Abstract

A laser ranging error budget is detailed, and a specific error budget is derived for the TOPEX/POSEIDON satellite. A ranging uncertainty of 0.76 cm is predicted for TOPEX/POSEIDON at 20° elevation using the presently designed laser retroreflector array and only modest improvements in present system operations. Atmospheric refraction and satellite attitude effects cause the predicted range error to vary with satellite elevation angle from 0.71 cm at zenith to 0.76 cm at 20° elevation. This a priori error budget compares well with the ~1.2-cm rms a posteriori polynomial orbital fit using existing data taken for an extant satellite of similar size and orbit.

© 1990 Optical Society of America

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References

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  1. J. W. Marini, C. W. Murray, “Correction of Laser Range Tracking Data for Atmospheric Refraction at Elevations Above 10 Degrees,” NASA Report X-591-73-351, Goddard Space Flight Center, Greenbelt, MD (Nov.1973).
  2. J. B. Abshire, C. S. Gardner, “Atmospheric Refractivity Corrections in Satellite Laser Ranging,” IEEE Trans. Geosci. Remote Sensing GE-23, 414–425 (1985).
    [CrossRef]
  3. D. McCollums, “MOBLAS 7 System Characterization for the Time Period 07/15/87 to 01/31/88,” Bendix Field Engineering Report (29Feb.1988).
  4. C. S. Gardner, U. Illinois, Urbana–Champaign; private communication (July1989).
  5. J. A. Schwartz, “Pulse Spreading and Range Correction Analysis for Satellite Laser Ranging,” Appl. Opt. 29, 3597–3602 (1990).
    [CrossRef] [PubMed]
  6. V. Nelson, Bendix Field Engineering Corp.; private communication (14Mar.1989).
  7. S. Dolinsky, “Range Correction Sensitivity to Attitude Control,” JPL Internal Memorandum 3391-88-37 (24Mar.1988).
  8. J. A. Schwartz, “Studies of Laser Ranging to the TOPEX Satellite,” Proc. Soc. Photo-Opt. Instrum. Eng. 885, 172–179 (1988).
  9. D. Sonnabend, Jet Propulsion Laboratory; personal communication.

1990 (1)

1988 (2)

S. Dolinsky, “Range Correction Sensitivity to Attitude Control,” JPL Internal Memorandum 3391-88-37 (24Mar.1988).

J. A. Schwartz, “Studies of Laser Ranging to the TOPEX Satellite,” Proc. Soc. Photo-Opt. Instrum. Eng. 885, 172–179 (1988).

1985 (1)

J. B. Abshire, C. S. Gardner, “Atmospheric Refractivity Corrections in Satellite Laser Ranging,” IEEE Trans. Geosci. Remote Sensing GE-23, 414–425 (1985).
[CrossRef]

Abshire, J. B.

J. B. Abshire, C. S. Gardner, “Atmospheric Refractivity Corrections in Satellite Laser Ranging,” IEEE Trans. Geosci. Remote Sensing GE-23, 414–425 (1985).
[CrossRef]

Dolinsky, S.

S. Dolinsky, “Range Correction Sensitivity to Attitude Control,” JPL Internal Memorandum 3391-88-37 (24Mar.1988).

Gardner, C. S.

J. B. Abshire, C. S. Gardner, “Atmospheric Refractivity Corrections in Satellite Laser Ranging,” IEEE Trans. Geosci. Remote Sensing GE-23, 414–425 (1985).
[CrossRef]

C. S. Gardner, U. Illinois, Urbana–Champaign; private communication (July1989).

Marini, J. W.

J. W. Marini, C. W. Murray, “Correction of Laser Range Tracking Data for Atmospheric Refraction at Elevations Above 10 Degrees,” NASA Report X-591-73-351, Goddard Space Flight Center, Greenbelt, MD (Nov.1973).

McCollums, D.

D. McCollums, “MOBLAS 7 System Characterization for the Time Period 07/15/87 to 01/31/88,” Bendix Field Engineering Report (29Feb.1988).

Murray, C. W.

J. W. Marini, C. W. Murray, “Correction of Laser Range Tracking Data for Atmospheric Refraction at Elevations Above 10 Degrees,” NASA Report X-591-73-351, Goddard Space Flight Center, Greenbelt, MD (Nov.1973).

Nelson, V.

V. Nelson, Bendix Field Engineering Corp.; private communication (14Mar.1989).

Schwartz, J. A.

J. A. Schwartz, “Pulse Spreading and Range Correction Analysis for Satellite Laser Ranging,” Appl. Opt. 29, 3597–3602 (1990).
[CrossRef] [PubMed]

J. A. Schwartz, “Studies of Laser Ranging to the TOPEX Satellite,” Proc. Soc. Photo-Opt. Instrum. Eng. 885, 172–179 (1988).

Sonnabend, D.

