Improving low-Earth orbit prediction precision with TLEs
May,2013,Beijing,China
National Space Science Center,CAS
Liu Wei ,Wang Ronglan ,Yan Ruidong
Contents
Introduction
Improvement principles and process
The determination of Fitting period
Improvement accuracy assessment
summary
Introduction • NORAD maintains general perturbation element sets called TLE on all
resident space objects. TLE are “mean” value, must be used with SGP4/
SDP4 model. However, TLE +SGP4/SDP4 prediction accuracy is limited.
• As for how to improve the forecast accuracy using TLE, domestic and
foreign scholars have done some research.
• For example:
Levit C, Marshall W. Improved orbit predictions using two-line elements. Advances in
Space Research 2011;47:1107. Mainly for laser satellite whose altitude greater
than 800km
Yang Yang et al. Xi’an Satellite Control Center near-earth debris prediction method
based TLEs
…………………………
Introduction
• Our approach is similar , future goals are the promotion and application
of non-cooperative objects.
Improvement principles and
process
• TLE+SGP4/SDP4 error source analysis The composition, properties and Improvement theory were analyzed.
• Improvement process Pseudo-observation data generation, the establishment of differential
correction equation
TLE+SGP4/SDP4 error source analysis
• TLE initial error
1. The measurement errors
2. Model errors in OD
Performed as Bias
Cannot be removed without more accurate
measurement data
Bias
True orbit
Fitting orbit
Variance
Periodic terms
Time
TLE initial errors
The prediction errors will accumulate and diverge quickly in
numerical orbit propagation caused by initial errors with the
converted osculate elements.
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
U error
N error
W error
Forcast time(days)
Err
ors
(k
m)
TLE+SGP4/SDP4 error source analysis
• SGP4/SDP4 model error
1. Only second-order flat rate perturbation,
ignoring the higher-order periodic terms
perturbation.
2. Exponential atmosphere model
Performed as Variances in the short-term
orbit prediction .
The variances is a random error
essentially and can be removed by the
statistical method of least squares or
Kalman filtering in the orbit fitting process.
Bias
True orbit
Fitting orbit
Variance Periodic terms
Time
• The exponential atmosphere density mode errors in SGP4/
SDP4 models , will cause greater forecast error during solar
maximum period.
• Fitted TLE+high-precision numerical propagator can weak
atmosphere model errors in orbit propagation.
Improvement process
• Pseudo-observation data generation
• Differential correction equations
Pseudo-observation data generation
Pseudo-observation data can gotten
by
1.forward and backward forecast for
historical data
2.station coordinates
3.target visibility criterion
station1 station2
Station n
Time axis 0t
1t nt 2t
Pseudo-observation data generation
Flow chart of data generation:
TLE data
Station coordinate User configSGP4/SDP4 model
Visible criterion
TEMEà BF
convert
yes
no Predicton
forward
Pre-observation
Differential correction equations
The measurement equation has Taylor expansion at the reference value ,omitting higher order terms then the differential correction equations are got:
where : is residual is correction value
We get the final status by continuous iteration.
y Bx V
y 1
0 0 0 0
k kx X X X X
0X
Measurement equation:
*
0 0
kX X x
( , )op H t X V
Differential correction equations
• (1) 70×70 degree GGM02C
• (2) 30×30 degree TOPEX 4.0 ocean tide model
• (3) NRLMSIS-00 atmosphere model
• (4)N body perturbation
• (5)Solar radiation, solid earth tide , pole tide.
Main models considered:
The determination of Fitting period
called fitting period, Its value will affect the orbit
improvement.
Time axis
0t
1t nt 2t
fitting period
0 - nt t
The determination of Fitting period
The orbit fitting residual consists of two parts:
The initial error of orbital elements
accumulate and diverge in numerical orbit propagation.
The main model error
type and magnitude depend on orbital altitude.
The fitting period is not the longer the better, when the fitting period exceeds
a certain threshold, the corrected value of the orbital elements will absorb la-
rge amounts of model error.
Therefore, the determination of the fitting period
is the result of a compromise of initial elements
error and model error .
