Abstract

Numerical simulations based on previously validated models for the wide-angle airborne laser ranging system are used here for assessing the precision in coordinate estimates of ground-based cube-corner retroreflectors (CCR’s). It is shown that the precision can be optimized to first order as a function of instrument performance, number of laser shots (LS’s), and network size. Laser beam divergence, aircraft altitude, and CCR density are only second-order parameters, provided that the number of echoes per LS is greater than 20. Thus precision in the vertical is ∼1 mm, with a signal-to-noise ratio of 50 at nadir, a 10-km altitude, a 20° beam divergence, and ∼5 × 103 measurements. Scintillation and fair-weather cumulus clouds usually have negligible influence on the estimates. Laser biases and path delay are compensated for by adjustment of aircraft offsets. The predominant atmospheric effect is with mesoscale nonuniform horizontal temperature gradients, which might lead to biases near 0.5 mm.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Dingwen, “Some general problems of the interpretation of geodetic deformation data,” in Proceedings of the IAG: Global and Regional Geodynamics, P. Vyskocil, C. Reigber, P. A. Cross, eds. (Springer-Verlag, Berlin, (1989), pp. 369–375.
  2. W. Bertoni, G. Brighenti, G. Gambolati, G. Ricceri, F. Vuillermin, “Land subsidence due to gas production in the on- and off-shore natural gas fields of the Ravenna area, Italy,” in Proceedings of the Fifth International Symposium on Land Subsidence, F. B. J. Barends, F. J. J. Brouwer, F. H. Schröder, ed. (IAHS, Wallingford, UK, 1995), pp. 13–20. Numerous other papers in this proceedings also address this subject.
  3. M. J. Bouteca, D. Fourmaintraux, Y. Meimon, “In-situ measurements and numerical modeling of the reservoir compacting and surface subsidence,” in Proceedings of the European Oil and Gas Conference, G. Imarisio, M. Frias, J. M. Bemtgen, eds. (Graham & Totman, London, 1990), pp. 127–135.
  4. W. D. Kahn, F. O. Vonbun, D. E. Smith, T. S. Englar, B. P. Gibbs, “Performance analysis of the spaceborne laser ranging system,” Bull. Geod. 54, 165–180 (1980).
    [CrossRef]
  5. S. C. Cohen, J. J. Degnan, J. L. Bufton, J. B. Garvin, J. B. Abshire, “The geoscience laser altimetry/ranging system,” IEEE Trans. Geosci. Remote Sens. GE-25, 581–592 (1987).
    [CrossRef]
  6. W. D. Kahn, J. J. Degnan, T. S. Englar, “The airborne laser ranging system, its capabilities and applications,” (NASA, Greenbelt, Md., 1982).
  7. M. Kasserthe Institut Géographique National, “Method for determining the spatial coordinates of points, applications of said method to high precision topography, system and optical device for carrying out said method,” U.S. patent774,038 (7October1991).
  8. O. Bock, Ch. Thom, M. Kasser, D. Fourmaintraux, “Development of a new airborne laser subsidence measurement system, aiming at mm-accuracy,” in Proceedings of the Fifth International Symposium on Land Subsidence, F. B. J. Barends, F. J. J. Brouwer, F. H. Schröder, eds. (Balkema, Rotterdam, The Netherlands, 1995), pp. 113–122.
  9. O. Bock, “Study of a wide angle airborne laser ranging system with ground based retroreflecting benchmarks for vertical ground deformations monitoring. Study of the adaptation to a spaceborne platform,” Ph.D. dissertation (University of Paris 7, Paris, 1996; in French).
  10. O. Bock, M. Kasser, Ch. Thom, “A wide angle airborne or spaceborne laser ranging instrumentation for subsidence measurement,” in Proceedings of the Tenth International Workshop on Laser Ranging Instrumentation, Y. Fumin, C. Wanzhen, eds. (Chinese Academy of Sciences, Shanghai, 1996), pp. 32–42.
  11. O. Bock, Ch. Thom, M. Kasser, J. Pelon, “Multilateration with the wide angle laser ranging system: ranging performance and first ground-based validation experiment,” IEEE Trans. Geosci. Remote Sens. 37, 739–747 (1999).
    [CrossRef]
  12. O. Bock, M. Kasser, Ch. Thom, J. Pelon, “Study of a wide angle laser ranging system for relative positioning of ground-based benchmarks with millimeter accuracy,” J. Geod. 72, 442–459 (1998).
    [CrossRef]
  13. J. J. Degnan, “Satellite laser ranging: current status and future prospects,” IEEE Trans. Geosci. Remote Sens. GE-23, 398–413 (1985).
    [CrossRef]
  14. J. W. Marini, C. W. Murray, “Correction of laser range tracking data for atmospheric refraction at elevation above 10 degrees,” (NASA, Greenbelt, Md., 1973).
  15. C. S. Gardner, “Correction of laser tracking data for the effects of horizontal refractivity gradients,” Appl. Opt. 16, 2427–2432 (1977).
    [CrossRef] [PubMed]
  16. J. Davis, T. Herring, I. Shapiro, A. Rogers, G. Elgered, “Geodesy by radio-interferometry: effects of atmospheric modeling errors on estimates of baseline lengths,” Radio Sci. 20, 1593–1607 (1985).
    [CrossRef]
  17. J. B. Abshire, C. S. Gardner, “Atmospheric refractivity corrections in satellite laser ranging,” IEEE Trans. Geosci. Remote Sens. GE-23, 414–425 (1985).
    [CrossRef]
  18. P. L. Bender, “Atmospheric refraction and satellite laser ranging,” in Proceedings of the Symposium on Refraction of Transatmospheric Signals in Geodesy, J. C. de Munck, T. A. Th. Spoelstra, eds. (Netherlands Geodetic Commission, Delft, The Netherlands, 1992), pp. 117–125.
  19. CCR coordinates between epochs can be compared because they are expressed in a local reference frame that is defined by a few (at least three) fixed CCR’s.
  20. PD cannot be treated as a parameter to be adjusted for each CCR because it is highly correlated with the vertical coordinates of CCR’s.
  21. The same analysis shows that including the PD in the forward model would reduce the precision to σUz = 1.2 cm in the reference experiment.
  22. P. O. Minott, “Design of retrodirector arrays for laser ranging of satellites,” (NASA, Greenbelt, Md., 1974).
  23. As long as NLS and NCCR are constant, NMeas/LS and NMeas/CCR are related by a constant factor.
  24. J. W. Strohbehn, “Modern theories in the propagation of optical waves in a turbulent medium,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer, New York, 1978), Chap. 3.
    [CrossRef]
  25. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer, New York, 1975), Chap. 2.
  26. R. B. Stull, An Introduction to Boundary Layer Meteorology (Kluwer Academic, Dordrecht, The Netherlands, 1988).
    [CrossRef]
  27. Of course, compensating for such systematic errors does not impair the detection of actual deformations with the same spatial signature.
  28. J. R. Holton, An Introduction to Dynamic Meteorology, 3rd ed. (Academic, New York, 1992).
  29. J. P. Hauser, “Effects of deviations from hydrostatic equilibrium on atmospheric corrections to satellite and lunar laser range measurements,” J. Geophys. Res. 94, 10,182–10,186 (1989).
    [CrossRef]
  30. Meteorological network of Meteo-France and radiosonde profiles taken at the station at Trappes, France, on 14 March 1995.
  31. J. C. André, G. DeMoor, P. Lacarrère, G. Therry, R. du Vachat, “Modeling the 24-hour evolution of the mean and turbulent structures of the planetary boundary layer,” J. Atmos. Sci. 35, 1861–1883 (1978).
    [CrossRef]
  32. D. H. Lenschow, P. L. Stephens, “The role of thermals in the convective boundary layer,” Boundary-Layer Meteorol. 19, 509–532 (1980).
    [CrossRef]
  33. M. A. LeMone, “The structure of horizontal roll vortices in the planetary boundary layer,” J. Atmos. Sci. 30, 1077–1091 (1971).
    [CrossRef]
  34. D. Atlas, B. Walter, S. H. Chou, P. J. Sheu, “The structure of unstable marine boundary layer viewed by lidar and aircraft observations,” J. Atmos. Sci. 43, 1301–1318 (1986).
    [CrossRef]
  35. R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communication,” Proc. IEEE 58, 1523–1545 (1970).
    [CrossRef]
  36. J. H. Churnside, “Aperture averaging of optical scintillations in the turbulent atmosphere,” Appl. Opt. 30, 1982–1994 (1991).
    [CrossRef] [PubMed]
  37. R. L. Fante, “Electromagnetic beam propagation in turbulent media: an update,” Proc. IEEE 68, 1424–1443 (1980).
    [CrossRef]
  38. Y. A. Kravtsov, A. I. Saichev, “Effects of double passage of waves in randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1982).
    [CrossRef]
  39. V. P. Aksenov, V. A. Banakh, V. L. Mironov, “Fluctuations of retroreflected laser radiation in a turbulent atmosphere,” J. Opt. Soc. Am. A 1, 263–274 (1984).
    [CrossRef]
  40. L. C. Andrews, R. L. Philipps, P. T. Yu, “Optical scintillations and fade statistics for a satellite-communication system,” Appl. Opt. 34, 7742–7751 (1995).
    [CrossRef] [PubMed]
  41. J. H. Churnside, S. F. Clifford, “Log-normal Rician probability-density function of optical scintillations in the turbulent atmosphere,” J. Opt. Soc. Am. A 1, 1923–1930 (1987).
    [CrossRef]
  42. L. C. Andrews, R. L. Phillips, B. K. Shivamoggi, “Relations of the parameters of the I–K distribution for irradiance fluctuations to physical parameters of the turbulence,” Appl. Opt. 27, 2150–2156 (1988).
    [CrossRef] [PubMed]
  43. R. E. Hufnagel, “Propagation through atmospheric turbulence,” in The Infrared Handbook (U.S. GPO, Washington, D.C., 1978), p. 6.
  44. V. P. Lukin, B. V. Fortes, E. V. Nosov, “Effective outer scale of turbulence for imaging through the atmosphere,” in Optics in Atmospheric Propagation and Adaptive Systems II, A. Kohnle, A. D. Devir, eds., Proc. SPIE3219, 98–106 (1998).
    [CrossRef]
  45. J. C. Kaimal, J. C. Wyngaard, D. A. Haugen, O. R. Coté, Y. Izumi, “Turbulence structure in the convective boundary layer,” J. Atmos. Sci. 33, 2152–2169 (1976).
    [CrossRef]
  46. Note that a major limitation in the prediction of positioning precision is due to the thresholds used for a priori data sorting [SNR ≥ 3 and στij ≤ 0.67 ns (10 cm)]. Hence it is not always possible to compensate for a small SNR0 by a strong NLS, as relation (16) would suggest.
  47. J. C. Owens, “Optical refractive index of air: dependence on pressure, temperature and composition,” Appl. Opt. 6, 51–59 (1967).
    [CrossRef] [PubMed]
  48. A. Tarantola, Inverse Problem Theory: Methods for Data Fitting and Model Parameters Estimation (Elsevier, Amsterdam, 1987).

