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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:


called fitting period, Its value will affect the orbit

improvement.

Time axis

0t

1t nt 2t

fitting period

0 - nt t


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 .


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


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

)


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 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

)


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.


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)


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


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


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)


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


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!

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Improving low-Earth orbit prediction precision with TLEsaero.tamu.edu/sites/default/files/faculty/alfriend/CTI2P/CT2013 S3... · Improving low-Earth orbit prediction precision with