The determination of Fitting period
In order to quantitatively get the relationship of the fitting period and
orbital altitude ,Two satellites were tested:
Table 1. The main parameters of selected satellite
NORAD Altitude eccentricity A/M(m2/kg)
37820 350km <0.0020 0.00414
16908 1490km <0.0012 0.0053
The determination of Fitting period
Take reference orbit as "truth " to get the forecast error
1.GPS precise ephemeris as reference orbit (object 37820)
0 1 2 3 4 5 6
0.0
1.5
3.0
4.5
6.0
7.5
9.0
10.5
12.0
Forecast time(Days)
fitting period 1day fitting period 2day fitting period 3day
Positio
n e
rrors
(km
)
The determination of Fitting period
① The improved results were similar when the fitting period selected 1 or 2
days .
② However ,the result was worse when the fitting period changed to 3days.
Verified the conclusion :
1. When the fitting period exceeds a certain threshold, the correction value
of orbital elements will absorb a large amount of model error.
2. 1 or 2 day fitting period is appropriate for near-Earth orbit .
The determination of Fitting period
The result of POD with Laser ranging data whose residual RMS is
about centimeter order as reference orbit . (object 16908)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
fitting period 3 days
fitting period 5 days
fitting period 10days
Forcast time(days)
Positio
n e
rror
(km
)
The determination of Fitting period
① The forecast accuracy was best among three situations,
when fitting period selected 10 days.
② With the increased fitting period, forecast accuracy
becomes better in the fitting process.
③ For object 16908 , 10 day fitting period is appropriate.
Improvement accuracy assessment
I. In order to further assess the forecast accuracy of
improved TLE, two satellites above were tested.
II. Five different independent time span
a. UNW errors were given
b. By comparing the fitted TLEs + numerical method
results with precise ephemeris
c. By comparing the TLE+SGP results with precise
ephemeris
Improvement accuracy assessment-37820
0 1 2 3 4 5 6
Forcast time(days)
0
20
40
60
80
100
120
140
TLE+SGP4/SDP4
0
5
10
15
20
25
30
fitting TLE+numerical propagatorU e
rrors
(k
m)
Improvement accuracy assessment-37820
N e
rrors
(km
)
0 1 2 3 4 5 6
Forcast time(days)
0.00.20.40.60.81.01.21.41.61.82.02.22.42.62.8
TLE+SGP4/SDP4
0.0
0.1
0.2
0.3
0.4
0.5fitting TLE+numerical propagator
Improvement accuracy assessment-37820
W e
rrors
(k
m)
0 1 2 3 4 5 6
fitting TLE+numerical propagator
Forcast time(days)
-0.4-0.20.00.20.40.60.81.01.21.41.61.82.02.22.42.6
TLE+SGP4/SDP4
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Improvement accuracy assessment-37820
Positio
n e
rrors
(k
m)
0 1 2 3 4 5 6
-20
0
20
40
60
80
100
120
140
160
TLE+SGP4/SDP4
-4-202468
101214161820222426283032
fitting TLE+numerical propagator
Forcast time(days)
Improvement accuracy assessment
From 4 figures above, we can see :
Forecast results of fitting TLE significantly better than
that of TLE + SGP4/SDP4.
U errors (km) Max Min Average
TLE+SGP 130 15 65
Fitted TLEs 28 5 13
Improvement accuracy assessment
A. Due SGP4/SDP4 models only take into account the second-
order flat rate perturbation, ignoring the higher order periodical
impact. The forecast error is very unstable, so the error has
very large fluctuations. This can be seen in the box plot.
B. The determination of the error ellipsoid in the collision
probability calculation becomes difficult, reducing early
warning confidence.
C. The forecast accuracy has improved greatly and fluctuations
was smaller in the fitting case.
D. It is very helpful to improve the early warning confidence.
SUMMARY
① TLE+SGP4/SDP4 prediction errors, the composition,
properties and improvement theory.
② Pseudo-observation data generation and the fitting
process.
③ the reference fitting period value of two satellites.
④ Improvement results assessment.
⑤ The fitting TLE prediction accuracy has been improved
greatly. Prediction errors was stable. improving
conjunction analysis.
The main problem :
1.The determination of non-cooperative object area-to-
mass ratio(A/M).
A/M initial value : B * of TLEs
evolution of the semi-major axis.
Then as a parameter to be corrected in the fitting
process. However, two errors absorb each other. introduce
new errors, also limits the length of the forecast period.
2. Removing the abnormal TLE data is also to be
considered.
In the Future
– Select more space objects for test
selecting more objects to accumulate experience for its application.
– The determination of area-to-mass ratio
Search effective method for determining the area-to-mass ratio of non-cooperative target.
Thanks for your attention!