SIMULATION OF STOCHASTICALLY ESTIMATING
J 2 AND J 3 VARIATIONS USING LAGEOS SLR DATA
Brian D. Hartman and George W. Rosborough
Department of Aerospace Engineering Sciences
University of Colorado, Boulder, CO 80309-0429 USA
ABSTRACT
Continual improvement in the satellite laser ranging (SLR) space geodetic technique has led
to the capability for estimating subtle temporal variations in a number of geodynamic
parameters. The approach generally taken is to estimate such geodynamic parameter
variations as piecewise constants (over some interval of time). Unfortunately, this strategy
naturally introduces an inherent limitation in the ability to accurately resolve such
variations.
The goal of this study is to analyze the feasibility of using a sequential process noise fIlter
for estimating geodynamic temporal variations using the Laser Geodynamics Satellite
(LAGEOS) SLR data. This evaluation is achieved by fIrst simulating a sequence of
LAGEOS laser ranging observations. These observations are generated using models with
known temporal variations in several geodynamic parameters (along track drag and the 1 2 ,
1 3 ,14 , and 15 geopotential coeffIcients). A standard (non-stochastic) fIlter and a stochastic
process noise fIlter are then utilized to estimate the model parameters from the simulated
observations.
The standard non-stochastic fIlter estimates these parameters as constants over
consecutive fIxed time intervals. The stochastic process noise fIlter estimates these
parameters as correlated process noise variables. As a result, the stochastic process noise
fIlter has the potential to estimate the temporal variations more accurately since the
constraint of estimating the parameters as piecewise constants is eliminated.
A comparison of the temporal resolution of solutions obtained from standard sequential
fIltering methods and process noise sequential fIltering methods shows that the accuracy is
signifIcantly improved using process noise. The results show that the positional accuracy
of the orbit is improved as well. The temporal resolution of the resulting solutions are
detailed, and conclusions drawn about the results.
INTRODUCTION
The current state of the art in fIltering Earth orbiting satellite data has reached the point
where temporal variations in the gravity fIeld (particularly 12 and 1 3 ) appear to be
observable. Determining these variations is of interest for determining global changes in
mass distribution as well as for insight into interior mass properties. The desire to then
obtain accurate estimates of these variations, as well as temporal variations in other
geophysical parameters, provides the motivation for this study. In particular, it is of
interest to determine if the relatively sparse, but accurate, laser range tracking of the
LAGEOS satellite can be used to resolve variations in the low degree coeffIcients of the
164
J 2 AND J 3 VARIATIONS USING LAGEOS SLR DATA
Brian D. Hartman and George W. Rosborough
Department of Aerospace Engineering Sciences
University of Colorado, Boulder, CO 80309-0429 USA
ABSTRACT
Continual improvement in the satellite laser ranging (SLR) space geodetic technique has led
to the capability for estimating subtle temporal variations in a number of geodynamic
parameters. The approach generally taken is to estimate such geodynamic parameter
variations as piecewise constants (over some interval of time). Unfortunately, this strategy
naturally introduces an inherent limitation in the ability to accurately resolve such
variations.
The goal of this study is to analyze the feasibility of using a sequential process noise fIlter
for estimating geodynamic temporal variations using the Laser Geodynamics Satellite
(LAGEOS) SLR data. This evaluation is achieved by fIrst simulating a sequence of
LAGEOS laser ranging observations. These observations are generated using models with
known temporal variations in several geodynamic parameters (along track drag and the 1 2 ,
1 3 ,14 , and 15 geopotential coeffIcients). A standard (non-stochastic) fIlter and a stochastic
process noise fIlter are then utilized to estimate the model parameters from the simulated
observations.
The standard non-stochastic fIlter estimates these parameters as constants over
consecutive fIxed time intervals. The stochastic process noise fIlter estimates these
parameters as correlated process noise variables. As a result, the stochastic process noise
fIlter has the potential to estimate the temporal variations more accurately since the
constraint of estimating the parameters as piecewise constants is eliminated.
A comparison of the temporal resolution of solutions obtained from standard sequential
fIltering methods and process noise sequential fIltering methods shows that the accuracy is
signifIcantly improved using process noise. The results show that the positional accuracy
of the orbit is improved as well. The temporal resolution of the resulting solutions are
detailed, and conclusions drawn about the results.
INTRODUCTION
The current state of the art in fIltering Earth orbiting satellite data has reached the point
where temporal variations in the gravity fIeld (particularly 12 and 1 3 ) appear to be
observable. Determining these variations is of interest for determining global changes in
mass distribution as well as for insight into interior mass properties. The desire to then
obtain accurate estimates of these variations, as well as temporal variations in other
geophysical parameters, provides the motivation for this study. In particular, it is of
interest to determine if the relatively sparse, but accurate, laser range tracking of the
LAGEOS satellite can be used to resolve variations in the low degree coeffIcients of the
164