is the
required bandwidth.
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1=×Bτc
rt
∆=∆
2
( )22 ττ cHcrpulse +=
(1.2)
(1.3)
However, such a huge bandwidth is not always available and would interfere with
the existing links on earth. Even if the bandwidth is available, it is not practicle to
transmit a high peak power in such a short time. 0.3 GHz bandwidth is allocated for
such applications. It turns out that due to roughness of the ocean surface 0.3 GHz of
bandwidth is adequate and it is still possible to reach high accuracy employing the
Brown model.
Another constraint comes from the limited pulse length. As a result of eqn. 1.3, 0.3
GHz bandwidth corresponds to a pulse length of 3 ns. In practice, 20 µs length
pulses are used in order to decrease peak power and distribute it over time. This
technique is called pulse compression. Pulse compression technique and its effect on
range resolution will be described in section 2.2. For a 3 ns pulse, using the relation
illustrated in fig. 1.1 L can be calculated as H+cτ. Keeping this in mind one can
solve the radius of the footprint as shown in eqn 1.4.
(1.4)
For a satellite at 800 km altitude taking the pulse length as 3 ns the maximum radius
of the footprint due to the pulse length can be found around 1.2 km. This radius
corresponds to a very small portion of the 3 dB beam angle therefore the function of
the reflected echo power will be a ramp function. Over the ocean reflected echo
waveform is consistent with the Hayne model (1980) [3]. Hayne model is based on
the model built by Brown in 1977 but “it includes skewness in the Gaussian
assumption of the point target response and in the height distribution of scatterers”
[3].
1.3 Echo Waveform Characteristics
Radar pulse travels towards the earth surface forming a spherical shell as shown in
fig. 1.2. This spherical shell has a thickness related with the pulse length. A surface
with roughness scales in the order of the wavelength is a diffuse scatterer [3]. Energy
reflected from such a surface will be proportional to the instantaneous illuminated
surface.
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Assuming the earth surface as flat, intersection of spherical radar pulse shell and this
surface will define the illuminated area. Therefore, reflected echo waveform will
consist of three regions. The first region will have an upwards slope as the surface
completely remains inside the shell as shown in fig. 1.2 part a. Part b of the same
figure defines the plateau region where the illuminated area remains almost constant,
due to the expansion of the outer and inner borders. As outer border reaches its
maximum, the power will start to diminish as the inner border continues its
expansion. Reflected echo waveform model is called Hayne model which is depicted
in fig. 1.2.
Fig. 1.2 – Reflected Echo Waveform, Hayne Model. [10]
Echo waveform reveals a lot of information about the surface underneath. It is
known that range information can be calculated using the time delay. Moreover,
slope of the rising edge reveals information about the surface roughness as rough
surfaces result into smaller slopes. Again from the slope of the rising edge it is
possible to measure “Significant Wave Height” (SWH), and mid-point of the rising
edge defines the average “Sea Surface Height” (SSH). Mid-point of the rising edge
is defined as the tracking point as the tracker tries to keep this point at the same bin
for each waveform. Additionally backscatter coefficient can be calculated, which is
estimated through the total area under the echo waveform.
These calculations are under the assumption of a surface with a roughness scale of
the order of wavelength. However, over Polar Regions or land it is possible to have
surfaces with roughness scales much more than the wavelength. In such cases it is
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not possible to define the tracking point as the mid-point of the rising edge, as there
is no rising edge in the waveform. Early radar altimeters were using trackers that are
conformed to the Brown Model. However, as there are no models for sea-ice, ice or
land, tracking point for such regions is defined as the centroid of the waveform.
1.4 Error Sources
It is well known that ionosphere introduces a group delay to the space borne systems.
Group delay is proportional to the carrier frequency and Total Electron Content
(TEC) which changes with time. Using two different frequencies in a radar altimeter
system it is possible to correct for ionospheric group delays.
Sea state bias is an effect caused by the crests and troughs of the ocean waves. The
crests disperse the radar pulse and the troughs focus them. As a result crests decrease
the power reflected and the troughs increase it. These two effects spoil the leading
edge smoothness and introduce a bias around 5 to 10% of the SWH [1].
Dry and wet tropospheric corrections are connected with the refractive index, which
is a function of air temperature, water vapor content and pressure. Dry tropospheric
error can go up to 2~3 meters while wet tropospheric error is around 0.06~0.3 meters
[1].
Orbit error is associated with the ambiguity of satellite position. Before installation
of GPS satellites around the world, this was one of the main limitations in satellite
ranging systems, however nowadays it is around 0.02 m for the satellites that
implements GPS tracking [1].
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2 ENVISAT RADAR ALTIMETER SYSTEM (RA-2)
2.1 Introduction
Envisat follows the same ground track as ERS-1 and ERS-2 which will construct a
time series of more than 15 years which will allow inter annual examination of
dynamic ocean circulation patterns, significant wave height climatology and ice-
sheet elevation [4].
Envisat uses two different frequencies to compensate for the ionospheric group
delay. Together with the Microwave Radiometer (MWR) and Doppler Orbitography
and Radio-positioning Integrated by Satellite (DORIS) RA-2 keeps an eye over the
oceans, sea-ice and Polar Regions as well as land surfaces.
Envisat RA-2 is a nadir looking instrument and is in continuous operation that
provides global coverage up to the latitude limit of 81.5 degrees north and south.
Envisat operates with an inclination of 98.5 degrees and it has a complete repeat
cycle of 35 days, consisting of 501 orbits [5]. Such an orbit gives a across track
sampling of 80 km at the equator. This orbit pattern has sub cycles of 3 days and 17
days providing global coverage with coarser sampling. RA provides 18 range
measurements per second which corresponds to a along track sampling interval of
around 400 m. Traveling around the Earth at an altitude of 800 km RA-2 has a
circular footprint of around 18 km in diameter, which may change with the surface
roughness
RA-2 has some advantages when compared with ERS-1 or ERS-2. It provides more
robust tracking due to model free tracker. RA-2 tracker is only responsible for
keeping the echo wave form in the window [4]. Geological calculations are done on
the ground. This simplification results into a more robust tracker. Furthermore, it
provides three different resolutions, allowing increase of the window size to capture
land and ice waveforms. Resolution change is done automatically on board. Another
drastic improvement of RA-2 is the number of samples. RA-2 provides 128 samples
which is double the number of samples for ERS. Moreover a 129th sample is
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2
τcr =∆
rnSAMPLE ∆×=RWS Size, WindowRange
available and can be positioned anywhere needed to increase precision [5]. Moreover
individual echoes mode makes it possible to obtain 1800Hz waveforms, which are
single waveforms that are not averaged. Envisat is programmed to average 100
consecutive waveforms and obtain range measurements at 18 Hz.
2.2 Technical Details
Main task of RA-2 is to determine the two way delay of the radar echo. It travels at
altitudes between 764 km and 825 km. It is expected for RA-2 to have a range
accuracy of around 5 cm over the ocean. In order to achieve this level of accuracy, a
chirp signal with a bandwidth of 320 MHz is used. Hayne model is applied after the
signal processing to accomplish the accuracy expectations. Due to the relationship
between bandwidth and pulse length given in eqn. 1.3, 320 MHz corresponds to
3.125 ns. Chirp signal is used as a part of pulse compression technique.
In typical radar systems, range resolution is proportional to the pulse length;
however, it is not practical to transmit very high powers for very short durations of
time. In the same manner, RA-2 uses a 20 µs linear frequency modulated signal to
decrease the transmitted peak power and disperse the pulse in time. However, even
with 320 MHz, it is not possible to attain 5 cm accuracy. Range resolution for a
pulse length of 3.125 ns is calculated as 0.46875 meters using the eqn. 2.1.
(2.1)
Range resolution is improved by averaging 100 waveforms and applying Hayne
Model for ocean waveforms. Number of sampling points is defined as 128 for
Envisat RA-2. Together with the range resolution, number of sample points defines
the range window size, 60 meters for high resolution, as shown in the eqn. 2.2.
(2.2)
Over non-ocean surfaces it is quite common that height variation is more than 60
meters. Therefore over such surfaces, range resolution is decreased autonomously to
keep the waveform inside the window. RA-2 possesses three different resolutions,
corresponding to three different bandwidths. 320 MHz, 80 MHz, and 20 MHz are the
three bandwidths corresponding to 0.46875 m, 1.875 m, and 7.5 m of range
resolutions respectively [9].
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RA-2 operates at two different bands, 13.575 GHz (Ku Band) and 3.2 (S Band), to
compensate for the ionospheric delay. For these two frequencies 3 dB beam widths
are 1.35 degrees and 5.5 degrees respectively. For the S Band RA-2 uses only one
chirp signal with a bandwidth of 160 MHz. It was mentioned that RA-2 provides 18
range measurements in Ku Band. Each of these measurements is averaged over 100
samples and this leads to a Pulse Repetition Frequency (PRF) of around 1800 Hz.
