GEOMETRY, ACCURACY, AND POSITION OF OCEAN REFLECTING POINTS IN BISTATIC SATELLITE ALTIMETRY

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GEOMETRY, ACCURACY, AND POSITION OF OCEAN
REFLECTING POINTS IN BISTATIC SATELLITE ALTIMETRY

• J. Klokocník, J. Kostelecký, M. Kocandrlová

IAG International Symposium Gravity, Geoid and
Space Missions GGSM2004, Porto, Portugal, 30th
August 3rd September, 2004
2
Authors

• Jaroslav Klokocník, CEDR - Astronom. Inst.
  Czech Acad. Sci., Ondrejov Obs., Czech
  Republic, jklokocn_at_asu.cas.cz
• Jan Kostelecký, CEDR- Res. Inst. Geod. Zdiby
  CTU Prague, Fac. Civil Eng., Czech Republic,
  kost_at_fsv.cvut.cz
• Milada Kocandrlová, CTU Prague, Fac. Civil Eng.,
  Dept. Mathem., Czech Republic,
  kocandrlova_at_mat.fsv.cvut.cz

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Abstract

• We analyse time and space distribution of
  specular points P in bistatic altimetry (BA)
  between LEO (e.g. CHAMP or SAC-C) and HEO (GPS,
  GALILEO).
• We clearly demonstrate significantly higher
  number and density of reflecting points P in the
  case of BA in a comparison with traditional
  monostatic radar nadir altimetry.
• We present accuracy assessments for position of
  reflecting points, accounting for measurement
  (delay) error and orbit errors of senders (GPS)
  and receiver (CHAMP)
• First attempts at determination of position of P
  on a reference surface different from a sphere.

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S
(Sender)
2
d
12
a
(Receiver)
S
d
2
1
2
d
1
a
1
g
P
g
r
2
r
h
e
r
1
r
e
b
b
1
2
Earth (h ocean height)
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CHAMP
6
SAC-C
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Formulae to compute position of the reflecting
point on a sphere by approximations
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Accuracy assessment for height of reflecting
points on a sphere accounting for measurement
(delay) error and orbit errors of senders (GPS)
and receiver (CHAMP)
approach I given error of t t1t2-t12 orbit
errors of senders and receiver
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Accuracy assessment for height of reflecting
points on a sphere accounting for measurement
(delay) error and orbit errors of senders (GPS)
and receiver (CHAMP)

• approach II
• given
• error of (d1d2),
• orbit errors of senders and receiver

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S
(Sender)
2
d
12
a
(Receiver)
S
d
2
1
2
d
1
a
1
g
P
g
r
2
r
h
e
r
1
r
e
b
b
1
2
Earth (h ocean height)
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S
d
2
S
2
1
d
1
P
d'
d'
1
2
 
g
g
g
g
P'
d'
- d
d'
- d
2
2
1
1
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S
2
e
c
S
2
e
r
e
c
S
2
a
S
d'
S
1
2
2
1
e
r
P'
d'
1
e
S
r
1
a
1
g
P'
g
e
c
P'
r
e
b
b
1
2
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S
2
a
d'
S
2
2
1
h
2
d'
1
a
1
g
h
P'
g
1
s
P'
s
2
O
s
r
1
e
b
b
1
2
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Seeking Reflecting Points on Reference Ellipsoid
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an intersection of 3 quadrics in a special
position
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S
2
S
1
P
v
q
Earth
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Choice of Cartesian coordinate frame


x
2
u
O
S
x
1
1
S
2
x
3
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Ellipsoid of revolution for reflecting points
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Rotational cone surface of reflected signals
S1 vertex
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Intersection of ellipsoid of revolution with the
cone resulting in a plane ellipse P
P
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Cut of plane P with the Earth reference ellipsoid
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Classification of mutual positions of
intersecting ellipses
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minimum distance between two ellipsoids
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Principle of solution

