casestudyfortheigsultra-rapidorbitrequirements · 2017-05-16 · inzenith(impact1:0).forsatellitein...
TRANSCRIPT
Case study for the IGS ultra-rapid orbit requirementsJan Dousa ([email protected]) Geodetic Observatory Pecny of the Research Institute of Geodesy, Topography and Cartography
IGS Analysis Center Workshop 2008 — MiamiBeach, Florida, USA, June 2 – 6, 2008.
Motivation
The quality of the orbits predicted for real-time plays a crutial role in
the ’GPS meteorology’ – precise troposphere delay estimation for the
numerical weather prediction. Two approaches are commonly used: a)
precise point positioning (PPP) using undifference observables and b)
network solution using double-difference observables, both very different
in the requirements for the orbit accuracy.
Since 2000, the International GNSS Service (IGS) provides the ultra-rapid
orbits, which are updated every 6 hours today. In (near) real-time, the use
of 3-10h prediction is thus necessary before getting a new IGS product.
Is the quality of current orbit prediction sufficient for ’GPS-meteorology’
application ? We monitor the quality of the orbit prediction performance
and relevance of the accuracy code at � � � �� � �� � � � �� � � �� � � � � →
� �� �� �� �� � .
The effect of ephemeris errors on PPP ZTD
Linearized equation for a carrier phase observable Lik (scaled to a distance)
can be written as:
Lik = |~Ri
k0| + ∆Di
k + ∆C ik + ∆Si
k + λN ik + εi
k (1)
where |~Rik| = | ~X i − ~Xk| is the geometrical distance (in vacuum) between
receiver k and satellite i, ∆Dik is the sum of the distance dependent biases
(receiver and satellite position corrections, delays due to the ionosphere
and troposphere), ∆C ik is the sum of the clock related biases (satellite
and receiver clock biases, relativistic corrections), ∆S ik is the sum of the
satellite and station dependent biases (phase center offsets and variations,
multipath), λ is wavelength, N ik is the initial ambiguity of the full cycles
in the range and εik is the noise.
We focus on a simplified model considering only a satellite position bias
(∆ ~X i) and the tropospheric path delay (∆T ik) terms from a sum of distance
dependent biases.
∆Dik =
~Rik0
|~Rik0|
∆ ~X i −~Ri
k0
|~Rik0|
∆ ~Xk + ∆I ik + ∆T i
k (2)
Other biases are considered as accurately provided in advance, modeled
or neglected in (near) real-time analysis. Additionally, the station co-
ordinates are usually kept fixed on a long-term estimated position (we
assume ∆ ~Xk = 0), and the ionosphere bias (∆I ik) can be eliminated for its
significant first order effect.
The precise satellite orbits are best estimated from a global network, while
preferably kept fixed in a regional analysis, thus we consider ∆ ~X i as a priori
introduced error (δ ~X i). In the simplest way, the troposphere parameters
are estimated as the time-dependent zenith total delays (ZTD) above
each station of the network
∆T ik = mf(zi
k) · ZTDk ≈1
cos(zik)
· ZTDk (3)
where a zenith dependent mapping function mf(zik) we approximated by
cos(zik). Because of their different magnitude, we are interested in express-
ing the orbit errors in a satellite coordinate system (radial, along-track
and cross-track; RAC). Using a transformation
δ ~X i = Rz(λi) · Ry(ϕ
i) · δ ~X iRAC (4)
we distinct only two components: radial and in orbit tangential plane
(along-track + cross-track). Hence, we do not need to consider the
satellite track orientation and we will investigate only the marginal errors.
The equation for our simplified model is
Lik = |~Ri
k0| + ~ei
k · Rz(λi) · Ry(ϕ
i) δ ~X iRAC +
1
cos(zik)
· ZTDk + mf(zik) · ZTDk + λ · N i
k + εik (5)
where ~eik represents a unit vector pointing from station k to satellite i. The
error stemming from the orbit prediction (δ ~X iRAC) is usually significantly
larger than the carrier phase observable noise εik. The orbit errors changes
rather slowly (in hours) and its 3D representation is projected into the
pseudorange (1D). A significant portion of this error can be mapped into
the estimated ZTD if not previously absorbed by the ambiguities (or clock
corrections in PPP).
