Sub-daily Earth rotation parameters from
GNSS and combined GNSS-SLR solutions
D. Thaller
(1),
M. Meindl (2), G. Beutler (1), R. Dach
A. Jäggi (1), K. Sośnica (1)
(1) Astronomical Institute, University of Bern, Switzerland
(2) ETH Zürich, Switzerland
IAU Commission 19, Scientific Meeting
Beijing, 30. August 2012
Astronomical Institute University of Bern
(1),
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
Overview

Orbit characteristics and artefacts in polar motion time
series:
 GPS / GLONASS orbits
 LAGEOS orbit

Handling of the correlation between PM and orbits:
 Blocking a retrograde-diurnal signal in PM
 Introduce orbits from 24-h ERP solution

Results of GNSS, SLR and combined solutions
Astronomical Institute University of Bern
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
GNSS-specific artefacts
Many spectral lines are different for GPS and GLONASS
⇒ Most likely system-specific artefacts
GLONASS
GPS
Meindl et al.: Processing Batch length in GNSS data analysis: Impact on daily and
subdaily Earth rotation parameters. Presented at EGU 2012
Astronomical Institute University of Bern
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
Theory


Any 3-dimensional rotation is described by 3 angles
Earth orientation is conventionally described by 5 angles
(polar motion x/y, UT1-UTC, nutation /)
 Angles are not independent
 Correlation between nutation and a retrograde-diurnal
signal in polar motion (PM)
Remark: Nutation is fixed in the GNSS/SLR solutions
presented hereafter
 Correlation avoided
Astronomical Institute University of Bern
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
Theory: Orbits and sub-daily ERPs

Transformation inertial – terrestrial with ERPs:
R3(-) · R1(y ) · R2(x )

Transformation inertial – terrestrial with orbits:
r(t) = a · R3() · R1(-i ) · R3(-u ) · e1
r’(t) = a · R3() · R1(-i –i ) · R3(-u-u ) · e1
= R3() · R2() · R1() · r (t)
Astronomical Institute University of Bern
No BLOCKRET; Orbit estimated
350
300
Amplitude [μas]
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
Retrograde-diurnal PM and orbits
250
200
150
100
50
0
−40

−30
−20
−10
0
Period [h]
10
20
30
Correlation with orbits produces big peaks in spectra
around retrograde-diurnal period
Astronomical Institute University of Bern
40
BLOCKRET; Orbit estimated
25
20
Amplitude [μas]
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
Retrograde-diurnal PM: BLOCKRET constraint
15
10
5
0
−40

−30
−20
−10
0
Period [h]
10
20
30
Blocking / constraining the retrograde-diurnal signal
removes the correlation with the orbits
Astronomical Institute University of Bern
40
No BLOCKRET; Orbit fixed to solution with 24−h ERP
25
20
Amplitude [μas]
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
Retrograde-diurnal PM: Orbit parameter fixed
15
10
5
0
−40
−30
−20
−10
0
Period [h]
10
20
30
Fix all orbital elements+empirical+stochastic parameters:
No
retrograde-diurnal polar motion
Other
frequencies blocked as well ?
Astronomical Institute University of Bern
√
??
40
No BLOCKRET; Orbit (i, omega, OMEGA) fixed to solution with 24−h ERP
30
25
Amplitude [μas]
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
Retrograde-diurnal PM: Correlated params fix
20
15
10
5
0
−40
−30
−20
−10
0
Period [h]
10
20
30
Fix only i, ,  (from theoretical considerations):
Small
retrograde-diurnal polar motion remains
Other
frequencies seem to be okay
??
√
Astronomical Institute University of Bern
40
No BLOCKRET; Orbit (i, omega, OMEGA, D0) fixed to solution with 24−h ERP
25
20
Amplitude [μas]
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
Retrograde-diurnal PM: Correlated params fix
15
10
5
0
−40
−30
−20
−10
0
Period [h]
10
20
Due to orbit perturbation: D0 (direct solar radiation
pressure) is additionally involved in correlation
⇒ Fix only i, ,  + D0:
No
retrograde-diurnal polar motion
Other
frequencies seem to be okay
√
√
Astronomical Institute University of Bern
30
40
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
GNSS-only solutions: Summary





Scatter in time-series of sub-daily polar motion (PM) is at
the level of 150 – 170 as
Constraint for blocking retrograde-diurnal PM works fine,
but neighbour frequencies are affected as well
Not only the orbital elements (i, , ) are correlated with
a retrograde-diurnal signal in PM
Empirical orbit parameters are involved as well
Introducing (and fixing) the orbit from a solution with
24-h ERPs gives promising results (but might remove
«real» signals)
Astronomical Institute University of Bern
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
SLR solutions
LAGEOS + ETALON satellites are taken into account.
Observation statistics for 2001 - 2011:

About 3000 observations per week

1-h resolution for ERPs = 168 intervals per week

Empty 1-h intervals: 622 out of 96’264 (=0.6%)
Astronomical Institute University of Bern
SLR 7−d: No BLOCKRET; Orbit estimated
500
400
Amplitude Δ PM [μas]
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
SLR solutions
300
200
100
0
−36

−30
−24
−18
−12
−6
0
6
Period [hours]
12
18
24
30
Full correlation between orbits and polar motion evokes
signals up to 500 as in retrograde spectra
Astronomical Institute University of Bern
36
SLR 7−d solutions: Orbits estimated
500
No constraint (prograde)
No constraint (retrograde)
BLOCKRET (prograde)
BLOCKRET (retrograde)
400
Amplitude Δ PM [μas]
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
SLR solutions
300
200
100
0
−36