• Correct theoretical result
• touch of two ellipsoids Q0 and Q1
• Practical result (due to observing errors)
  imaginary or real intersection of the two
  ellipsoids
• Possible solution seeking of minimum distance
  between the two ellipsoids

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Algorithm of solution
matrices of ellipsoids

centers of ellipsoids
in
vector in normal direction
tangent vector

radius of normal curvature
in direction
in
centre of curvature
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Iterative solution of minimum distance between
two ellipsoids
as a progression of distances X0X1 X0X1
X0X1 etc
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Conclusion

• BA between LEO and HEO may yield many more
  reflecting points than traditional altimetry of
  LEO
• If the technology can be proven, the space BA
  promises a distinct gain in coverage of the
  oceans at fine scales in time and space in
  comparison with traditional altimetry
• Accuracy of reflecting points decreases only
  slowly with off-nadir angles ?
• In total error budget at a centimeter level, the
  orbit errors of HEO and LEO must be accounted for
  together with a measurement error
• 
  cont.

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cont., Conclusion II

• Mathematical model for determination of position
  of reflecting point on reference rotational
  ellipsoid utilizes mutual position between two
  ellipses. Ellipse 1 is intersection of cone of
  rotation (with vertex in S1) and ellipsoid of
  rotation around S1S2. Ellipse 2 is in the same
  plane as Ellipse 1 and is intersection of this
  plane and reference ellipsoid of the Earth.
  Position of P on this ellipsoid is found
  iteratively.
• Another iterative solution (without any cone)
  distance between two ellipsoids

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BA has potentially many geo-applications
mesoscale eddies, ocean surface roughness,
winds, mean sea surface, sea-ice, namely in polar
areas Space data of sufficient accuracy is
urgently needed
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Literature

• Komjathy A., Garrison J.L., Zavorotny V. (1999)
  GPS A new tool for Ocean science, GPS World,
  April, 50-56.
• Lowe et al (2002) 5-cm precision aircraft ocean
  altimetry using GPS reflections, Geophys. Res.
  Letts. 2910.
• Martin-Neira, M. (1993) A passive reflectometry
  system application to ocean altimetry, ESA
  Journal 17 331-356.
• Ruffini, G., Soulat, F. (2000) PARIS
  Interferometric Processor analysis and
  experimental results, theoretical feasibility
  analysis, IEEC-CSIC Res. Unit., Barcelona,
  PIAER-IEEC-TN-1100/2200, ESTEC Contr. No.
  14071/99/NL/MM, ftp//ftp.estec.esa.nl/pub/eopp/p
  ub/
• Truehaft, R., Lowe, S., C. Zuffada, Chao, Y.
  (2001) 2-cm GPS-altimetry over Crater Lake,
  Geophys. Res. Letters 2823, 4343-4346.
• Wagner, C., Klokocník, J. (2001) Reflection
  Altimetry for oceanography and geodesy, presented
  at 2001 An Ocean Odyssey, IAPSO-IABO Symp.
  Gravity, Geoid, and Ocean Circulation as Inferred
  from Altimetry, Mar del Plata, Argentina.
• Wagner, C., Klokocník, J. (2003) The value of
  ocean reflections of GPS signals to enhance
  satellite altimetry data distribution and error
  analysis, J. Geod. (in print).
• Zuffada, C., Elfouhaily, T., Lowe, S. (2002a)
  Sensitivity Analysis of Wind Vector Measurements
  for Ocean Reflected GPS Signals, it Remote
  Sensing Env. (in print).

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Acknowledgments

• This research has been supported by the grant
  LN00A005 (CEDR) provided by Ministry of Education
  of the Czech Republic and by the grant of GA AV
  CR number 3003407
• We thank Carl A. Wagner, Cinzia Zuffada, Markus
  Nitschke,
• Giulio Ruffini and Martin Wiehl for
  consultations/literature.

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Reflection Point Problemspherical and ellipsoid
casein Bistatic Satellite Altimetry

• anonymous FTP sunkl.asu.cas.cz
• cd pub/jklokocn/ PPT_BA_PORTO.ppt
• The End