PRF of the S-Band is four times less than the Ku Band PRF. Consequently, S Band
measurements are averaged over 25 samples, not 100.
Table 2.1 – Specifications of RA-2 [4, 5]
Parameter Name Description Value Orbit Range km 764 to 825
Operative Frequencies GHz 13.575 and 3.2 Pulse Length µsec 20
Ku chirp bandwidths MHz 320, 80, 20 Ku Range Resolution m 0.46875, 1.875, 7.5 Range Window Width m 60, 240, 960
S chirp bandwidth MHz 160 Transmitter peak power W 60 (Ku) / 60 (S) Number of FFT points 128 (Ku) / 64 (S)
3 dB Beam width Degrees 1.35 (Ku) / 5.5 (S) Pulse Repetition Frequency Hz 1795.33(Ku) / 448.83(S)
Pulse Repetition Interval ms 557 (Ku) / 2228 (S) Antenna Gain dBi 41.6 (Ku) / 29.2 (S)
IF centre frequencies MHz 1223 (Ku)/ 75 (S) RF Losses dB 1.8 (Ku) / 1.7 (S)
Receiver Maximum Gain dB 107 AGC dynamic range dB 60
Receiver Noise Bandwidth MHz 6.4 Receiver Noise Figure dB 3 (Ku) / 2.5 (S)
Spatial Sampling m ~390 Ku Geometric Resolution km ~19
2.3 Full Deramp Technique
The range resolution of RA-2 is around half a meter (3.125 ns) in high resolution
mode. In conventional radar systems to achieve this accuracy a pulse length of 3.125
ns is needed. This approach is commonly used in LADAR (Laser Detection and
Ranging) systems. However in radar altimeters pulse compression techniques are
used. As a result, it is possible to acquire data using lower peak powers using a linear
frequency modulated signal which is called as “chirp signal”. The compressed pulse
resolution is inversely proportional to the chirp bandwidth as shown in eqn. 2.3.
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B
cr
2 ,Resolution Range =∆ (2.3)
In radar altimeter systems dispersive delay lines are commonly used to generate
linear frequency modulation of the chirp signals. The reflected echo is then passed
through an inverse matched filter to decompress the signal. This whole procedure is
called as “Pulse Compression”. However to obtain 3.125 ns pulse length, 320 MHz
of bandwidth is needed. Dispersive delay lines are the only practical way of
generating chirp signals with such bandwidths. Unfortunately, this fact introduces a
new problem: It is not possible to build an inverse matched filter as the
corresponding frequency division is unattainable [6]. To get around this problem,
“Full Deramp Technique” is used.
When the reflected radar echo is received it is mixed with a replica of the transmitted
chirp. Thus, constant frequency tones appear for different facets at different ranges.
As the process continues, signals from different facets that are at the same range start
to build up. Fig. 2.1 shows the receiver block diagram of RA-2. After multiplication,
the resultant signal is amplified and multiplied with the second local oscillator with a
90 degree phase shift to attain Inverse (I), and Quadrature (Q) channels. I and Q
signals are then sampled and quantized. Hamming window is then utilized to these
signals. FFT is applied to convert time domain samples to frequency domain. At the
end, result of the FFT circuitry is fed to the tracker to close the loop and generate the
chirp signal for the consequent received signal.
Fig. 2.1 – RA-2 Receiver Block Diagram (Ku Band)
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2.4 Model Free Tracker
RA-2 utilizes a Model Free Tracker (MFT) that does not depend on any waveform
model as the name implies. Rather than a waveform model, MFT uses Offset Center
of Gravity (OCoG) algorithm.
There are several steps to determine the height error using OCoG algorithm. This
algorithm is based on the assumption that the envelope of the echo waveform can be
estimated by a rectangle [7]. First, center of gravity (CoG) of the waveform is
calculated. Double the power level of this CoG defines the height of the rectangle.
Sum of all the power levels give an estimate for the rectangle area, therefore width
of the rectangle can be estimated as the sum of all bins divided by double the CoG
power level. Together with the CoG, rectangle width defines the location of leading
edge. In other words, tracking point is determined by CoG and the width of
rectangle. Envisat uses bins 46, 59.5 and 62.875 as tracking points for high, medium
and low resolutions, respectively [9]. Deviation of tracking point from these
predefined locations indicates height error. Fig. 2.2 illustrates the OCoG algorithm.
Another point worth to mention about the final version of this algorithm is that, as
linear weighting is applied in the computations of CoG location, algorithm is quite
sensitive to noise. To circumvent this problem, samples are squared to increase the
dynamic range artificially [7].
Fig. 2.2 – Illustration of OCoG Algorithm
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Model Free Tracker, works basically in the same way as the OCoG algorithm,
however, it simplifies it more in order to decrease the computational load. It applies
a threshold to the echo waveform and converts it to binary. Once converted to binary
in most of the cases, mid-point of ones indicate the center of gravity. The offset error
controls the range resolution of the altimeter autonomously. Increase in the offset
error indicates that the echo waveform is moving outside of the receive window.
Therefore the resolution is decreased by changing the chirp bandwidth to keep the
waveform inside the receive window.
2.5 Data Format
Data is distributed on the web and with DVDs delivered courier service. See
Appendix A for the data file format.
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3 RESOLUTION ENHANCEMENT
3.1 Introduction
In this work a simulator based on Envisat Radar Altimeter-2 has been developed in
order to analyze characteristics of reflected waveforms over different surface types.
Using this simulator new approaches have been developed to enhance the spatial
resolution of RA-2.
Purpose of this project is to add new capabilities to RA-2 and increase its efficiency.
Currently, RA-2 is used to measure ocean parameters such as significant wave
height, mean sea surface, sea state bias, and etc. It is also used to monitor sea-ice and
polar ice sheets. Its large footprint and centimeter scale range resolution makes it
very suitable for ocean monitoring. Thanks to the MFT, RA-2 is capable of keeping
the echo in the range window for most of the cases. As geophysical information is
extracted using on-ground processors, it is possible to run and optimize different re-
tracker algorithms on collected waveforms. Echo waveforms scattered over land are
harder to analyze compared to ocean waveforms as there is no available model. In
this work, spatial resolution of RA-2 is increased using two new concepts, namely
crescents and annuluses.
3.2 Simulator
The aim of this study is to increase spatial sampling resolution. This will be achieved
using coherency analysis of consecutive return echo signals and investigating the
effect of annuluses on the echo waveform. Such analyses not only require the
simulation of envisat radar altimeter processor, but also require having control over
the surface types. First, the simulator is designed to match the characteristics of RA-
2 as described below.
Simulation is carried out using a modified stretch (active correlation) processor
algorithm. Fig.3.1 demonstrates how the stretch processor operates. Linear frequency
modulation (LFM) is used to implement pulse compression. A general name for
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'0;'2
2exp)( 2 ττ
π ≤≤
−= ttB
tfjts tt
∆−−∆−= 2)('2
)(2exp)( ττ
τπσ tB
tfjts tr
∆−∆+∆−−= 2'2'
)(2exp ττ
ττ
τπBB
tftffjAs trtLPF
LFM signals is “chirp” and equation of the transmitted chirp signal is given in (3.1).
Change of frequency with time for a LFM signal is depicted in fig. 3.1., B stands for
band width, t is time, τ’ is uncompressed pulse length and ft is center frequency in
(3.1).
(3.1)
Fig. 3.1 – Block Diagram of the simulator
From each facet of the surface, transmitted signal will be reflected at a different
time, proportional to range of facets. This round trip delay will take around 5.3
milliseconds. In fig. 3.1 such signals with different round trip delays are drawn.
Additionally, each facet will have a different backscatter coefficient. Keeping these
in mind one can write the equation of a reflected echo as shown in (3.2). Here σ
represent backscatter coefficient and ∆τ symbolize round trip delay.
(3.2)
Reflected signal is mixed with a reference chirp signal, which has the same rate of
frequency change with transmitted signal. Purpose of this operation is to convert
time delays into constant frequency tones, and this is called deramping process. A
low pass filter (LPF) is utilized right after the mixer in order to exclude high
frequency components.
(3.3)
-
23
2
''22)(2 τ
τπτ
τπτππφ ∆−∆+∆−−=
Bt
Bfff trt
)('
2)(2
'
22
2
1)(
2
1 111 rtrt ff
c
BRff
c
RB
dt
df −−=
−−==τ
πτπ
πφ
π
'
1
2'
2
'
2
τττ==
∆=∆
B
c
c
B
c
RBf
fN∆=Size WindowReceive RWS,
.'
)(2
'
)(2
2minmax
ττ cRRB
c
RWSBfN −=>
∆
Round trip time delays, ∆τ, contain valuable range information of the target and it is
possible to extract it by taking the derivative of the phase of sLPF. Derivative of the
phase term is also named as instantaneous frequency.