1999 (1)

O. Bock, Ch. Thom, M. Kasser, J. Pelon, “Multilateration with the wide angle laser ranging system: ranging performance and first ground-based validation experiment,” IEEE Trans. Geosci. Remote Sens. 37, 739–747 (1999).
[CrossRef]

1998 (1)

O. Bock, M. Kasser, Ch. Thom, J. Pelon, “Study of a wide angle laser ranging system for relative positioning of ground-based benchmarks with millimeter accuracy,” J. Geod. 72, 442–459 (1998).
[CrossRef]

1995 (1)

1991 (1)

1989 (1)

J. P. Hauser, “Effects of deviations from hydrostatic equilibrium on atmospheric corrections to satellite and lunar laser range measurements,” J. Geophys. Res. 94, 10,182–10,186 (1989).
[CrossRef]

1988 (1)

1987 (2)

J. H. Churnside, S. F. Clifford, “Log-normal Rician probability-density function of optical scintillations in the turbulent atmosphere,” J. Opt. Soc. Am. A 1, 1923–1930 (1987).
[CrossRef]

S. C. Cohen, J. J. Degnan, J. L. Bufton, J. B. Garvin, J. B. Abshire, “The geoscience laser altimetry/ranging system,” IEEE Trans. Geosci. Remote Sens. GE-25, 581–592 (1987).
[CrossRef]

1986 (1)

D. Atlas, B. Walter, S. H. Chou, P. J. Sheu, “The structure of unstable marine boundary layer viewed by lidar and aircraft observations,” J. Atmos. Sci. 43, 1301–1318 (1986).
[CrossRef]

1985 (3)

J. Davis, T. Herring, I. Shapiro, A. Rogers, G. Elgered, “Geodesy by radio-interferometry: effects of atmospheric modeling errors on estimates of baseline lengths,” Radio Sci. 20, 1593–1607 (1985).
[CrossRef]

J. B. Abshire, C. S. Gardner, “Atmospheric refractivity corrections in satellite laser ranging,” IEEE Trans. Geosci. Remote Sens. GE-23, 414–425 (1985).
[CrossRef]

