Earth's gravity field with the use of a stochastic filter. Conventional filtering methods
typically estimate these types of variations as piecewise constants over a given data arc
[Nerem et ai., 1993]. This results in a discontinuous solution for the variations with
limited temporal resolution. Stochastic filtering methods can estimate these variations as
continuous process noise parameters which are correlated in time. This type of estimation
procedure has the potential for resolving these variations much more accurately.
Many types of orbit determination filters exist for a variety of applications. For this
study, two specific orbit determination filters are of interest: a standard (non-stochastic)
Square Root Information Filter (SRIF) and a process noise (stochastic) SRIF. These two
filters are compared and their ability to resolve specific temporal variations in the model
parameters is assessed. The main objective of this study is to assess the ability of a
sequential process noise SRIF to resolve specific variations embedded in simulated
LAGEOS SLR data. The accuracies of the estimated parameter variations and the satellite
state are analyzed by comparing them to the known truth used in the simulated orbit.
Specifically, variations in an along track drag parameter (C t ) and the second and third
degree zonal geopotential coefficients (J 2 and J 3 ) are introduced into a simulated one year
orbit and temporally resolved by a stochastic filter. Variations in the fourth and fifth degree
zonal geopotential coefficients (J4 and J 5 ) are also introduced into the simulated orbit, but
are not estimated. Comparisons are made to a solution generated with a standard nonstochastic filter.
DATA SIMULATION
To fully understand how well model parameter variations can be resolved using stochastic
estimation, the variations themselves must be known. In this study, the true temporal
variations of the particular parameters being estimated must be specified before conclusions
can be drawn as to the effectiveness of particular filtering methods in estimating these
variations. Thus, simulated LAGEOS SLR observations are generated with specific
temporal parameter variations (referred to hereafter as model deviation signals) in the model
used for generating the observations. This permits the direct comparison of the estimates to
the known truth.
LAGEOS SLR data is generated for a period of one year for this study. White noise with
1 cm RMS is added to all range measurements once generated. This random error
corresponds to the current ideal levels of accuracy and precision associated with SLR
observations. Actual data may suffer from biases which are being ignored in this
simulation.
Typically, dozens of laser ranging tracking stations are able to track LAGEOS using the
SLR technique. In generating the simulated observations for this study, only eight tracking
stations are assumed. This conservative tracking network was chosen to represent a worst
case tracking scenario. Also, using a subset of the actual tracking network will reveal any
problems that might result from the lack of a dense data distribution.
Figure 1 shows the tracking station network. Six of the eight tracking stations are located
in the northern hemisphere, reflecting the fact that the majority of SLR tracking stations are
in the northern hemisphere. The tracking stations are assumed to operate from 6:00 PM to
6:00 AM local time. Four of the northern hemisphere stations track five days per week
(Monday through Friday), as is the case with many NASA stations, while the remaining
stations track every day.
Observations are generated every three minutes (representing compressed normal point
observations) for a specific tracking station only if the tracking station is operating during
the particular pass, and the satellite is above 20° elevation. All observations are then
decimated by randomly eliminating 75% of the passes in an attempt to model data outages
165
typically estimate these types of variations as piecewise constants over a given data arc
[Nerem et ai., 1993]. This results in a discontinuous solution for the variations with
limited temporal resolution. Stochastic filtering methods can estimate these variations as
continuous process noise parameters which are correlated in time. This type of estimation
procedure has the potential for resolving these variations much more accurately.
Many types of orbit determination filters exist for a variety of applications. For this
study, two specific orbit determination filters are of interest: a standard (non-stochastic)
Square Root Information Filter (SRIF) and a process noise (stochastic) SRIF. These two
filters are compared and their ability to resolve specific temporal variations in the model
parameters is assessed. The main objective of this study is to assess the ability of a
sequential process noise SRIF to resolve specific variations embedded in simulated
LAGEOS SLR data. The accuracies of the estimated parameter variations and the satellite
state are analyzed by comparing them to the known truth used in the simulated orbit.
Specifically, variations in an along track drag parameter (C t ) and the second and third
degree zonal geopotential coefficients (J 2 and J 3 ) are introduced into a simulated one year
orbit and temporally resolved by a stochastic filter. Variations in the fourth and fifth degree
zonal geopotential coefficients (J4 and J 5 ) are also introduced into the simulated orbit, but
are not estimated. Comparisons are made to a solution generated with a standard nonstochastic filter.
DATA SIMULATION
To fully understand how well model parameter variations can be resolved using stochastic
estimation, the variations themselves must be known. In this study, the true temporal
variations of the particular parameters being estimated must be specified before conclusions
can be drawn as to the effectiveness of particular filtering methods in estimating these
variations. Thus, simulated LAGEOS SLR observations are generated with specific
temporal parameter variations (referred to hereafter as model deviation signals) in the model
used for generating the observations. This permits the direct comparison of the estimates to
the known truth.
LAGEOS SLR data is generated for a period of one year for this study. White noise with
1 cm RMS is added to all range measurements once generated. This random error
corresponds to the current ideal levels of accuracy and precision associated with SLR
observations. Actual data may suffer from biases which are being ignored in this
simulation.
Typically, dozens of laser ranging tracking stations are able to track LAGEOS using the
SLR technique. In generating the simulated observations for this study, only eight tracking
stations are assumed. This conservative tracking network was chosen to represent a worst
case tracking scenario. Also, using a subset of the actual tracking network will reveal any
problems that might result from the lack of a dense data distribution.
Figure 1 shows the tracking station network. Six of the eight tracking stations are located
in the northern hemisphere, reflecting the fact that the majority of SLR tracking stations are
in the northern hemisphere. The tracking stations are assumed to operate from 6:00 PM to
6:00 AM local time. Four of the northern hemisphere stations track five days per week
(Monday through Friday), as is the case with many NASA stations, while the remaining
stations track every day.
Observations are generated every three minutes (representing compressed normal point
observations) for a specific tracking station only if the tracking station is operating during
the particular pass, and the satellite is above 20° elevation. All observations are then
decimated by randomly eliminating 75% of the passes in an attempt to model data outages
165