(3.4)
(3.5)
Equation (3.5) points out a one to one relationship between instantaneous frequency
and range of targets. Therefore it is important to realize what the minimum
frequency separation should be in order to differentiate two distinct targets located
close to each other in range. Substituting target range in (3.5) with range resolution,
one can get the equation of frequency resolution. Range resolution is defined as c/2B
[8].
(3.6)
Together with number of samples, frequency resolution determine the receive
window size (RWS) in frequency. RWS is an important parameter as it shows the
resolvable maximum difference between closest and furthest target ranges. It is also
known that Fourier transform produces unsymmetrical results for complex inputs.
Hence maximum frequency displayed in frequency window will be all of the RWS.
(3.7)
Limitation for minimum number of samples for a given bandwidth and pulse length
can be calculated combining (3.7) and (3.6).
(3.8)
Above presented is the detailed information about the simulator and how it works. In
general, the processor mentioned above takes two input maps, elevation and
reflectivity. Elevation maps are then converted to range maps as they are easier to
process.
There is a tricky part of the simulation process, which deserves a lot of attention. As
the timings used in the above formulas are all relative, so that ∆t is subtracted from
every t term of received echo, range is also relative! In other words, the receive
window is located around 800 km away from the satellite. Therefore R1 is equal to
-
24
'τβ
µ =
ββτ
τµ1'
'
1==
∆=∆
frT
R1-Rmin in above equations. Rmin is defined by the tracker and adds constant
frequency shift to the above terms. After preparing 128 time samples for every single
scatterer in the range map, each scatterer’s response is applied to the Fourier
transform and summed up.
3.3 Annuluses
It is described in section 1.3 that the footprint of radar altimeter systems are circular
and usually form annuluses because the pulse width is too short compared with the 3
dB beam width.
Returning back to fig. 1.2, and making a deeper analysis, it is clear that the rising
edge forms during the expansion of external boundary of the footprint, and when
there is no blank circle in the middle. For Envisat, pulse compression ratio µ is
16×1012, and can be calculated as given in eqn 3.9 where β represents “Chirp
Bandwidth (320 MHz)” and τ’ denotes uncompressed pulse length (20 µs).
(3.9)
Together with the frequency resolution (eqn. 3.6), compression ratio can be used to
verify range resolution after pulse compression. In Eqn. 3.10 relationship between
frequency resolution, compression ratio and range resolution in time domain is
given.
(3.10)
This result indicates that even though the actual pulse length of radar signal is 20 µs,
with regard to frequency modulation our range resolution can be increased
drastically. Given that range resolution after pulse compression is 0.46875 m it is
possible to define equi-range areas inside the footprint. These are the areas that are
represented by a single bin in the frequency receive window. Obviously, these areas
will have circular boundaries due to the spherical pulse shape. Using simple
geometrical relations radius for the kth equi-range circle can be calculated as:
(3.11) ( ) .46875.0)( 22 HkHkradius −×+=
-
25
Computing eqn. 3.11 for every k values from 0 to 127 the exponential curve
illustrated in fig. 3.2 is achieved. Radius values for each k value are given in
appendix B.
Fig. 3.2 – Graphical Result of Annulus Radiuses
Last column of Table B.1 in appendix B draw attention to equal areas of annuluses.
Given that each bin after the leading edge indicates an annulus, analysis of surface
reflectivity can be done for each annulus. In other words, if each bin contains the
power of radar pulse scattered from a single annulus, it is possible to look for back
scatter coefficient (annulus radar cross section) changes among them. However, due
to the effect of incident angle on antenna gain, it is likely that the accuracy of this
analysis will decrease for incident angles close to half of the 3 dB beam width. Fig.
3.3 shows the connection between the antenna gain and annuluses. Antenna gain for
an angle of α less than half of 3 dB beam width can be calculated as shown in eqn.
3.12.
(3.12)
( ) ( ) [dB] /12 23max dBGainGain θαα ×−=
-
26
Fig. 3.3 – Relationship between Annuluses and Antenna Gain.
3.4 Crescents
Envisat travels around 400 m on its path on Earth between two measurements. Each
measurement is an average of 100 echoes. The diameter of the circular footprint is
around 18 km. In other words, the footprint covers almost the same area for two
consecutive measurements. As a result, difference of two consecutive waveforms
will include information about the area that is covered in the first measurement but
not in the second one, and likewise information about the area that is covered in the
second footprint but not in the first one. Therefore it is possible to analyze along
track coherency by taking differences of consecutive waveforms.
For instance assume Envisat is traveling over the ocean and approaching to a
shoreline a little higher than the mean sea surface (MSS). In such a case at some
point in time one of the two consecutive waveforms will be completely over the
ocean and the next one will have some parts on the land surface. This is going to
introduce a difference in the last bins of the waveform. The radius of annuluses get
closer around 3 dB beam width, therefore a shift of 400 m would change around 6-8
frequency bins at the end of the receive window. Fig. 3.4 illustrates crescents for
consecutive measurements, where:
-
27
- First footprint consists of areas a, b, and c.
- Second footprint consists of areas b, c, and d.
- Third footprint consists of areas c, d, and e.
Fig. 3.4 – Forming of crescents in consecutive measurements
Additionally, back scatter coefficient differences can also be tracked using the
benefits of crescents, however as mentioned in the previous part due to the antenna
gain decline at incident angles close to 3dB beam width it is not going to be accurate
when two consecutive measurements are compared. On the other hand, such an
analysis might be employed between every 20th samples as the footprint of RA-2
will have changed almost around 50%.
-
28
4 CONCLUSION
4.1 Overview
In this work several techniques to improve Envisat Radar Altimeter System have
been developed and tested. Two promising new techniques are covered in the
previous section. Next part will illustrate achievements reached by using these
methods.
It worth’s to mention that Envisat also provides individual echoes mode, where this
study may generate more interesting results. Taking the average of 100 echoes cause
them to decoralate which makes it harder to analyze.
4.2 Results
This section contains two simulation and one real data example. One of the
simulation results represents the first technique that employs Annuluses and the
other one demonstrates the second technique that uses Crescents. Only the example
of second method can be illustrated for Envisat data as compensation of gain
controller systems could not be accomplished, which is a necessary step for method
of annuluses. As it is depicted in fig. 4.5, even for consecutive waveforms the power
values change a huge amount. More analysis on Automatic Gain Controller (AGC)
of RA-2 has to be completed before taking further steps.
4.2.1 Simulation Result for Annuluses
As mentioned in section 3 part 3, analysis of annuluses let us differentiate surface
reflectivity changes. Fig. 4.1 shows a sample output of simulator for a zero elevation,
flat surface. Fig. 4.1 also includes its compensated form for the change of antenna
gain regarding the incident angle.
-
29
Fig. 4.1 – Simulator Generated Waveform for a Flat Surface and Its Corrected Form against Antenna Gain Factor
Fig. 4.1 points out a problematic situation at the last portions of the echo reply. This
fluctuation is a result of simulation map resolution where pixels of 100m on each
side are used. As shown in Table B.1, radius differences for consecutive annuluses
decrease exponentially, and as a result, map resolution does not provide sufficient
number of scatterers for a smooth sum at the edges of footprint.
In order to show how analysis of annuluses is performed, a 0.9km2 (3 by 3) areas
reflectivity coefficients have been increased by ten percent. This area is located on
the eastern side of annulus 3. Fig.4.2 shows both the new simulation result and
difference of results for this elevation map, from the one displayed in fig. 4.1. In
other words, to make the reflectivity change more visible, flat surface response is
subtracted from modified surface response. The curve for relative change has been
given the offset of positive 2000 in order to prevent confusion of two signals.
Moreover, looking at the tiny yellow boxes in fig.4.1 it can be seen that the position
of this reflectivity anomaly lies inside the third annulus (8-5=3rd annulus). As there is
no MFT employed in the simulator, bin 5 corresponds to the end of the leading edge,
which is also the first annulus.
-
30
Fig. 4.2 – Tracking Surface Reflectivity using Annuluses
4.2.2 Simulation Result for Crescents
Good part of crescents is that they only form in the direction of movement, which
indicates that the satellite is going right on to the target. Along track coherency can
be implemented in the same way, however; it is not possible to pin point the target,
as the footprint is symmetric in across range. Fig. 4.3 illustrates geometric
relationship of crescent analysis. In fig. 4.3, d is the displacement of satellite along
the ground track, elevation is target elevation, “D” is the distance from nadir to new
coming target, H is the altitude and r1, and r2 define different ranges.
Fig. 4.3 – Geometrical Analysis of Crescent Approach
-
31
Equations for r1 and r2 can be written as:
(4.1)
(4.2a)
(4.2b)
Using these equations it is possible to solve for D and E.