J. J. Degnan, “Satellite laser ranging: current status and future prospects,” IEEE Trans. Geosci. Remote Sens. GE-23, 398–413 (1985).
[CrossRef]

1984 (1)

1982 (1)

Y. A. Kravtsov, A. I. Saichev, “Effects of double passage of waves in randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1982).
[CrossRef]

1980 (3)

W. D. Kahn, F. O. Vonbun, D. E. Smith, T. S. Englar, B. P. Gibbs, “Performance analysis of the spaceborne laser ranging system,” Bull. Geod. 54, 165–180 (1980).
[CrossRef]

R. L. Fante, “Electromagnetic beam propagation in turbulent media: an update,” Proc. IEEE 68, 1424–1443 (1980).
[CrossRef]

D. H. Lenschow, P. L. Stephens, “The role of thermals in the convective boundary layer,” Boundary-Layer Meteorol. 19, 509–532 (1980).
[CrossRef]

1978 (1)

J. C. André, G. DeMoor, P. Lacarrère, G. Therry, R. du Vachat, “Modeling the 24-hour evolution of the mean and turbulent structures of the planetary boundary layer,” J. Atmos. Sci. 35, 1861–1883 (1978).
[CrossRef]

1977 (1)

1976 (1)

J. C. Kaimal, J. C. Wyngaard, D. A. Haugen, O. R. Coté, Y. Izumi, “Turbulence structure in the convective boundary layer,” J. Atmos. Sci. 33, 2152–2169 (1976).
[CrossRef]

1971 (1)

M. A. LeMone, “The structure of horizontal roll vortices in the planetary boundary layer,” J. Atmos. Sci. 30, 1077–1091 (1971).
[CrossRef]

1970 (1)

R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communication,” Proc. IEEE 58, 1523–1545 (1970).
[CrossRef]

1967 (1)

Abshire, J. B.

S. C. Cohen, J. J. Degnan, J. L. Bufton, J. B. Garvin, J. B. Abshire, “The geoscience laser altimetry/ranging system,” IEEE Trans. Geosci. Remote Sens. GE-25, 581–592 (1987).
[CrossRef]

J. B. Abshire, C. S. Gardner, “Atmospheric refractivity corrections in satellite laser ranging,” IEEE Trans. Geosci. Remote Sens. GE-23, 414–425 (1985).
[CrossRef]

Aksenov, V. P.

André, J. C.

J. C. André, G. DeMoor, P. Lacarrère, G. Therry, R. du Vachat, “Modeling the 24-hour evolution of the mean and turbulent structures of the planetary boundary layer,” J. Atmos. Sci. 35, 1861–1883 (1978).
[CrossRef]

Andrews, L. C.

Atlas, D.

D. Atlas, B. Walter, S. H. Chou, P. J. Sheu, “The structure of unstable marine boundary layer viewed by lidar and aircraft observations,” J. Atmos. Sci. 43, 1301–1318 (1986).
[CrossRef]

Banakh, V. A.

Bender, P. L.

P. L. Bender, “Atmospheric refraction and satellite laser ranging,” in Proceedings of the Symposium on Refraction of Transatmospheric Signals in Geodesy, J. C. de Munck, T. A. Th. Spoelstra, eds. (Netherlands Geodetic Commission, Delft, The Netherlands, 1992), pp. 117–125.

Bertoni, W.

W. Bertoni, G. Brighenti, G. Gambolati, G. Ricceri, F. Vuillermin, “Land subsidence due to gas production in the on- and off-shore natural gas fields of the Ravenna area, Italy,” in Proceedings of the Fifth International Symposium on Land Subsidence, F. B. J. Barends, F. J. J. Brouwer, F. H. Schröder, ed. (IAHS, Wallingford, UK, 1995), pp. 13–20. Numerous other papers in this proceedings also address this subject.

Bock, O.

O. Bock, Ch. Thom, M. Kasser, J. Pelon, “Multilateration with the wide angle laser ranging system: ranging performance and first ground-based validation experiment,” IEEE Trans. Geosci. Remote Sens. 37, 739–747 (1999).
[CrossRef]

O. Bock, M. Kasser, Ch. Thom, J. Pelon, “Study of a wide angle laser ranging system for relative positioning of ground-based benchmarks with millimeter accuracy,” J. Geod. 72, 442–459 (1998).
[CrossRef]

O. Bock, “Study of a wide angle airborne laser ranging system with ground based retroreflecting benchmarks for vertical ground deformations monitoring. Study of the adaptation to a spaceborne platform,” Ph.D. dissertation (University of Paris 7, Paris, 1996; in French).

O. Bock, M. Kasser, Ch. Thom, “A wide angle airborne or spaceborne laser ranging instrumentation for subsidence measurement,” in Proceedings of the Tenth International Workshop on Laser Ranging Instrumentation, Y. Fumin, C. Wanzhen, eds. (Chinese Academy of Sciences, Shanghai, 1996), pp. 32–42.

O. Bock, Ch. Thom, M. Kasser, D. Fourmaintraux, “Development of a new airborne laser subsidence measurement system, aiming at mm-accuracy,” in Proceedings of the Fifth International Symposium on Land Subsidence, F. B. J. Barends, F. J. J. Brouwer, F. H. Schröder, eds. (Balkema, Rotterdam, The Netherlands, 1995), pp. 113–122.

Bouteca, M. J.

M. J. Bouteca, D. Fourmaintraux, Y. Meimon, “In-situ measurements and numerical modeling of the reservoir compacting and surface subsidence,” in Proceedings of the European Oil and Gas Conference, G. Imarisio, M. Frias, J. M. Bemtgen, eds. (Graham & Totman, London, 1990), pp. 127–135.

Brighenti, G.

W. Bertoni, G. Brighenti, G. Gambolati, G. Ricceri, F. Vuillermin, “Land subsidence due to gas production in the on- and off-shore natural gas fields of the Ravenna area, Italy,” in Proceedings of the Fifth International Symposium on Land Subsidence, F. B. J. Barends, F. J. J. Brouwer, F. H. Schröder, ed. (IAHS, Wallingford, UK, 1995), pp. 13–20. Numerous other papers in this proceedings also address this subject.

Bufton, J. L.

S. C. Cohen, J. J. Degnan, J. L. Bufton, J. B. Garvin, J. B. Abshire, “The geoscience laser altimetry/ranging system,” IEEE Trans. Geosci. Remote Sens. GE-25, 581–592 (1987).
[CrossRef]

Chou, S. H.