−30
−24
−18
−12
−6
0
6
Period [hours]
12
18
24
BLOCKRET removes retrograde-diurnal signal
But:

Several (artefactual) signals remain
Astronomical Institute University of Bern
30
36
SLR 7−d solutions: Orbits estimated
500
k=1,
i=5
k=1,
i=3
400
Amplitude Δ PM [μas]
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
SLR solutions
No constraint (retrograde)
BLOCKRET (retrograde)
k=1,
i=5
300
200
k=1,
i=3
k=3,
i=3
100
0
−36
−33
−30
−27
−24
−21
−18
−15
Period [hours]
−12
−9
−6
−3
Combinations of the LAGEOS revolution period (nL = 2/ 3.75h)
and the revolution period of the Earth (nE = 2/ 23.93 h):
2
k · nL  i · nE
Astronomical Institute University of Bern
0
SLR 7−d: No BLOCKRET; Orbit fixed to solution with 24−h ERPs
200
Amplitude Δ PM [μas]
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
SLR solutions
150
100
50
0
−36 −33 −30 −27 −24 −21 −18 −15 −12 −9

−6
−3
0
3
6
Period [hours]
9
12
15
18
21
24
Fixing orbital elements (osculating elements only)
reduces the noise level
But:

«Signals» around 24 h remain -> artefacts
Astronomical Institute University of Bern
27
30
33
36
SLR 7−d: Orbit (osculating + empirical) fixed to solution with 24−h ERPs
50
40
Amplitude Δ PM [μas]
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
SLR solutions
30
20
10
0
−36

−30
−24
−18
−12
−6
0
Period [hours]
6
12
18
24
Fixing orbits (osculating elements and empirical
parameters) further reduces the noise level

No artefactual signals left

But: «Real» signals are hardly detectable
Astronomical Institute University of Bern
30
36
Single−technique solutions: Orbits fixed to solution with 24−h ERPs
50
SLR (prograde)
SLR (retrograde)
GNSS (prograde)
GNSS (retrograde)
40
Amplitude Δ PM [μas]
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
SLR vs. GNSS solutions
30
20
10
0
−36
−30
−24
−18
−12
−6
0
Period [hours]
6
12
18
24
30
The noise level in the SLR series is 6-10 times larger than in
the GNSS series.
Astronomical Institute University of Bern
36
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
Combined GNSS-SLR solutions

Microwave data: GPS / GLONASS

SLR data:
GPS / GLONASS

SLR data:
LAGEOS / ETALON
Common orbit
parameters
Complication for estimation of sub-daily ERPs due to
different arc-lengths:

GNSS satellites:
3 days (overlapping)

LAGEOS, ETALON:
7 days (no overlaps)
Astronomical Institute University of Bern
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
Combined GNSS-SLR solutions
Weekly combined solutions:
 7-day arc LAGEOS/ETALON
 3-day arc GNSS satellites
<- BLOCKRET for 7 days
=> «LAGEOS» artefacts and small correlations w.r.t. 3-day
GNSS arcs remain
Astronomical Institute University of Bern
2.5
GNSS−SLR 7−d combined: LAG/ETA orbits fixed to 24−h ERP solution; GNSS orbits estimated
2
1.5
Δ x−pole [mas]
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
Combined GNSS-SLR solutions
1
0.5
0
−0.5
−1
−1.5
−2
−2.5
2001
2002
2003
2004
2005
Weekly combined solutions:
7-day arc LAGEOS/ETALON
3-day arc GNSS satellites
2006
2007
2008
2009
2010
2011
<- fixed to 24-h ERP solution
=> No remaining correlations ?
Astronomical Institute University of Bern
GNSS−SLR 7−d combined
30
BLOCKRET
LAG/ETA orbit+S0+oprS+oprW fixed
25
Amplitude Δ PM [μas]
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
Combined GNSS-SLR solutions
20
15
10
5
0
−25


−24
Period [hours]
Fixing the orbits of the LAGEOS/ETALON satellites
(osculating elements + empirical orbit parameters) fully
removes the correlation
GNSS orbits do not need to be fixed additionally
Astronomical Institute University of Bern
−23
GNSS−SLR 7−d combined
80
BLOCKRET
LAG/ETA orbit+S0+oprS+oprW fixed
70
60
Amplitude Δ PM [μas]
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
Combined GNSS-SLR solutions
50
40
30
20
10
0
−36−35−34−33−32−31−30−29−28−27−26−25−24−23−22−21−20−19−18−17−16−15−14−13−12−11−10 −9 −8 −7 −6 −5 −4 −3 −2 −1
Period [hours]
Many artefactual periods are still present
-> less pronounced if orbits are fixed
Astronomical Institute University of Bern
0
D. Thaller et al.: Sub-daily ERPs from GNSS and combined GNSS-SLR solutions
IAU Commission 19, 30. August 2012
Conclusions


Orbits with different characteristics evoke different
artefacts in subdaily polar motion (PM) series
GNSS (revolution period ≈ 0.5 * diurnal):
 Blocking the retrograde-diurnal PM is enough
 Alternatively: Fixing the orbit of a 24-h ERP solution
(orbital elements AND empirical parameters!)

SLR-LAGEOS (revolution period ≪ diurnal):
 Blocking the retrograde-diurnal PM is not sufficient
 Fixing the orbit of a 24-h ERP solution is the preferred
method

Combined GNSS-SLR solutions:
 All orbital characteristics show up in PM series
 Fixing one type of orbit is enough
Astronomical Institute University of Bern