(4.3)
(4.4)
Using the equations above E can be retrieved. Figures 4.4 and 4.5 illustrate how to
implement these equations using the waveforms. Echo 0, represents the waveform of
a complete flat surface and Echo 1 denotes a waveform with a target at 9.1 km east
from the nadir location. Echo 2 is the next waveform of the same scenario, where the
satellite is moving towards east there fore the new location of target is at 8.7 km east
from the nadir point. Fig. 4.5 shows the difference of Echo 2 and Echo 1.
Fig. 4.4 – Difference of Echo 0 and Echo 1.
( ) 2221 DEHr +−=
( ) ( )2222 dDEHr −+−=
d
drrD
2
221
22
−−−
=
( )d
drrrEH
2
221
222
12
−−−
−=−
( ) 22222 2 ddDDEHr +−+−=
-
32
Fig. 4.5 – Difference of Echo 2 and Echo 1.
In theory, it is possible to use the echo waveform instead of taking difference of two
consequent waveforms. However, as the antenna gain decreases sharply near the
footprint edges, it is not possible to analyze power differences at such locations. The
starting point of the rising edge in fig. 4.4 is at 107 whereas; the same point is on 98
in fig. 4.5. Looking at table B.1, at row 98 and 107 gives us the annulus radius
values as 8.5733 km and 8.9584 km. Difference of these two radiuses, show that the
target appears almost 400 m west according to its previous location. Elevation of the
target can be calculated using the eqn 4.4. Values for r1 and r2 can be calculated
using the equation given below.
(4.5a)
As an example for the given situation in fig. 4.4 r1 is equal to this:
(4.5b)
4.2.3 RA-2 Example for Crescents
Using the Envisat sample data product crescents approach has been tested.
However, it was not possible to apply the method without any modifications. For
instance, the antenna gain is so low at the edge of the footprints that it is usually not
possible to differentiate up coming targets inside the outermost crescent. Fig. 4.5
shows three consequent Envisat RA-2 measurements obtained on 05 July, 2002 at -
68.89° latitude, 156.39° longitude, just before the start of Antarctic ice sheet.
( )Resolution RangePoint) Tracking-BinStart Edge Leading(
Point Trackingat Range
×
+=r
mkmr 46875.0)287(8001 ×−+=
-
33
As seen from fig. 4.5 tracking points are different for each waveform. The first
tracking point is almost 49, the other one is a little below 48 and the measurement at
the bottom has a tracking point of around 47.5. However, for simplicity, waveforms
are not shifted to match the tracking points. On the other hand, they are fed to
antenna gain compensation algorithm to decrease non-linear effects of it. It is clear
that the compensation algorithm can not work successfully on real Envisat data.
These particular measurements are chosen, because the nadir point is just off the
shore. Therefore, satellite is moving towards the shore line which is consistent with
crescents approach. It is not possible to pin out differences on the waveforms by just
looking at them. Fig. 4.6 shows the differences between consecutive waveforms.
Fig. 4.6 – Envisat RA-2 Measurements
-
34
Fig. 4.7 – Differences between Consecutive Measurements
As seen from the figure above, there is a difference of one bin between tracking
points and similar waveforms have a difference of 6 bins in between. For the upper
figure there are 43 bins difference between predefined points. For the lower figure
there are 38 bins. Looking up the surface distances for these points from table B.1 it
can be seen that these points have almost ~400 m in between which is equal to the
displacement of satellite on its ground path between two consecutive measurements.
-
35
REFERENCES
1. Sandwell, D., n.d., “Radar Altimetry”, Retrieved Apr. 14, 2005, from UCSD
Remote Sensing (SIO 236) Web site: http://topex.ucsd.edu/rs/altimetry.pdf.
2. ESA, 2002, “RA-2”, Retrieved Apr. 14, 2005, from Envisat Web site:
http://envisat.esa.int/instruments/ra2/.
3. ESA, 2002, “Concept”, Retrieved Apr. 14, 2005, from Envisat Web site:
http://envisat.esa.int/instruments/ra2/descr/concept.html.
4. Resti. A., Benveniste J., Roca M., Levrini G., and Johannessen J., 1999, The
Envisat Radar Altimeter System (RA-2), ESA Bulletin, (98).
5. ESA, 2002, “ENVISAT RA-2/MWR Handbook, Retrieved Apr. 14, 2005, from
Envisat Web site:
http://envisat.esa.int/pub/ESA_DOC/ENVISAT/RA2/ra2.ProductHandbook.1_2e.pdf.zi
p.
6. ESA, 2002, “Full Deramp”, Retrieved Apr. 14, 2005, from Envisat Web site:
http://envisat.esa.int/instruments/ra2/descr/full-deramp.html.
7. ESA, 2002, “Tracking”, Retrieved Apr. 14, 2005, from Envisat Web site:
http://envisat.esa.int/instruments/ra2/descr/tracking.html.
8. Mahafza, B., 2000. Radar Systems Analysis and Design using Matlab. 1st ed.
Boca Raton, FL: Chapman & Hall/CRC.
9. Garlick, D. James, 2004, Special Conversation.
10. Osmanoglu, B., Kartal, M., 2005, Analysis of Land Topography Using Radar
Altimeter 2, 2nd International Conference on Recent Advances in Space
Technologies, 9-11 June 2005,(not published yet).
-
36
APPENDIX A - DATA FORMATS
Range information is very important for crescent approach and unfortunately,
receive window does not show the pulse transmit time. Range and other related
information for several retrackers can be obtained from the data set described below.
Table A.1 RA - 2 MDS
RA-2 MDS (from the GDR product) # Description Units Count Type Size
Data Record
0 dsr_time [i] [q]
MDSR Time stamp. Time fields
based on UTC are computed for
each record and referred to the
center of the averaged waveform.
MJD 1 mjd 12 byte(s)
1 quality_flag [i] [q]
Quality Indicator (-1 for blank MDSR, 0 otherwise)
flag 1 BooleanFlag 1 byte(s)
2 spare_1 [i] [q]
Spare
- 1 SpareField 3 byte(s)
3 lat [i] [q]
Geodetic Latitude (positive N, negative S)
(1e-6)
degrees
1 GeoCoordinate 4 byte(s)
4 lon [i] [q]
Longitude (positive E, 0 at
Greenwich, negative W)
(1e-6)
degrees
1 GeoCoordinate 4 byte(s)
5 src_pack_cnt [i] [q]
Source Packet Counter
- 1 ul 4 byte(s)
6 instr_mode_id_flags [i] [q]
Instrument Mode ID
flags 1 ul 4 byte(s)
7 meas_conf_data_flags [i] [q]
Measurement Confidence Data
flags 1 ul 4 byte(s)
8 alt_cog_ellip [i] [q]
Altitude of CoG above reference
ellipsoid
mm 1 ul 4 byte(s)
9 hz18_diff_1hz_alt [i] [q]
18 Hz altitude differences from 1 Hz
altitude [20].
mm 20 ss 20*2
byte(s)
-
37
10 instant_alt_rate [i] [q]
Instantaneous altitude rate
mm/s 1 Ss 2
byte(s)
11 spare_2 [i] [q]
Spare
- 1 SpareField 50
byte(s)
12 hz18_ku_trk_cog [i] [q]
18 Hz Ku tracker range referenced to the
COG (no Doppler correction) [20]
mm 20 ul 20*4
byte(s)
13 hz18_s_trk_cog [i] [q]
18 Hz S tracker range referenced to the
COG (no Doppler correction) [20]
mm 20 ul 20*4
byte(s)
14 map_18hz_ku_trk_flags [i] [q]
Map of valid points for 18 Hz Ku-band
tracker range.
flags 1 ul 4
byte(s)
15 spare_3 [i] [q]
Spare
- 1 SpareField 4
byte(s)
16 ku_band_ocean_range [i] [q]
Ku-band ocean range
mm 1 ul 4
byte(s)
17 s_band_ocean_range [i] [q]
S-band ocean range
mm 1 ul 4
byte(s)
18 hz18_ku_band_ocean [i] [q] 18 Hz Ku-band ocean ranges [20]
mm 20 ul 20*4 byte(s)
19 hz18_s_band_ocean [i] [q] 18 Hz S-band ocean ranges [20]
mm 20 ul 20*4 byte(s)
20 sd_18hz_ku_ocean [i] [q]
Standard deviation of 18 Hz Ku-band ocean range
mm 1 us 2
byte(s)
21 sd_18hz_s_ocean [i] [q]
Standard deviation of 18 Hz S-band ocean
range
mm 1 us 2
byte(s)
22 num_18hz_ku_ocean [i] [q] Number of 18 Hz valid points for Ku-band
ocean range
- 1 us 2 byte(s)
23 num_18hz_s_ocean [i] [q] Number of 18 Hz valid points for S-band
ocean range
- 1 us 2 byte(s)
24 map_18hz_ku_ocean_flags [i] [q]
Map of 18 Hz valid points for Ku-band ocean
range. First 20 least significant bits (bits 0-19) correspond to the 20 values (one per