D. Atlas, B. Walter, S. H. Chou, P. J. Sheu, “The structure of unstable marine boundary layer viewed by lidar and aircraft observations,” J. Atmos. Sci. 43, 1301–1318 (1986).
[CrossRef]

Churnside, J. H.

J. H. Churnside, “Aperture averaging of optical scintillations in the turbulent atmosphere,” Appl. Opt. 30, 1982–1994 (1991).
[CrossRef] [PubMed]

J. H. Churnside, S. F. Clifford, “Log-normal Rician probability-density function of optical scintillations in the turbulent atmosphere,” J. Opt. Soc. Am. A 1, 1923–1930 (1987).
[CrossRef]

Clifford, S. F.

J. H. Churnside, S. F. Clifford, “Log-normal Rician probability-density function of optical scintillations in the turbulent atmosphere,” J. Opt. Soc. Am. A 1, 1923–1930 (1987).
[CrossRef]

Cohen, S. C.

S. C. Cohen, J. J. Degnan, J. L. Bufton, J. B. Garvin, J. B. Abshire, “The geoscience laser altimetry/ranging system,” IEEE Trans. Geosci. Remote Sens. GE-25, 581–592 (1987).
[CrossRef]

Coté, O. R.

J. C. Kaimal, J. C. Wyngaard, D. A. Haugen, O. R. Coté, Y. Izumi, “Turbulence structure in the convective boundary layer,” J. Atmos. Sci. 33, 2152–2169 (1976).
[CrossRef]

Davis, J.

J. Davis, T. Herring, I. Shapiro, A. Rogers, G. Elgered, “Geodesy by radio-interferometry: effects of atmospheric modeling errors on estimates of baseline lengths,” Radio Sci. 20, 1593–1607 (1985).
[CrossRef]

Degnan, J. J.

S. C. Cohen, J. J. Degnan, J. L. Bufton, J. B. Garvin, J. B. Abshire, “The geoscience laser altimetry/ranging system,” IEEE Trans. Geosci. Remote Sens. GE-25, 581–592 (1987).
[CrossRef]

J. J. Degnan, “Satellite laser ranging: current status and future prospects,” IEEE Trans. Geosci. Remote Sens. GE-23, 398–413 (1985).
[CrossRef]

W. D. Kahn, J. J. Degnan, T. S. Englar, “The airborne laser ranging system, its capabilities and applications,” (NASA, Greenbelt, Md., 1982).

DeMoor, G.

J. C. André, G. DeMoor, P. Lacarrère, G. Therry, R. du Vachat, “Modeling the 24-hour evolution of the mean and turbulent structures of the planetary boundary layer,” J. Atmos. Sci. 35, 1861–1883 (1978).
[CrossRef]

Dingwen, L.

L. Dingwen, “Some general problems of the interpretation of geodetic deformation data,” in Proceedings of the IAG: Global and Regional Geodynamics, P. Vyskocil, C. Reigber, P. A. Cross, eds. (Springer-Verlag, Berlin, (1989), pp. 369–375.

du Vachat, R.

J. C. André, G. DeMoor, P. Lacarrère, G. Therry, R. du Vachat, “Modeling the 24-hour evolution of the mean and turbulent structures of the planetary boundary layer,” J. Atmos. Sci. 35, 1861–1883 (1978).
[CrossRef]

Elgered, G.

J. Davis, T. Herring, I. Shapiro, A. Rogers, G. Elgered, “Geodesy by radio-interferometry: effects of atmospheric modeling errors on estimates of baseline lengths,” Radio Sci. 20, 1593–1607 (1985).
[CrossRef]

Englar, T. S.

W. D. Kahn, F. O. Vonbun, D. E. Smith, T. S. Englar, B. P. Gibbs, “Performance analysis of the spaceborne laser ranging system,” Bull. Geod. 54, 165–180 (1980).
[CrossRef]

W. D. Kahn, J. J. Degnan, T. S. Englar, “The airborne laser ranging system, its capabilities and applications,” (NASA, Greenbelt, Md., 1982).

Fante, R. L.

R. L. Fante, “Electromagnetic beam propagation in turbulent media: an update,” Proc. IEEE 68, 1424–1443 (1980).
[CrossRef]

Fortes, B. V.

V. P. Lukin, B. V. Fortes, E. V. Nosov, “Effective outer scale of turbulence for imaging through the atmosphere,” in Optics in Atmospheric Propagation and Adaptive Systems II, A. Kohnle, A. D. Devir, eds., Proc. SPIE3219, 98–106 (1998).
[CrossRef]

Fourmaintraux, D.

O. Bock, Ch. Thom, M. Kasser, D. Fourmaintraux, “Development of a new airborne laser subsidence measurement system, aiming at mm-accuracy,” in Proceedings of the Fifth International Symposium on Land Subsidence, F. B. J. Barends, F. J. J. Brouwer, F. H. Schröder, eds. (Balkema, Rotterdam, The Netherlands, 1995), pp. 113–122.

M. J. Bouteca, D. Fourmaintraux, Y. Meimon, “In-situ measurements and numerical modeling of the reservoir compacting and surface subsidence,” in Proceedings of the European Oil and Gas Conference, G. Imarisio, M. Frias, J. M. Bemtgen, eds. (Graham & Totman, London, 1990), pp. 127–135.

Gambolati, G.

W. Bertoni, G. Brighenti, G. Gambolati, G. Ricceri, F. Vuillermin, “Land subsidence due to gas production in the on- and off-shore natural gas fields of the Ravenna area, Italy,” in Proceedings of the Fifth International Symposium on Land Subsidence, F. B. J. Barends, F. J. J. Brouwer, F. H. Schröder, ed. (IAHS, Wallingford, UK, 1995), pp. 13–20. Numerous other papers in this proceedings also address this subject.

Gardner, C. S.

J. B. Abshire, C. S. Gardner, “Atmospheric refractivity corrections in satellite laser ranging,” IEEE Trans. Geosci. Remote Sens. GE-23, 414–425 (1985).
[CrossRef]

C. S. Gardner, “Correction of laser tracking data for the effects of horizontal refractivity gradients,” Appl. Opt. 16, 2427–2432 (1977).
[CrossRef] [PubMed]

Garvin, J. B.

S. C. Cohen, J. J. Degnan, J. L. Bufton, J. B. Garvin, J. B. Abshire, “The geoscience laser altimetry/ranging system,” IEEE Trans. Geosci. Remote Sens. GE-25, 581–592 (1987).
[CrossRef]

Gibbs, B. P.