D. Sonnabend, Jet Propulsion Laboratory; personal communication.

Appl. Opt. (1)

IEEE Trans. Geosci. Remote Sensing (1)

J. B. Abshire, C. S. Gardner, “Atmospheric Refractivity Corrections in Satellite Laser Ranging,” IEEE Trans. Geosci. Remote Sensing GE-23, 414–425 (1985).
[CrossRef]

JPL Internal Memorandum 3391-88-37 (1)

S. Dolinsky, “Range Correction Sensitivity to Attitude Control,” JPL Internal Memorandum 3391-88-37 (24Mar.1988).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

J. A. Schwartz, “Studies of Laser Ranging to the TOPEX Satellite,” Proc. Soc. Photo-Opt. Instrum. Eng. 885, 172–179 (1988).

Other (5)

D. Sonnabend, Jet Propulsion Laboratory; personal communication.

J. W. Marini, C. W. Murray, “Correction of Laser Range Tracking Data for Atmospheric Refraction at Elevations Above 10 Degrees,” NASA Report X-591-73-351, Goddard Space Flight Center, Greenbelt, MD (Nov.1973).

D. McCollums, “MOBLAS 7 System Characterization for the Time Period 07/15/87 to 01/31/88,” Bendix Field Engineering Report (29Feb.1988).

C. S. Gardner, U. Illinois, Urbana–Champaign; private communication (July1989).

V. Nelson, Bendix Field Engineering Corp.; private communication (14Mar.1989).

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Figures (5)

Fig. 1
Fig. 1

TOPEX nadir panel with LRA and altimeter antenna.

Fig. 2
Fig. 2

Projected TOPEX error budget for an overhead pass.

Fig. 3
Fig. 3

Satellite laser ranging geometry.

Fig. 4
Fig. 4

Spacecraft center of mass uncertainty constituents.

Fig. 5
Fig. 5

LRA range correction variation for TOPEX/POSEIDON.

Tables (2)

Tables Icon

Table I Summary of TOPEX/POSEIDON Laser Ranging Errors

Tables Icon

Table II Standard Deviation of Radiosonde Data as Corrected by the Marini and Murray Model1,2

Equations (23)

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Δ R f ( λ ) F ( φ , H ) × A + B sin E + B ( A + B ) sin E + 0.01 ,
A = 0.002357 P o + 0.000141 e o ,
B = ( 1.084 × 10 - 8 P o T o K + ( 4.734 × 10 - 8 ) P 0 2 T 0 2 ( 3 - 1 K ) ,
K = 1.163 - 0.00968 cos 2 φ - 0.00104 T o + 0.0001435 P o ,
f ( λ ) + 0.9650 + 0.0164 λ 2 + 0.000228 λ 4 ,
F ( φ , H ) = 1 - 0.0026 cos 2 φ - 0.00031 H .
σ Δ R = [ ( δ Δ R δ P σ P ) 2 + ( δ Δ R δ T σ T ) 2 + ( δ Δ R δ R H σ R H ) 2 ] 1 / 2 .
δ Δ R δ P f ( λ ) F ( φ , H ) 0.2357 sin E ( cm / mbar ) ,
δ Δ R δ T f ( λ ) 1.084 × 10 - 6 P o K sin 3 E ( cm / K ) ,
δ Δ R δ R H f ( λ ) F ( φ , H ) 8.615 × 10 - 4 sin E × exp [ 7.5 ( T s - 273.15 ) 273.3 + ( T s - 273.15 ) ] ( cm / percent ) .
line 6 ( a ) = ( δ Δ R δ P σ P ) , line 6 ( b ) = ( δ Δ R δ T σ T ) , line 6 ( c ) = ( δ Δ R δ R H σ R H ) .
CM = ( DU ) 2 + ( CU ) 2 + ( AU ) 2 + ( MU ) 2 .
CS = ( AU ) 2 + ( MU ) 2 ,
AU = Δ R α ( θ z ) · 5.7296 × 10 - 5 ( deg / μ rad ) × ( Δ A x ) 2 + ( Δ A y ) 2 + ( Δ A z ) 2 ,
MU = Δ R α ( θ z ) · 5.7296 × 10 - 5 ( deg / μ rad ) × ( Δ M x ) 2 + ( Δ M y ) 2 + ( Δ M z ) 2 ,
R = ( R e 2 + h 1 ) 2 - ( R e sin θ z ) 2 - R e cos ( θ z ) .
R = R e 2 + ( R e + h 1 ) 2 - 2 R e ( R e + h 1 ) 2 cos ϕ .
d R d t = ½ [ 2 R e ( R e + h 1 ) sin ϕ ] R e 2 + ( R e + h 1 ) 2 - 2 R e ( R e + h 1 ) cos ϕ d ϕ d t .
T = 2 π R e g R e ( R e + h 1 ) 3 / 2 ,
d ϕ d t = R e g R e ( R e + h 1 ) - 3 / 2 .
d R d t = R e 2 g R e sin ϕ R e 2 + ( R e + h 1 ) + ( R e + h 1 ) 3 - 2 R e ( R e + h 1 ) 2 cos ϕ .
ϕ = θ z - sin - 1 [ sin θ z ( 1 + h 1 R e ) ] .
R e = 6.367 × 10 6 m ;             h 1 = 1.334 × 10 6 m ;             ϕ = 19.02 ° ; d R d t = 4.136 × 10 13 7.412 × 10 9 = 5580 ms - 1 at θ z = 70 ° .

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