data bock) containing : 0= valid
measurement, 1= invalid. Unused bits set to
0. Bit 0 applies to the first data block.
flags 1 ul 4
byte(s)
25 map_18hz_s_ocean_flags [i] [q]
Map of 18 Hz valid points for S-band ocean range. First 20 least significant bits (bits 0-
19) correspond to the 20 values(one per
data bock) containing : 0= valid
measurement, 1= invalid. Unused bits set to
0. Bit 0 applies to the first data block.
flags 1 ul 4
byte(s)
26 hz18_ku_ice1 [i] [q] 18 Hz Ku-band ice1 ranges [20]
mm 20 ul 20*4 byte(s)
27 hz18_s_ice1 [i] [q] 18 Hz S-band ice1 ranges [20]
mm 20 ul 20*4 byte(s)
28 hz18_ku_ice2 [i] [q]
18 Hz Ku-band ice2 ranges [20]
mm 20 ul 20*4
byte(s)
-
38
29 hz18_s_ice2 [i] [q]
18 Hz S-band ice2 ranges [20]
mm 20 ul 20*4
byte(s)
30 hz18_ku_seaice [i] [q]
18 Hz Ku-band sea-ice ranges [20]
mm 20 ul 20*4
byte(s)
31 spare_4 [i] [q]
Spare
- 1 SpareField 80
byte(s)
32 hz18_ku_instr_corr [i] [q]
18 Hz Ku-band range instrumental
correction [20]
mm 20 ss 20*2
byte(s)
33 hz18_s_instr_corr [i] [q] 18 Hz S-band range instrumental correction
[20]
mm 20 ss 20*2 byte(s)
34 hz18_ku_dopp_corr [i] [q]
18 Hz Ku-band Doppler correction [20]
mm 20 ss 20*2
byte(s)
35 hz18_s_dopp_corr [i] [q] 18 Hz S-band Doppler correction [20]
mm 20 ss 20*2 byte(s)
36 hz18_ku_dopp_slp_corr [i] [q] 18 Hz Ku-band Delta Doppler Slope
correction [20]
mm 20 ss 20*2 byte(s)
37 hz18_s_dopp_slp_corr [i] [q] 18 Hz S-band Delta Doppler Slope
correction [20]
mm 20 ss 20*2 byte(s)
38 mod_dry_tropo_corr [i] [q]
Model dry tropospheric correction
mm 1 ss 2
byte(s)
39 inv_barom_corr [i] [q] Inverted barometer correction
mm 1 ss 2 byte(s)
40 mod_wet_tropo_corr [i] [q]
Model wet tropospheric correction
mm 1 ss 2
byte(s)
41 mwr_wet_tropo_corr [i] [q]
MWR derived wet tropospheric correction
mm 1 ss 2
byte(s)
42 ra2_ion_corr_ku [i] [q]
RA2 ionospheric correction on Ku-band
mm 1 ss 2
byte(s)
43 ra2_ion_corr_s [i] [q]
RA2 ionospheric correction on S-band
mm 1 ss 2
byte(s)
44 ion_corr_doris_ku [i] [q] Ionospheric correction from DORIS on Ku-
band
mm 1 ss 2 byte(s)
45 ion_corr_doris_s [i] [q]
Ionospheric correction from DORIS on S-
band
mm 1 ss 2
byte(s)
46 ion_corr_mod_ku [i] [q]
Ionospheric correction from model on Ku-
band
mm 1 ss 2
byte(s)
47 ion_corr_mod_s [i] [q]
Ionospheric correction from model on S-band
mm 1 ss 2
byte(s)
48 sea_bias_ku [i] [q]
Sea state bias on Ku-band
mm 1 ss 2
byte(s)
49 sea_bias_s [i] [q]
Sea state bias on S-band
mm 1 ss 2
byte(s)
50 spare_5 [i] [q]
Spare
- 1 SpareField 20
byte(s)
51 ku_sig_wv_ht [i] [q] Ku-band Significant wave height
mm 1 ss 2 byte(s)
-
39
52 s_sig_wv_ht [i] [q]
S-band Significant wave height
mm 1 ss 2
byte(s)
53 sd_18hz_ku_swh [i] [q]
Standard deviation of 18 Hz Ku-band SWH
mm 1 ss 2
byte(s)
54 sd_18hz_s_swh [i] [q]
Standard deviation of 18 Hz S-band SWH
mm 1 ss 2
byte(s)
55 num_18hz_ku_ocean_swh [i] [q]
Number of 18 Hz valid points for Ku-band
ocean SWH
- 1 us 2
byte(s)
56 num_18hz_s_ocean_swh [i] [q] Number of 18 Hz valid points for S-band
ocean SWH
- 1 us 2 byte(s)
57 slp_mod_flags [i] [q]
Slope model present flags [20 bits]: First 20
least significant bits (bits 0-19) correspond to the 20 values (one per data block)
containing: 0= valid measurement, 1=
invalid. Unused bits set to 0. Bit 0 applies to
the first data block
flags 1 ul 4
byte(s)
58 elev_echo_pt [i] [q]
1 Hz Elevation of echoing point
cm 1 sl 4
byte(s)
59 hz18_diff_mean_ech_pt [i] [q]
18 Hz Elevation differences of echoing point
from mean [20]
cm 20 ss 20*2
byte(s)
60 hz18_diff_1hz_lat [i] [q]
18 Hz slope-corrected latitude differences from 1 Hz latitude [20]
10 x m-
degree
20 ss 20*2
byte(s)
61 hz18_diff_1hz_long [i] [q]
18 Hz slope-corrected longitude differences from 1 Hz longitude [20]
10 x m-
degree
20 ss 20*2
byte(s)
62 hz18_ku_ice2_edge_width [i] [q]
18 Hz Ku-band Ice 2 leading edge width
[20]
mm 20 ss 20*2
byte(s)
63 hz18_s_ice2_edge_width [i] [q]
18 Hz S-band Ice 2 leading edge width [20]
mm 20 ss 20*2
byte(s)
64 spare_6 [i] [q] Spare
- 1 SpareField 40 byte(s)
65 hz18_ku_k_cal_ku [i] [q]
18 Hz Ku-band K_cal_Ku [20]
dB/100 20 ss 20*2
byte(s)
66 hz18_s_k_cal_s [i] [q]
18 Hz S-band K_cal_S [20]
dB/100 20 ss 20*2
byte(s)
67 map_18hz_k_cal_ku_flags [i] [q]
Map of valid points for 18 Hz K-cal_Ku: First
20 least significant bits (bits 0-19) correspond to the 20 values (one per data
block) containing: 0= valid measurement,
1= invalid. Unused bits set to 0. Bit 0
applies to the first data block
flags 1 ul 4
byte(s)
68 spare_7 [i] [q]
Spare
- 1 SpareField 4
byte(s)
69 ku_ocean_bscat_coeff [i] [q]
Ku-band corrected Ocean backscatter coefficient
dB/100 1 ss 2
byte(s)
70 s_ocean_bscat_coeff [i] [q]
S-band corrected Ocean backscatter
dB/100 1 ss 2
byte(s)
-
40
coefficient
71 sd_18hrz_ku_ocean_bscat [i] [q] Standard deviation of 18 Hz Ku-band ocean
backscatter coefficient
dB/100 1 ss 2 byte(s)
72 sd_18hrz_s_ocean_bscat [i] [q]
Standard deviation of 18 Hz S-band ocean
backscatter coefficient
dB/100 1 ss 2
byte(s)
73 num_18hrz_ku_ocean_bscat [i] [q]
Number of 18 Hz valid points for Ku-band
ocean backscatter coefficient
- 1 us 2
byte(s)
74 num_18hrz_s_ocean_bscat [i] [q]
Number of 18 Hz valid points for S-band
ocean backscatter coefficient
- 1 us 2
byte(s)
75 hz18_ku_ice1_bscat [i] [q]
18 Hz Ku-band Ice1 backscatter coefficient [20]
dB/100 20 ss 20*2
byte(s)
76 hz18_s_ice1_bscat [i] [q]
18 Hz S-band Ice1 backscatter coefficient [20]
dB/100 20 ss 20*2
byte(s)
77 hz18_ku_ice2_edge_bscat [i] [q]
18 Hz Ku-band Ice2 leading edge
backscatter coefficient [20]
dB/100 20 ss 20*2
byte(s)
78 hz18_s_ice2_edge_bscat [i] [q] 18 Hz S-band Ice2 leading edge backscatter
coefficient [20]
dB/100 20 ss 20*2 byte(s)
79 hz18_ku_ice2_bscat [i] [q] 18 Hz Ku-band Ice2 backscatter coefficient
[20]
dB/100 20 ss 20*2 byte(s)
80 hz18_s_ice2_bscat [i] [q]
18 Hz S-band Ice2 backscatter coefficient
[20]
dB/100 20 ss 20*2
byte(s)
81 hz18_ku_seaice_bscat [i] [q]
18 Hz Ku-band sea-ice backscatter
coefficient [20]
dB/100 20 ss 20*2
byte(s)
82 spare_8 [i] [q]
Spare
- 1 SpareField 40
byte(s)
83 ku_net_instr_corr_agc [i] [q]
Ku-band net instrument correction for AGC
dB/100 1 ss 2
byte(s)
84 s_net_instr_corr_agc [i] [q]
S-band net instrument correction for AGC
dB/100 1 ss 2
byte(s)
85 ku_atm_atten_corr [i] [q]
Ku-band atmospheric attenuation
correction.
