process noise filtering techniques to improve the temporal resolutions and accuracies of
LAGEOS along track drag variations and second and third degree zonal harmonic
coefficient variations. By using the process noise filter, the residual RMS errors for the
total 3-d orbit position are reduced to approximately 15% of the residual RMS errors
obtained using the standard filter. Thus, both the orbit positional accuracy and the temporal
resolution of geodynamic parameters can be improved simultaneously.
These
improvements in the estimates of the C t , J 2 , and J 3 parameters and the orbit itself translate
into a 50% reduction in the RMS error in the range residuals.
The advantages obtained with the stochastic approach cannot be emulated by simply
modifying the boxcar approach to obtain more frequent estimates; or by interpolating the
boxcar results in order to obtain estimates that are continuous in time. Stochastic filtering
provides optimally smoothed estimates based on the complete set of tracking data, and not
discrete subsets of that data.
Finally, the possibilities of using stochastic filtering to improve orbit accuracies and
temporal resolutions of geodynamic parameters should be kept in perspective. Although it
is very encouraging to verify via simulated LAGEOS SLR data that variations in parameters
such as along track drag, J 2 , and J 3 can be recovered and estimated more accurately with
process noise parameters while improving the orbit position accuracy, overly optimistic
extensions of these findings without similar verification would be inappropriate.
ACKNOWLEDGMENTS
This research was supported by NASA Grant No. NAGW-1944. The authors thank J. C.
Ries of the University of Texas at Austin for providing the data shown in Figure 2b.
REFERENCES
Bierman, G. J., Factorization Methods for Discrete Sequential Estimation, Academic
Press, New York, 1977.
Chao, B. F., and A. Y. Au, ''Temporal Variation of the Earth's Low-Degree Zonal
Gravitational Field Caused by Atmospheric Mass Redistribution: 1980-1988," Journal
of Geophysical Research, Vol. 96, No. B4, pp. 6569-6575, 1991.
Hartman, B. D., "A Simulation to Study the Feasibility of Improving the Temporal
Resolution of LAGEOS Geodynamic Solutions by Using a Sequential Process Noise
Filter," Ph. D. Dissertation, University of Colorado at Boulder, Department of
Aerospace Engineering Sciences, 1995.
Nerem, R. S., B. F. Chao, A. Y. Au, J. C. Chan, S. M. Klosko, N. K. Pavlis, and R. G.
Williamson, "Temporal Variations of the Earth's Gravitational Field from Satellite
Laser Ranging to LAGEOS," Geophysical Research Letters, Vol. 20, No.7, pp. 595598, 1993.
Nerem, R. S., F. J. Lerch, J. A. Marshall, E. C. Pavlis, B. H. Putney, B. D. Tapley, R.
J. Eanes, J. C. Ries, B. E. Schutz, C. K. Shum, M. M. Watkins, S. M. Klosko, J. C.
Chan, S. B. Luthcke, G. B. Patel, N. K. Pavlis, R. G. Williamson, R. H. Rapp, R.
Biancale, and F. Nouel, "Gravity Model Development for TOPEXIPOSEIDON: Joint
Gravity Models 1 and 2," Journal of Geophysical Research, Vol. 99, No. C12, pp.
24421-24447, 1994.
Ries, J. c., R. J. Eanes, C. K. Shum, and M. M. Watkins, "Progress in the Determination
of the Gravitational Coefficient of the Earth," Geophysical Research Letters, Vol. 19,
No.6, pp. 529-531, 1992.
Tapley, B. D., B. E. Schutz, R. J. Eanes, J. C. Ries, and M. M. Watkins, "Lageos Laser
Ranging Contributions to Geodynamics, Geodesy, and Orbital Dynamics,"
Contributions of Space Geodesy to Geodynamics: Earth Dynamics, Geodynamics
Series, Vol. 24, pp. 147-173, 1993.
173
LAGEOS along track drag variations and second and third degree zonal harmonic
coefficient variations. By using the process noise filter, the residual RMS errors for the
total 3-d orbit position are reduced to approximately 15% of the residual RMS errors
obtained using the standard filter. Thus, both the orbit positional accuracy and the temporal
resolution of geodynamic parameters can be improved simultaneously.
These
improvements in the estimates of the C t , J 2 , and J 3 parameters and the orbit itself translate
into a 50% reduction in the RMS error in the range residuals.
The advantages obtained with the stochastic approach cannot be emulated by simply
modifying the boxcar approach to obtain more frequent estimates; or by interpolating the
boxcar results in order to obtain estimates that are continuous in time. Stochastic filtering
provides optimally smoothed estimates based on the complete set of tracking data, and not
discrete subsets of that data.
Finally, the possibilities of using stochastic filtering to improve orbit accuracies and
temporal resolutions of geodynamic parameters should be kept in perspective. Although it
is very encouraging to verify via simulated LAGEOS SLR data that variations in parameters
such as along track drag, J 2 , and J 3 can be recovered and estimated more accurately with
process noise parameters while improving the orbit position accuracy, overly optimistic
extensions of these findings without similar verification would be inappropriate.
ACKNOWLEDGMENTS
This research was supported by NASA Grant No. NAGW-1944. The authors thank J. C.
Ries of the University of Texas at Austin for providing the data shown in Figure 2b.
REFERENCES
Bierman, G. J., Factorization Methods for Discrete Sequential Estimation, Academic
Press, New York, 1977.
Chao, B. F., and A. Y. Au, ''Temporal Variation of the Earth's Low-Degree Zonal
Gravitational Field Caused by Atmospheric Mass Redistribution: 1980-1988," Journal
of Geophysical Research, Vol. 96, No. B4, pp. 6569-6575, 1991.
Hartman, B. D., "A Simulation to Study the Feasibility of Improving the Temporal
Resolution of LAGEOS Geodynamic Solutions by Using a Sequential Process Noise
Filter," Ph. D. Dissertation, University of Colorado at Boulder, Department of
Aerospace Engineering Sciences, 1995.
Nerem, R. S., B. F. Chao, A. Y. Au, J. C. Chan, S. M. Klosko, N. K. Pavlis, and R. G.
Williamson, "Temporal Variations of the Earth's Gravitational Field from Satellite
Laser Ranging to LAGEOS," Geophysical Research Letters, Vol. 20, No.7, pp. 595598, 1993.
Nerem, R. S., F. J. Lerch, J. A. Marshall, E. C. Pavlis, B. H. Putney, B. D. Tapley, R.
J. Eanes, J. C. Ries, B. E. Schutz, C. K. Shum, M. M. Watkins, S. M. Klosko, J. C.
Chan, S. B. Luthcke, G. B. Patel, N. K. Pavlis, R. G. Williamson, R. H. Rapp, R.
Biancale, and F. Nouel, "Gravity Model Development for TOPEXIPOSEIDON: Joint
Gravity Models 1 and 2," Journal of Geophysical Research, Vol. 99, No. C12, pp.
24421-24447, 1994.
Ries, J. c., R. J. Eanes, C. K. Shum, and M. M. Watkins, "Progress in the Determination
of the Gravitational Coefficient of the Earth," Geophysical Research Letters, Vol. 19,
No.6, pp. 529-531, 1992.
Tapley, B. D., B. E. Schutz, R. J. Eanes, J. C. Ries, and M. M. Watkins, "Lageos Laser
Ranging Contributions to Geodynamics, Geodesy, and Orbital Dynamics,"
Contributions of Space Geodesy to Geodynamics: Earth Dynamics, Geodynamics
Series, Vol. 24, pp. 147-173, 1993.
173