W. D. Kahn, F. O. Vonbun, D. E. Smith, T. S. Englar, B. P. Gibbs, “Performance analysis of the spaceborne laser ranging system,” Bull. Geod. 54, 165–180 (1980).
[CrossRef]

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer, New York, 1975), Chap. 2.

Haugen, D. A.

J. C. Kaimal, J. C. Wyngaard, D. A. Haugen, O. R. Coté, Y. Izumi, “Turbulence structure in the convective boundary layer,” J. Atmos. Sci. 33, 2152–2169 (1976).
[CrossRef]

Hauser, J. P.

J. P. Hauser, “Effects of deviations from hydrostatic equilibrium on atmospheric corrections to satellite and lunar laser range measurements,” J. Geophys. Res. 94, 10,182–10,186 (1989).
[CrossRef]

Herring, T.

J. Davis, T. Herring, I. Shapiro, A. Rogers, G. Elgered, “Geodesy by radio-interferometry: effects of atmospheric modeling errors on estimates of baseline lengths,” Radio Sci. 20, 1593–1607 (1985).
[CrossRef]

Holton, J. R.

J. R. Holton, An Introduction to Dynamic Meteorology, 3rd ed. (Academic, New York, 1992).

Hufnagel, R. E.

R. E. Hufnagel, “Propagation through atmospheric turbulence,” in The Infrared Handbook (U.S. GPO, Washington, D.C., 1978), p. 6.

Izumi, Y.

J. C. Kaimal, J. C. Wyngaard, D. A. Haugen, O. R. Coté, Y. Izumi, “Turbulence structure in the convective boundary layer,” J. Atmos. Sci. 33, 2152–2169 (1976).
[CrossRef]

Kahn, W. D.

W. D. Kahn, F. O. Vonbun, D. E. Smith, T. S. Englar, B. P. Gibbs, “Performance analysis of the spaceborne laser ranging system,” Bull. Geod. 54, 165–180 (1980).
[CrossRef]

W. D. Kahn, J. J. Degnan, T. S. Englar, “The airborne laser ranging system, its capabilities and applications,” (NASA, Greenbelt, Md., 1982).

Kaimal, J. C.

J. C. Kaimal, J. C. Wyngaard, D. A. Haugen, O. R. Coté, Y. Izumi, “Turbulence structure in the convective boundary layer,” J. Atmos. Sci. 33, 2152–2169 (1976).
[CrossRef]

Kasser, M.

O. Bock, Ch. Thom, M. Kasser, J. Pelon, “Multilateration with the wide angle laser ranging system: ranging performance and first ground-based validation experiment,” IEEE Trans. Geosci. Remote Sens. 37, 739–747 (1999).
[CrossRef]

O. Bock, M. Kasser, Ch. Thom, J. Pelon, “Study of a wide angle laser ranging system for relative positioning of ground-based benchmarks with millimeter accuracy,” J. Geod. 72, 442–459 (1998).
[CrossRef]

O. Bock, M. Kasser, Ch. Thom, “A wide angle airborne or spaceborne laser ranging instrumentation for subsidence measurement,” in Proceedings of the Tenth International Workshop on Laser Ranging Instrumentation, Y. Fumin, C. Wanzhen, eds. (Chinese Academy of Sciences, Shanghai, 1996), pp. 32–42.

M. Kasserthe Institut Géographique National, “Method for determining the spatial coordinates of points, applications of said method to high precision topography, system and optical device for carrying out said method,” U.S. patent774,038 (7October1991).

O. Bock, Ch. Thom, M. Kasser, D. Fourmaintraux, “Development of a new airborne laser subsidence measurement system, aiming at mm-accuracy,” in Proceedings of the Fifth International Symposium on Land Subsidence, F. B. J. Barends, F. J. J. Brouwer, F. H. Schröder, eds. (Balkema, Rotterdam, The Netherlands, 1995), pp. 113–122.

Kravtsov, Y. A.

Y. A. Kravtsov, A. I. Saichev, “Effects of double passage of waves in randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1982).
[CrossRef]

Lacarrère, P.

J. C. André, G. DeMoor, P. Lacarrère, G. Therry, R. du Vachat, “Modeling the 24-hour evolution of the mean and turbulent structures of the planetary boundary layer,” J. Atmos. Sci. 35, 1861–1883 (1978).
[CrossRef]

Lawrence, R. S.

R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communication,” Proc. IEEE 58, 1523–1545 (1970).
[CrossRef]

LeMone, M. A.

M. A. LeMone, “The structure of horizontal roll vortices in the planetary boundary layer,” J. Atmos. Sci. 30, 1077–1091 (1971).
[CrossRef]

Lenschow, D. H.

D. H. Lenschow, P. L. Stephens, “The role of thermals in the convective boundary layer,” Boundary-Layer Meteorol. 19, 509–532 (1980).
[CrossRef]

Lukin, V. P.

V. P. Lukin, B. V. Fortes, E. V. Nosov, “Effective outer scale of turbulence for imaging through the atmosphere,” in Optics in Atmospheric Propagation and Adaptive Systems II, A. Kohnle, A. D. Devir, eds., Proc. SPIE3219, 98–106 (1998).
[CrossRef]

Marini, J. W.

J. W. Marini, C. W. Murray, “Correction of laser range tracking data for atmospheric refraction at elevation above 10 degrees,” (NASA, Greenbelt, Md., 1973).

Meimon, Y.

M. J. Bouteca, D. Fourmaintraux, Y. Meimon, “In-situ measurements and numerical modeling of the reservoir compacting and surface subsidence,” in Proceedings of the European Oil and Gas Conference, G. Imarisio, M. Frias, J. M. Bemtgen, eds. (Graham & Totman, London, 1990), pp. 127–135.

Minott, P. O.

P. O. Minott, “Design of retrodirector arrays for laser ranging of satellites,” (NASA, Greenbelt, Md., 1974).

Mironov, V. L.

Murray, C. W.

J. W. Marini, C. W. Murray, “Correction of laser range tracking data for atmospheric refraction at elevation above 10 degrees,” (NASA, Greenbelt, Md., 1973).

Nosov, E. V.

V. P. Lukin, B. V. Fortes, E. V. Nosov, “Effective outer scale of turbulence for imaging through the atmosphere,” in Optics in Atmospheric Propagation and Adaptive Systems II, A. Kohnle, A. D. Devir, eds., Proc. SPIE3219, 98–106 (1998).
[CrossRef]

Owens, J. C.

Pelon, J.

O. Bock, Ch. Thom, M. Kasser, J. Pelon, “Multilateration with the wide angle laser ranging system: ranging performance and first ground-based validation experiment,” IEEE Trans. Geosci. Remote Sens. 37, 739–747 (1999).
[CrossRef]

O. Bock, M. Kasser, Ch. Thom, J. Pelon, “Study of a wide angle laser ranging system for relative positioning of ground-based benchmarks with millimeter accuracy,” J. Geod. 72, 442–459 (1998).
[CrossRef]

Philipps, R. L.