dB/100 1 ss 2
byte(s)
86 s_atm_atten_corr [i] [q]
S-band atmospheric attenuation correction.
dB/100 1 ss 2
byte(s)
87 k_rai_atten [i] [q] Ku-band rain attenuation
dB/100 1 sl 4 byte(s)
88 off_nad_ang_platf [i] [q]
Off nadir angle of the satellite from platform data
deg^2/10^4 1 ss 2
byte(s)
89 off_nad_ang_wvform [i] [q] Off nadir angle of the satellite from
waveform data
deg^2/10^4 1 ss 2 byte(s)
90 hz18_1st_edge_ice2_ku [i] [q] 18 Hz Ku-band slope of the first part of the
s-1 20 sl 20*4 byte(s)
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41
trailing edge from ice-2 retracker [20]
91 hz18_1st_edge_ice2_s [i] [q] 18 Hz S-band slope of the first part of the
trailing edge from ice-2 retracker [20]
s-1 20 sl 20*4 byte(s)
92 hz18_2nd_edge_ice2_ku [i] [q]
18 Hz Ku-band slope of the second part of
the trailing edge from ice-2 retracker [20]
s-1 20 sl 20*4
byte(s)
93 hz18_2nd_edge_ice2_s [i] [q]
18 Hz S-band slope of the second part of
the trailing edge from ice-2 retracker [20]
s-1 20 sl 20*4
byte(s)
94 spare_9 [i] [q]
Spare
- 1 SpareField 40
byte(s)
95 m_sea_surf_ht [i] [q]
Mean sea-surface height
mm 1 sl 4
byte(s)
96 geoid_ht [i] [q] Geoid height
mm 1 sl 4 byte(s)
97 ocean_depland_elev [i] [q] Ocean depth/land elevation
mm 1 sl 4 byte(s)
98 tot_geocen_ocn_tide_ht_sol1 [i] [q]
Total geocentric ocean tide height (solution 1)
mm 1 ss 2
byte(s)
99 tot_geocen_ocn_tide_ht_sol2 [i] [q] Total geocentric ocean tide height(solution
2)
mm 1 ss 2 byte(s)
100 long_period_ocn_tide_ht [i] [q] Long period Tide height
mm 1 ss 2 byte(s)
101 tidal_load_ht [i] [q]
Tidal loading height
mm 1 ss 2
byte(s)
102 solid_earth_tide_ht [i] [q]
Solid earth tide height
mm 1 ss 2
byte(s)
103 geocen_pole_tide_ht [i] [q]
Geocentric pole tide height
mm 1 ss 2
byte(s)
104 mod_surf_atm_pres [i] [q]
Model surface atmospheric pressure
10 Pa 1 ss 2
byte(s)
105 mwr_wvapour_cont [i] [q] MWR water vapour content
10-2 g/cm2 1 ss 2 byte(s)
106 mwr_liq_vapour_cont [i] [q]
MWR liquid water content
10-2 kg/m2 1 ss 2
byte(s)
107 ra2_elec_cont [i] [q]
RA2 Total electron content.
10-1 TECU 1 ss 2
byte(s)
108 ra2_wind_sp [i] [q]
RA2 wind speed
mm/s 1 ss 2
byte(s)
109 mod_wind_sp_u [i] [q]
u component of the model wind vector
mm/s 1 ss 2
byte(s)
110 mod_wind_sp_v [i] [q]
v component of the model wind vector
mm/s 1 ss 2
byte(s)
111 spare_10 [i] [q]
Spare
- 1 SpareField 10
byte(s)
112 interpole_238_temp_mwr [i] [q] Interpolated 23.8 GHz brightness
temperature from MWR
K/100 1 ss 2 byte(s)
113 interpole_365_temp_mwr [i] [q] Interpolated 36.5 GHz brightness
K/100 1 ss 2 byte(s)
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42
temperature from MWR
114 interpole_sd_238_temp_mwr [i] [q] Interpolated standard deviation of MWR
23.8 GHz brightness temperature.
K/100 1 ss 2 byte(s)
115 interpole_sd_365_temp_mwr [i] [q]
Interpolated standard deviation of MWR
36.5 GHz brightness temperature.
K/100 1 ss 2
byte(s)
116 spare_11 [i] [q]
Spare
- 1 SpareField 2
byte(s)
117 ave_ku_chirp [i] [q] Average Ku chirp band
- 1 us 2 byte(s)
118 ku_chirp_id_flags [i] [q] Ku chirp band id [40 bits] First 40 least
significant bits (bits 0-39) correspond to the
20 values (one per data block). Unused bits set to 0. Bits 0-1 apply to the first data
block.
flags 2 ul 2*4 byte(s)
119 error_flag_chirp_id_flags [i] [q] Error flag for chirp band id [20 bits]First 20
least significant bits (bits 0-19) correspond
to the 20 values (one per data block) containing: 0= valid measurement, 1=
invalid. Unused bits set to 1. Bit 0 applies to
the first data block.
flags 1 ul 4 byte(s)
120 instr_flags [i] [q]
Instrument flag
flags 1 ul 4
byte(s)
121 fault_id_flags [i] [q]
Fault identifier [20 bits] First 20 least
significant bits (bits 0-19) correspond to the 20 values (one per data block) containing:
0= valid measurement, 1= invalid. Unused
bits set to 1. Bit 0 applies to the first data block.
flags 2 ul 2*4
byte(s)
122 spare_12 [i] [q]
Spare
- 1 SpareField 8
byte(s)
123 wvform_fault_id_flags [i] [q]
Waveforms samples fault identifier [40
bits]First 40 least significant bits (bits 0-39) correspond to the 20 values (one per data
block). Unused bits set to 0. Bits 0-1 apply
to the first data block.
flags 2 ul 2*4
byte(s)
124 instr_id_data_level_flags [i] [q]
Instrument mode ID at data block level [80 bits]First 80 least significant bits (0-79)
correspond to the 20 values (one per data
block). Unused bits set to 0. Bits 0 to 3
apply to the first data block.
flags 3 ul 3*4
byte(s)
125 num_meas_ku_calibr [i] [q]
No. of measures for Ku flight calibration factor evaluation.
- 1 us 2
byte(s)
126 num_meas_s_calibr [i] [q]
No. of measures for Ku flight calibration factor evaluation.
- 1 us 2
byte(s)
127 mwr_instr_flags [i] [q] MWR instrument flag
flags 1 us 2 byte(s)
128 spare_13 [i] [q]
Spare
- 1 SpareField 6
byte(s)
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43
129 spare_14 [i] [q]
Spare
- 1 SpareField 8
byte(s)
130 spare_15 [i] [q]
Spare
- 1 SpareField 8
byte(s)
131 ku_ocean_retrk_qua_flags [i] [q]
Ku-band ocean retracking quality [20 bits].
First 20 least significant bits (bits 0-19)
correspond to the 20 values (one per data block) containing: 0=valid, 1=invalid.
Unused bits set to 0. Bit 0 applies to the
first data block.
flags 1 ul 4
byte(s)
132 s_ocean_retrk_qua_flags [i] [q]
S-band ocean retracking quality [20 bits]. First 20 least significant bits (bits 0-19)
correspond to the 20 values (one per data
block) containing: 0=valid, 1=invalid. Unused bits set to 0. Bit 0 applies to the
first data block.
flags 1 ul 4
byte(s)
133 ku_ice1_retrk_qua_flags [i] [q] Ku-band ice1 retracking quality [20 bits].
First 20 least significant bits (bits 0-19)
correspond to the 20 values (one per data block) containing: 0=valid, 1=invalid.
Unused bits set to 0. Bit 0 applies to the
first data block.
flags 1 ul 4 byte(s)
134 s_ice1_retrk_qua_flags [i] [q]
S-band ice1 retracking quality [20 bits].
First 20 least significant bits (bits 0-19) correspond to the 20 values (one per data
block) containing: 0=valid, 1=invalid.
Unused bits set to 0. Bit 0 applies to the first data block.
flags 1 ul 4
byte(s)
135 ku_ice2_retrk_qua_flags [i] [q]
Ku-band ice2 retracking quality [20 bits]. First 20 least significant bits (bits 0-19)
correspond to the 20 values (one per data
block) containing: 0=valid, 1=invalid.