Phillips, R. L.

Ricceri, G.

W. Bertoni, G. Brighenti, G. Gambolati, G. Ricceri, F. Vuillermin, “Land subsidence due to gas production in the on- and off-shore natural gas fields of the Ravenna area, Italy,” in Proceedings of the Fifth International Symposium on Land Subsidence, F. B. J. Barends, F. J. J. Brouwer, F. H. Schröder, ed. (IAHS, Wallingford, UK, 1995), pp. 13–20. Numerous other papers in this proceedings also address this subject.

Rogers, A.

J. Davis, T. Herring, I. Shapiro, A. Rogers, G. Elgered, “Geodesy by radio-interferometry: effects of atmospheric modeling errors on estimates of baseline lengths,” Radio Sci. 20, 1593–1607 (1985).
[CrossRef]

Saichev, A. I.

Y. A. Kravtsov, A. I. Saichev, “Effects of double passage of waves in randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1982).
[CrossRef]

Shapiro, I.

J. Davis, T. Herring, I. Shapiro, A. Rogers, G. Elgered, “Geodesy by radio-interferometry: effects of atmospheric modeling errors on estimates of baseline lengths,” Radio Sci. 20, 1593–1607 (1985).
[CrossRef]

Sheu, P. J.

D. Atlas, B. Walter, S. H. Chou, P. J. Sheu, “The structure of unstable marine boundary layer viewed by lidar and aircraft observations,” J. Atmos. Sci. 43, 1301–1318 (1986).
[CrossRef]

Shivamoggi, B. K.

Smith, D. E.

W. D. Kahn, F. O. Vonbun, D. E. Smith, T. S. Englar, B. P. Gibbs, “Performance analysis of the spaceborne laser ranging system,” Bull. Geod. 54, 165–180 (1980).
[CrossRef]

Stephens, P. L.

D. H. Lenschow, P. L. Stephens, “The role of thermals in the convective boundary layer,” Boundary-Layer Meteorol. 19, 509–532 (1980).
[CrossRef]

Strohbehn, J. W.

R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communication,” Proc. IEEE 58, 1523–1545 (1970).
[CrossRef]

J. W. Strohbehn, “Modern theories in the propagation of optical waves in a turbulent medium,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer, New York, 1978), Chap. 3.
[CrossRef]

Stull, R. B.

R. B. Stull, An Introduction to Boundary Layer Meteorology (Kluwer Academic, Dordrecht, The Netherlands, 1988).
[CrossRef]

Tarantola, A.

A. Tarantola, Inverse Problem Theory: Methods for Data Fitting and Model Parameters Estimation (Elsevier, Amsterdam, 1987).

Therry, G.

J. C. André, G. DeMoor, P. Lacarrère, G. Therry, R. du Vachat, “Modeling the 24-hour evolution of the mean and turbulent structures of the planetary boundary layer,” J. Atmos. Sci. 35, 1861–1883 (1978).
[CrossRef]

Thom, Ch.

O. Bock, Ch. Thom, M. Kasser, J. Pelon, “Multilateration with the wide angle laser ranging system: ranging performance and first ground-based validation experiment,” IEEE Trans. Geosci. Remote Sens. 37, 739–747 (1999).
[CrossRef]

O. Bock, M. Kasser, Ch. Thom, J. Pelon, “Study of a wide angle laser ranging system for relative positioning of ground-based benchmarks with millimeter accuracy,” J. Geod. 72, 442–459 (1998).
[CrossRef]

O. Bock, M. Kasser, Ch. Thom, “A wide angle airborne or spaceborne laser ranging instrumentation for subsidence measurement,” in Proceedings of the Tenth International Workshop on Laser Ranging Instrumentation, Y. Fumin, C. Wanzhen, eds. (Chinese Academy of Sciences, Shanghai, 1996), pp. 32–42.

O. Bock, Ch. Thom, M. Kasser, D. Fourmaintraux, “Development of a new airborne laser subsidence measurement system, aiming at mm-accuracy,” in Proceedings of the Fifth International Symposium on Land Subsidence, F. B. J. Barends, F. J. J. Brouwer, F. H. Schröder, eds. (Balkema, Rotterdam, The Netherlands, 1995), pp. 113–122.

Vonbun, F. O.

W. D. Kahn, F. O. Vonbun, D. E. Smith, T. S. Englar, B. P. Gibbs, “Performance analysis of the spaceborne laser ranging system,” Bull. Geod. 54, 165–180 (1980).
[CrossRef]

Vuillermin, F.

W. Bertoni, G. Brighenti, G. Gambolati, G. Ricceri, F. Vuillermin, “Land subsidence due to gas production in the on- and off-shore natural gas fields of the Ravenna area, Italy,” in Proceedings of the Fifth International Symposium on Land Subsidence, F. B. J. Barends, F. J. J. Brouwer, F. H. Schröder, ed. (IAHS, Wallingford, UK, 1995), pp. 13–20. Numerous other papers in this proceedings also address this subject.

Walter, B.

D. Atlas, B. Walter, S. H. Chou, P. J. Sheu, “The structure of unstable marine boundary layer viewed by lidar and aircraft observations,” J. Atmos. Sci. 43, 1301–1318 (1986).
[CrossRef]

Wyngaard, J. C.

J. C. Kaimal, J. C. Wyngaard, D. A. Haugen, O. R. Coté, Y. Izumi, “Turbulence structure in the convective boundary layer,” J. Atmos. Sci. 33, 2152–2169 (1976).
[CrossRef]

Yu, P. T.

Appl. Opt. (5)

Boundary-Layer Meteorol. (1)

D. H. Lenschow, P. L. Stephens, “The role of thermals in the convective boundary layer,” Boundary-Layer Meteorol. 19, 509–532 (1980).
[CrossRef]

Bull. Geod. (1)

W. D. Kahn, F. O. Vonbun, D. E. Smith, T. S. Englar, B. P. Gibbs, “Performance analysis of the spaceborne laser ranging system,” Bull. Geod. 54, 165–180 (1980).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (4)

S. C. Cohen, J. J. Degnan, J. L. Bufton, J. B. Garvin, J. B. Abshire, “The geoscience laser altimetry/ranging system,” IEEE Trans. Geosci. Remote Sens. GE-25, 581–592 (1987).
[CrossRef]

O. Bock, Ch. Thom, M. Kasser, J. Pelon, “Multilateration with the wide angle laser ranging system: ranging performance and first ground-based validation experiment,” IEEE Trans. Geosci. Remote Sens. 37, 739–747 (1999).
[CrossRef]

J. B. Abshire, C. S. Gardner, “Atmospheric refractivity corrections in satellite laser ranging,” IEEE Trans. Geosci. Remote Sens. GE-23, 414–425 (1985).
[CrossRef]

J. J. Degnan, “Satellite laser ranging: current status and future prospects,” IEEE Trans. Geosci. Remote Sens. GE-23, 398–413 (1985).
[CrossRef]

J. Atmos. Sci. (4)

M. A. LeMone, “The structure of horizontal roll vortices in the planetary boundary layer,” J. Atmos. Sci. 30, 1077–1091 (1971).
[CrossRef]

D. Atlas, B. Walter, S. H. Chou, P. J. Sheu, “The structure of unstable marine boundary layer viewed by lidar and aircraft observations,” J. Atmos. Sci. 43, 1301–1318 (1986).
[CrossRef]

J. C. André, G. DeMoor, P. Lacarrère, G. Therry, R. du Vachat, “Modeling the 24-hour evolution of the mean and turbulent structures of the planetary boundary layer,” J. Atmos. Sci. 35, 1861–1883 (1978).
[CrossRef]

J. C. Kaimal, J. C. Wyngaard, D. A. Haugen, O. R. Coté, Y. Izumi, “Turbulence structure in the convective boundary layer,” J. Atmos. Sci. 33, 2152–2169 (1976).
[CrossRef]

J. Geod. (1)

O. Bock, M. Kasser, Ch. Thom, J. Pelon, “Study of a wide angle laser ranging system for relative positioning of ground-based benchmarks with millimeter accuracy,” J. Geod. 72, 442–459 (1998).
[CrossRef]

J. Geophys. Res. (1)

J. P. Hauser, “Effects of deviations from hydrostatic equilibrium on atmospheric corrections to satellite and lunar laser range measurements,” J. Geophys. Res. 94, 10,182–10,186 (1989).
[CrossRef]

J. Opt. Soc. Am. A (2)

V. P. Aksenov, V. A. Banakh, V. L. Mironov, “Fluctuations of retroreflected laser radiation in a turbulent atmosphere,” J. Opt. Soc. Am. A 1, 263–274 (1984).
[CrossRef]

J. H. Churnside, S. F. Clifford, “Log-normal Rician probability-density function of optical scintillations in the turbulent atmosphere,” J. Opt. Soc. Am. A 1, 1923–1930 (1987).
[CrossRef]

Proc. IEEE (2)

R. L. Fante, “Electromagnetic beam propagation in turbulent media: an update,” Proc. IEEE 68, 1424–1443 (1980).
[CrossRef]

R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communication,” Proc. IEEE 58, 1523–1545 (1970).
[CrossRef]

Radio Sci. (1)

J. Davis, T. Herring, I. Shapiro, A. Rogers, G. Elgered, “Geodesy by radio-interferometry: effects of atmospheric modeling errors on estimates of baseline lengths,” Radio Sci. 20, 1593–1607 (1985).
[CrossRef]

Sov. Phys. Usp. (1)

Y. A. Kravtsov, A. I. Saichev, “Effects of double passage of waves in randomly inhomogeneous media,” Sov. Phys. Usp. 25, 494–508 (1982).
[CrossRef]

Other (25)

Meteorological network of Meteo-France and radiosonde profiles taken at the station at Trappes, France, on 14 March 1995.

J. W. Marini, C. W. Murray, “Correction of laser range tracking data for atmospheric refraction at elevation above 10 degrees,” (NASA, Greenbelt, Md., 1973).

L. Dingwen, “Some general problems of the interpretation of geodetic deformation data,” in Proceedings of the IAG: Global and Regional Geodynamics, P. Vyskocil, C. Reigber, P. A. Cross, eds. (Springer-Verlag, Berlin, (1989), pp. 369–375.

W. Bertoni, G. Brighenti, G. Gambolati, G. Ricceri, F. Vuillermin, “Land subsidence due to gas production in the on- and off-shore natural gas fields of the Ravenna area, Italy,” in Proceedings of the Fifth International Symposium on Land Subsidence, F. B. J. Barends, F. J. J. Brouwer, F. H. Schröder, ed. (IAHS, Wallingford, UK, 1995), pp. 13–20. Numerous other papers in this proceedings also address this subject.

M. J. Bouteca, D. Fourmaintraux, Y. Meimon, “In-situ measurements and numerical modeling of the reservoir compacting and surface subsidence,” in Proceedings of the European Oil and Gas Conference, G. Imarisio, M. Frias, J. M. Bemtgen, eds. (Graham & Totman, London, 1990), pp. 127–135.

W. D. Kahn, J. J. Degnan, T. S. Englar, “The airborne laser ranging system, its capabilities and applications,” (NASA, Greenbelt, Md., 1982).

M. Kasserthe Institut Géographique National, “Method for determining the spatial coordinates of points, applications of said method to high precision topography, system and optical device for carrying out said method,” U.S. patent774,038 (7October1991).

O. Bock, Ch. Thom, M. Kasser, D. Fourmaintraux, “Development of a new airborne laser subsidence measurement system, aiming at mm-accuracy,” in Proceedings of the Fifth International Symposium on Land Subsidence, F. B. J. Barends, F. J. J. Brouwer, F. H. Schröder, eds. (Balkema, Rotterdam, The Netherlands, 1995), pp. 113–122.

O. Bock, “Study of a wide angle airborne laser ranging system with ground based retroreflecting benchmarks for vertical ground deformations monitoring. Study of the adaptation to a spaceborne platform,” Ph.D. dissertation (University of Paris 7, Paris, 1996; in French).

O. Bock, M. Kasser, Ch. Thom, “A wide angle airborne or spaceborne laser ranging instrumentation for subsidence measurement,” in Proceedings of the Tenth International Workshop on Laser Ranging Instrumentation, Y. Fumin, C. Wanzhen, eds. (Chinese Academy of Sciences, Shanghai, 1996), pp. 32–42.

P. L. Bender, “Atmospheric refraction and satellite laser ranging,” in Proceedings of the Symposium on Refraction of Transatmospheric Signals in Geodesy, J. C. de Munck, T. A. Th. Spoelstra, eds. (Netherlands Geodetic Commission, Delft, The Netherlands, 1992), pp. 117–125.

CCR coordinates between epochs can be compared because they are expressed in a local reference frame that is defined by a few (at least three) fixed CCR’s.

PD cannot be treated as a parameter to be adjusted for each CCR because it is highly correlated with the vertical coordinates of CCR’s.