Unused bits set to 0. Bit 0 applies to the
first data block.
flags 1 ul 4
byte(s)
136 s_ice2_retrk_qua_flags [i] [q]
S-band ice2 retracking quality [20 bits].
First 20 least significant bits (bits 0-19) correspond to the 20 values (one per data
block) containing: 0=valid, 1=invalid.
Unused bits set to 0. Bit 0 applies to the
first data block.
flags 1 ul 4
byte(s)
137 ku_seaice_retrk_qua_flags [i] [q]
Ku-band sea-ice retracking quality [20 bits]. First 20 least significant bits (bits 0-19)
correspond to the 20 values (one per data
block) containing: 0=valid, 1=invalid.
Unused bits set to 0. Bit 0 applies to the
first data block.
flags 1 ul 4
byte(s)
138 ku_peak [i] [q]
1 Hz Ku-band peakiness
0.001 1 us 2
byte(s)
139 s_peak [i] [q]
1 Hz S-band peakiness
0.001 1 us 2
byte(s)
140 altim_landocean_flag [i] [q] flag 1 us 2
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44
Altimeter surface type flag byte(s)
141 radio_landocean_flag [i] [q] Radiometer land/ocean flag
flag 1 us 2 byte(s)
142 mwr_qua_interp_flag [i] [q]
MWR Quality interpolation flag
flag 1 us 2
byte(s)
143 rain_flag [i] [q]
Altimeter rain flag
flag 1 us 2
byte(s)
144 interpole_flag [i] [q]
Interpolation flag
flag 1 us 2
byte(s)
145 spare_16 [i] [q]
Spare
- 1 SpareField 6
byte(s)
Record Length : 2492
18 Hz averaged waveform data is used through out the studies and below is given the dataset for it.
Table A.2 18 Hz Waveforms
MDS
18 Hz Waveforms MDS
# Description Units Count Type Size
Data Record
0 dsr_time [i] [q]
Time stamp
MJD 1 mjd 12 byte(s)
1 quality_flag [i] [q]
Quality Indicator (-1 for blank
MDSR, 0 otherwise)
flag 1 BooleanFlag 1 byte(s)
2 spare_1 [i] [q]
Spare
- 1 SpareField 3 byte(s)
3 src_pack_cnt [i] [q]
Source Packet Counter
- 1 ul 4 byte(s)
4 spare_2 [i] [q]
Spare
- 1 SpareField 8 byte(s)
5 data_blk_info [i] [q]
Data Block information. The structure is repeated 20 times, once
for each data block.
- 20 data_blk_infoStruct 20*428.0
byte(s)
a ave_ku_wvforms_if [i] [q]
Average Ku band waveforms corrected
for IF transfer function (128 samples)
FFT
power
units
128 us 128*2
byte(s)
b cen_ku_dft_if [i] [q] Central Ku band filters from DFT
corrected for IF transfer function (2
samples)
FFT power
units
2 us 2*2 byte(s)
c ave_s_wvforms_if [i] [q]
Average S band waveforms corrected
for IF transfer function (64 samples)
FFT
power
units
64 us 64*2
byte(s)
d ind_2_dft_samp [i] [q] - 2 ss 2*2
-
45
# Description Units Count Type Size
Indexes of 2 DFT samples byte(s)
e offset_fft_filt [i] [q] Delta offset in FFT filters units
1/256 1 ss 2 byte(s)
f spare_1 [i] [q]
Spare
- 1 SpareField 18
byte(s)
g noise_pow_meas [i] [q]
Noise power measurement
dB/100 1 ss 2 byte(s)
h agc_noise_pow_meas [i] [q]
AGC of noise power measurement
dB/100 1 us 2 byte(s)
i ref_pow_val [i] [q]
reference power value
dB/100 1 us 2 byte(s)
j spare_2 [i] [q] Spare
- 1 SpareField 10 byte(s)
Record Length : 8588
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46
APPENDIX B – ANNULUS ANNALYSIS RESULTS
Table B.1 holds every important parameter in analysis of annuluses. “k” denotes the index of the annulus, where 0 indicates the most inner circle. “∆r” indicates the range difference between kth annuluses and 0th annulus. “Radius” is the radius of the kth annulus and “alfa” is the incident angle. Alfa is calculated by:
(B.1)
As described in part “1.2 General Measurement Principles” alfa is limited by half of the 3 dB beam width, which is 0.675 degrees. According to this, number of annuluses is 118 not 127. Additionally, as Envisat uses bin 46 as the tracking point the actual number of annuluses represented in a single waveform is even less than 118.
Another important information is given in last column, which holds the area for each annulus. It is clear that each annulus has almost the same area or same number of scatterers. Using this result and taking back the effects of antenna gain loss due to incident angle, it is possible to analyze differences in back scatter coefficients for each annulus.
Table B.1 Analysis results on annuluses
ANALYSIS RESULTS ON ANNULUSES K ∆r [m] Radius
[km] Alfa
[degree] Area [km2]
0 0 0 0 0 1 0.46875 0.866 0.062024486 2.356056 2 0.9375 1.2247 0.087715195 2.355987 3 1.40625 1.5 0.107432629 2.35654 4 1.875 1.7321 0.12405599 2.35673 5 2.34375 1.9365 0.138695416 2.35576 6 2.8125 2.1213 0.151931046 2.355822 7 3.28125 2.2913 0.164106666 2.356641 8 3.75 2.4495 0.175437141 2.356177 9 4.21875 2.5981 0.18608004 2.356425
10 4.6875 2.7386 0.196142796 2.355586 11 5.15625 2.8723 0.205718518 2.356752 12 5.625 3 0.214864503 2.355857 13 6.09375 3.1225 0.223638049 2.356214 14 6.5625 3.2404 0.23208213 2.356779 15 7.03125 3.3541 0.240225395 2.355549 16 7.5 3.4641 0.248103654 2.356201
.tan 1
= −Altitude
radiusalfa
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47
17 7.96875 3.5707 0.255738394 2.355911 18 8.4375 3.6742 0.263151102 2.355714 19 8.90625 3.7749 0.270363265 2.356585 20 9.375 3.873 0.277389206 2.357008 21 9.84375 3.9686 0.28423609 2.355117 22 10.3125 4.062 0.290925401 2.356377 23 10.78125 4.1533 0.297464302 2.356373 24 11.25 4.2427 0.303867118 2.358087 25 11.71875 4.3301 0.310126687 2.353878 26 12.1875 4.4159 0.316271657 2.357472 27 12.65625 4.5 0.322294866 2.355652 28 13.125 4.5826 0.328210639 2.356894 29 13.59375 4.6637 0.334018976 2.355802 30 14.0625 4.7434 0.339727039 2.355396 31 14.53125 4.8218 0.34534199 2.355917 32 15 4.899 0.350870992 2.357595 33 15.46875 4.975 0.356314044 2.357527 34 15.9375 5.0498 0.361671147 2.355739 35 16.40625 5.1235 0.366949463 2.355479 36 16.875 5.1962 0.372156154 2.356955 37 17.34375 5.2679 0.37729122 2.357061 38 17.8125 5.3386 0.382354662 2.355816 39 18.28125 5.4084 0.38735364 2.356636 40 18.75 5.4773 0.392288157 2.356272 41 19.21875 5.5453 0.39715821 2.354739 42 19.6875 5.6125 0.401970964 2.355579 43 20.15625 5.6789 0.406726417 2.355406 44 20.625 5.7446 0.411431732 2.357841 45 21.09375 5.8095 0.416079746 2.355758 46 21.5625 5.8737 0.420677623 2.356388 47 22.03125 5.9372 0.425225362 2.35617 48 22.5 6 0.429722963 2.355114 49 22.96875 6.0622 0.434177588 2.357039 50 23.4375 6.1238 0.438589237 2.35826 51 23.90625 6.1847 0.442950749 2.354899 52 24.375 6.245 0.447269285 2.354658 53 24.84375 6.3048 0.451552008 2.357696 54 25.3125 6.364 0.455791754 2.356172 55 25.78125 6.4227 0.459995688 2.358014 56 26.25 6.4808 0.464156646 2.355231 57 26.71875 6.5384 0.468281791 2.355899 58 27.1875 6.5955 0.472371122 2.356024 59 27.65625 6.6521 0.47642464 2.355611 60 28.125 6.7083 0.480449507 2.358879 61 28.59375 6.7639 0.484431398 2.353224 62 29.0625 6.8192 0.4883918 2.359793 63 29.53125 6.8739 0.492309228 2.353092 64 30 6.9283 0.496205166 2.358832
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48