The same analysis shows that including the PD in the forward model would reduce the precision to σUz = 1.2 cm in the reference experiment.

P. O. Minott, “Design of retrodirector arrays for laser ranging of satellites,” (NASA, Greenbelt, Md., 1974).

As long as NLS and NCCR are constant, NMeas/LS and NMeas/CCR are related by a constant factor.

J. W. Strohbehn, “Modern theories in the propagation of optical waves in a turbulent medium,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer, New York, 1978), Chap. 3.
[CrossRef]

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer, New York, 1975), Chap. 2.

R. B. Stull, An Introduction to Boundary Layer Meteorology (Kluwer Academic, Dordrecht, The Netherlands, 1988).
[CrossRef]

Of course, compensating for such systematic errors does not impair the detection of actual deformations with the same spatial signature.

J. R. Holton, An Introduction to Dynamic Meteorology, 3rd ed. (Academic, New York, 1992).

Note that a major limitation in the prediction of positioning precision is due to the thresholds used for a priori data sorting [SNR ≥ 3 and στij ≤ 0.67 ns (10 cm)]. Hence it is not always possible to compensate for a small SNR0 by a strong NLS, as relation (16) would suggest.

R. E. Hufnagel, “Propagation through atmospheric turbulence,” in The Infrared Handbook (U.S. GPO, Washington, D.C., 1978), p. 6.

V. P. Lukin, B. V. Fortes, E. V. Nosov, “Effective outer scale of turbulence for imaging through the atmosphere,” in Optics in Atmospheric Propagation and Adaptive Systems II, A. Kohnle, A. D. Devir, eds., Proc. SPIE3219, 98–106 (1998).
[CrossRef]

A. Tarantola, Inverse Problem Theory: Methods for Data Fitting and Model Parameters Estimation (Elsevier, Amsterdam, 1987).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

View of the WAALRS operated over a network of ground-based CCR’s. The measured signal, presented here for illustration, was obtained from a ground-based experiment. A set of eight simultaneous PR estimates is achieved from this signal.

Fig. 2
Fig. 2

Single-shot ranging accuracy predicted with an avalanche photodiode versus nadir angle for several experimental configurations: α = 15°, 20°, 25° and h = 5, 10 km. The saturation at small angles for h = 5 km is due to sampling uncertainty in the additive signal.

Fig. 3
Fig. 3

Results from numerical simulations showing (a), (c) a posteriori uncertainties and (b), (d) typical adjustment errors in X and Z coordinates of CCR’s on a horizontal grid corresponding to the location of CCR’s in the network. Results in Y (not shown) are roughly the same as in X. For the reference experiment SNR0 = 50, α = 20°, and h = 10 km.

Fig. 4
Fig. 4

Average precision in the Z coordinates of CCR’s as a function of α, plotted versus SNR at nadir, for two different instruments: ◆, SNR0 = 50; ■, SNR0 = 16, operated at two different altitudes: solid curves, h = 10 km; dashed curves, h = 7.5 km.

Fig. 5
Fig. 5

Adjustment errors in Z coordinates of CCR’s when an actual offset is simulated in the aircraft trajectory: (a) model without aircraft offsets and drifts, (b) model with aircraft offsets and drifts.

Fig. 6
Fig. 6

Adjustment errors in the Z coordinates of CCR’s when laser biases of 7.5 mm at FHWM are simulated: (a) net effect of laser biases on CCR coordinates, (b) compensation by the aircraft offset.

Tables (6)

Tables Icon

Table 1 Average Positioning Precision As a Function of α with SNR0 = 50 and h = 10 kma

Tables Icon

Table 2 Average Positioning Precision As a Function of α with SNR0 = 50 and h = 7.5 km

Tables Icon

Table 3 Average Positioning Precision As a function of CCR Density with SNR0 = 50, α = 20°, and h = 10 km

Tables Icon

Table 4 Average Positioning Precision As a Function of CCR Density with SNR0 = 16, α = 10°, and h = 7.5 kma

Tables Icon

Table 5 Average Positioning Precision As a Function of ANet with a CCR Density of 1 km-2, SNR0 = 50, α = 20°, and h = 10 km

Tables Icon

Table 6 Average Positioning Precision (σX and σZ), Observed rms Error (σ̂X and σ̂Z), and Precision in Aircraft Offsets (σW0,X and σW0,Z) As Functions of A Priori Uncertainties in Aircraft Positions [σV (prior)], in Aircraft Offsets and Drifts [σW0 (prior) and σWd (prior)], and in PRO’s [σb (prior)] with SNR0 = 50, α = 20°, and h = 10 km

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

c/2τij=dij+bj+sij+lij+rij+nij,
στij2KSNRij2+σs2,
ρijc/2τij-sij0-rij0,
ρij=PRijp+eij,
pˆ=p0+ATCee-1A+Cpp-1-1ATCee-1v,
dijp=μ=x,y,zUμ,i-Vμ,j-Wμp, tj21/2.
γθEr/Etγ1h, α×γ2θ, α,
γ1h, α=ηoTa2Ac2Arπh4α2λ2,γ2θ, α=cos5 θηcθ2 exp-2θ/α2,
a=γθPˆtZTηIR,
SNR0=SNRα=20°, h=10 km, θ=0.
SNR0=50,  h=10 km,  α=20°,NLS=22×103,  NCCR=100,ANet=10×10 km2.
ΔdWo,z1-½θ2.
Δd+b-rWo,z+b-rz-½θ2Wo,z+rz,
σlnI2=2.24k7/6sec11/6θ0H Cn2hh/H5/6H-h5/6dh,
DSρ=2.92k2ρ5/3sec θ0H Cn2h1-h/H5/3dh,
σZ0.76 mmANet100 km21/2SNR050-1/2×NLS22×103-1/2fα, h, NCCR,
rijz=106×khUz,iVz,j ρdh+106×kνUz,iVz,j ρνdhrijz,h+rijz,v,
rijz,hmm0.023Pi-PjPa,rijz,vmm2.05×10-3Piqi.
δrzkhzbzt ρδPP-δTTdz+kν-0.61kh×zbztρ1+0.61q δqdz,
δrzmm=0.017δPsPa-6.6δTsK-0.4δqsg/kg.
ρij=PRijp, q+eij,
v=AΔp+BΔq+e,
Δpˆ=N-1ATCee-1v-BΔq,N=ATCee-1A+Cpp-1,
ε=-N-1ATCee-1BΔq.
Cεε=N-1ATCee-1BCqqBTCee-1AN-1,
Cpˆpˆ=N-1+Cεε,

Metrics