65 30.46875 6.9822 0.500065291 2.355491 66 30.9375 7.0357 0.503896765 2.356061 67 31.40625 7.0888 0.507699589 2.356229 68 31.875 7.1415 0.511473761 2.355996 69 32.34375 7.1938 0.515219282 2.355366 70 32.8125 7.2458 0.518943314 2.358894 71 33.28125 7.2973 0.522631534 2.352958 72 33.75 7.3485 0.526298265 2.35577 73 34.21875 7.3994 0.529943507 2.358293 74 34.6875 7.4499 0.533560098 2.355848 75 35.15625 7.5001 0.5371552 2.357734 76 35.625 7.5499 0.540721652 2.354592 77 36.09375 7.5994 0.544266615 2.35585 78 36.5625 7.6486 0.54779009 2.356828 79 37.03125 7.6975 0.551292075 2.357527 80 37.5 7.7461 0.554772572 2.357951 81 37.96875 7.7943 0.558224419 2.353201 82 38.4375 7.8423 0.561661939 2.357944 83 38.90625 7.89 0.565077971 2.357548 84 39.375 7.9374 0.568472513 2.356882 85 39.84375 7.9845 0.571845568 2.355948 86 40.3125 8.0313 0.575197134 2.354748 87 40.78125 8.0779 0.578534373 2.358358 88 41.25 8.1241 0.581842963 2.351584 89 41.71875 8.1702 0.585144387 2.359861 90 42.1875 8.2159 0.588417162 2.352565 91 42.65625 8.2615 0.591682771 2.360497 92 43.125 8.3067 0.594919731 2.352684 93 43.59375 8.3518 0.598149526 2.360273 94 44.0625 8.3965 0.601350671 2.35195 95 44.53125 8.4411 0.604544651 2.359201 96 45 8.4854 0.607717144 2.355704 97 45.46875 8.5295 0.61087531 2.357316 98 45.9375 8.5733 0.614011988 2.353375 99 46.40625 8.617 0.617141501 2.360015
100 46.875 8.6604 0.620249526 2.355689 101 47.34375 8.7036 0.623343225 2.356587 102 47.8125 8.7466 0.626422598 2.357321 103 48.28125 8.7893 0.629480483 2.352371 104 48.75 8.8319 0.632531203 2.358278 105 49.21875 8.8743 0.635567597 2.358528 106 49.6875 8.9164 0.638582504 2.353017 107 50.15625 8.9584 0.641590245 2.358524 108 50.625 9.0001 0.6445765 2.352643 109 51.09375 9.0417 0.647555589 2.357887 110 51.5625 9.0831 0.650520353 2.357347 111 52.03125 9.1243 0.653470791 2.35665 112 52.5 9.1653 0.656406902 2.355797
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49
113 52.96875 9.2061 0.659328688 2.354791 114 53.4375 9.2468 0.662243309 2.35944 115 53.90625 9.2872 0.665136443 2.352342 116 54.375 9.3275 0.668022412 2.356736 117 54.84375 9.3677 0.670901217 2.361055 118 55.3125 9.4076 0.673758535 2.353475 119 55.78125 9.4474 0.676608688 2.357542 120 56.25 9.487 0.679444516 2.355573 121 56.71875 9.5264 0.682266018 2.353455 122 57.1875 9.5657 0.685080355 2.357198 123 57.65625 9.6049 0.687887528 2.360868 124 58.125 9.6438 0.690673215 2.352344 125 58.59375 9.6826 0.693451736 2.355768 126 59.0625 9.7213 0.696223094 2.359119 127 59.53125 9.7598 0.698980126 2.356265
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50
APPENDIX C – SIMULATOR CODES
MatLab codes of the simulator are given below. RunSimulator.m, is responsible for preparing the surface map and calling simstrecth.m processor function accordingly.
RunSimulator.m
function [out]=RunSimulator %Define Map Size(As each pixel is 100 m & footprint diameter is around 19 km) mapw=199; %Map Width; maph=mapw; %Map Height; %Nadir Point Coordinates mpw=(mapw+1)/2; %Mid Point of Width mph=mpw; %Mid Point of Height %Pixel Size: How many meters is a side of each pixel symbolize? pixelwidth=1e2; %[m] %Define Simulation Constants H=8e5; %Altitude [m] nscat=mapw*maph; %Number of Scatterers pulselen=20e-6; %Uncompressed Pulse Length [s] centerfreq=13575e6; %Carrier Frequency [Hz] BandWidth=320e6; %Chirp Bandwidth [Hz] windowsize=60; %Frequency Window Size winid=1; %Smoothing Window ID, [1=Hamming] w=1:1:mapw; %Horizontal Axis Vector h=1:1:maph; %Vertical Axis Vector nmaps=1; %number of maps mwh=0; %maximum wave height out=zeros(1,128); %Output Variable for n=1:nmaps %Cycle Through each map %Prepare Elevation Map %Map 1: Single Elevation, Smooth Surface elev=mwh.*ones(mapw,maph); %Map 2: Wavy Surface %fi=0.1*n; %Phase term, to get different maps.(if nmaps>1) %elev=5*(sin(2*pi*2/mapw.*w+fi)'*cos(2*pi*2/maph.*h+fi)); reflectivity=0.1*ones(mapw,maph); %Defines Reflectivity Map for each pixel mapdata=[mapw maph mpw mph pixelwidth]; %Put All Map Data in an Array... %Prepare Range Map for hh=1:1:maph for ww=1:1:mapw
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51
%Calculate Range... range(ww, hh)=sqrt(((ww-mpw)^2+(hh-mph)^2)*pixelwidth^2+(H - elev(ww,hh))^2); %Calculate Look Angle teta(ww, hh)=atan(sqrt((ww-mpw)^2+(hh-mph)^2)*pixelwidth/(H - elev(ww,hh))); end end %Output the Map Number to show progress... display(['Range Map ',num2str(n),' of ',num2str(nmaps),' Complete. Starting Simulation']); %Run Simulator1(works with exp function) out_prime=simstretch(H, pulselen,centerfreq,BandWidth,windowsize,range,reflectivity,teta,winid,mapdata); %Run Simulator2(works with cos function) %out_prime=simstretchos(H, pulselen,centerfreq,BandWidth,windowsize,range,reflectivity,teta,winid,mapdata); out=out+abs(out_prime); %Sum Up all the outputs... save('backup.mat', 'out', 'n'); end figure(1);plot(out) %Plot Output... end
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simstretch.m function [out] = simstretch(H,pulselen,centerfreq,BandWidth,windowsize,scat_range,reflectivity,teta,winid, mapdata) %pulselen: Uncompressed Pulse Length [s] %centerfreq: Carrier Frequency [Hz] %BandWidth: Chirp Bandwidth [Hz] %windowsize: Size of Frequency Window %scat_range: Array of Scatterer Ranges %Reflectivity: Array of Scatterer Reflectivities %teta: Array of Scatterer incident angles %winid: Smoothing window ID %mapdata: Consists of Map dimensions, nadir point location and pixelwidth c = 3.e8; %Define speed of Light [m/s] %Extract Map Dimensions mapw = mapdata(1); %map width maph = mapdata(2); %map height mpw = mapdata(3); %nadir point location/antenna boresight mph = mapdata(4); %nadir point location/antenna boresight pixelwidth=mapdata(5); %Pixel Width beamwidth=(1.35/180)*pi; %3 dB Beamwidth [radian] nscat=mapw*maph; %Number of Scatterers delta_t = 2. * windowsize / c; %Maximum two way time delay n = fix(delta_t * BandWidth); %number of samples, 128 m = power_integer_2(n); %m is a dummy variable, 7 nfft = 2.^m; %nfft, number of fft samples is 128, so m=7 xsingle(1:n) = 0.; %initialize reflected echo variable for single scatterer(Receiver Input) ysingle(1:n) = 0.; %initialize fft result variable for single scatterer(System Output) y(1:n) = 0.; %initialize fft result variable (System Output) %Set Smoothing Window if( winid == 0.) win(1:n) = 1.; win =win'; else if(winid == 1.) win = hamming(n); else if( winid == 2.) win = kaiser(n,pi); else if(winid == 3.) win = chebwin(n,60); end end
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end end %end of set Smoothing Window... delta_r = c / (2.* BandWidth); %Range Resolution. max_ws = delta_r * nfft; %maximum window size minr= min(min(scat_range)); %minimum scatterer range trout=45*0.46875; %Tracker Output (Previous) fr=12352e6; %Reference Chirp Carrier Frequency. (13575-12352=1.223GHz, IF Freq=1.223GHz) frr=1223e6;%1223e6; %2nd Local Oscillator Freq. to produce base band signal... for w = 1:1:mapw for h=1:1:maph if teta(w,h)G(teta)=41.6-12(teta/beamwidth)^2 gain=33.02/2 - 12*(teta(w,h)/beamwidth)^2; %[dB] gain=10^(gain/10); xsingle(k) = reflectivity(w,h) * gain .* exp(i * phase1 + i * phase2); %calculate instantaneous output %Add Noise %snr=10; %Define Signal to No