For a priori orbit errors compensated mostly by ZTDs, we can write
X i
iA
R
ZiA
iR
iψA
XA
RadialTangent
RA
~eik · Rz(λ
i) · Ry(ϕi) · δ ~X i
RAC +1
cos(zik)
· δZTDk ≈ 0 (6)
Neither the receiver position nor the satellite po-
sition nor the velicity have to be known if we
express the impact of the satellite radial and tan-
gential errors only as a function of zenith distance
to the satellite. Following the figure we express
~eBA · Rz(λ
i) · Ry(ϕi) · δ ~X i
RAC = cos(ΨiA) · δX i
Rad + sin(ΨiA) · δX i
Tan (7)
where
ΨiA = arcsin(sin(zi
A) ∗ RA/Ri) (8)
and we derive the plot for the impact of the radial and tangential orbit
errors to the range δLiA and their potential mapping into the ZTDA.
0.000.100.200.300.400.500.600.700.800.901.00
0 10 20 30 40 50 60 70 80 90
impa
ct (t
o ra
nge,
to Z
TD)
zenith distance
Zero-diff: Impact of radial/tangent orbit error
Jan
Dou
ša -
ZTD
erro
rs.g
pt 2
008-
04-2
5Radial error to δLAi
Tangent error to δLAi
Radial error to δZTDATangent error to δZTDA
Maximal impact of the radial error is
in zenith (impact 1.0). For satellite in
horizon, it only slightly decreases to
0.97 for error in δLiA and to 0.0 for δZTDA.
The impact of the tangential errors
is much smaller with maximum 0.13 at
zik = 45deg and minimum 0.0 when tan-
gential error is perpendicular to ∆ ~X ik.
For example, 10 cm tangential or 1 cm radial error in orbit can cause max.
1.3 cm or 1.0 cm in ZTD, respectively.
The effect in the difference observables
Commonly used double-difference phase carier observations are written
Lijkl = Li
kl − Ljkl = (Li
k − Lil) − (Lj
k − Ljl ). (9)
This approach cancels a significant portion of common biases for two re-
ceivers or two satellites. Some biases are canceled perfectly (e.g. satellite
clocks), others are more or less significantly reduced depending on base-
line length (e.g. satellite position errors, troposphere path delays).
We investigate here an orbit error impact from a single satellite and thus
we can use solely single-difference observations. According to (5) and
(9), they are written as
Likl = |~Ri
k| − |~Ril| + (~ei
k − ~eil) · δ
~X i + mf(zik) · ZTDk − mf(zi
l) · ZTDl (10)
Any orbit error is simply projected into the single-difference observation
by a difference in the unit vectors (eik − ei
l). If it is compensated by the
difference of the estimated ZTDs (also in pseudorange projection), then
(~eik − ~ei
l) · Rz(λi) · Ry(ϕ
i)δ ~X iRAC + mf(zi
k) · δZTDk − mf(zil) · δZTDl ≈ 0 (11)
We need to know the baseline length, the zenith distance of the satellite
at one of the stations and the direction of the satellite with respect to the
baseline. This is a bit more complicated case to generalize and we will
thus study its two marginal cases which both meet in the zenith above
the mid of a baseline:
•� �� �� � � �� � � � � - satellite and second station are in equal azimuths•� �� �� � � � � � � - zeniths to satellite are equal for both stations
X i
iA
R
ZiA
iR
XA
ZiB
iRB
iBψ
iψA
XB
RadialTangent
ABS
RA RB
Again, we do not need to know the satellite ve-
locity vector if we distiguish the ephemeris errors
only in radial and tangential direction, but base-
line lenght is still necessary. According to (7), (8)
and (10), we get a relation for the impact (12)
which is evaluated for two cases above and the
baseline SAB = 1000km) in the plots.
(~eiA − ~ei
A) · Rz(λi) · Ry(ϕ
i) · δ ~X iRAC = (12)
(cos(ΨiA) · δX i
Rad + sin(ΨiA) · δX i
Tan) − (cos(ΨiB) · δX i
Rad + sin(ΨiB) · δX i
Tan)
0.00
0.01
0.02
0 10 20 30 40 50 60 70 80 90
impa
ct (t
o ra
nge,
to Z
TD)
zenith distance
Single-diff: Impact of radial orbit error
Jan
Dou
ša -
ZTD
erro
rs.g
pt 2
008-
04-2
5
Baseline SAB = 1000 km
δLABi [case: equal azimuths]
δLABi [case: equal zeniths]
δZTDA = - δZTDB [case: equal azimuths]δZTDA = - δZTDB [case: equal zeniths]
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0 10 20 30 40 50 60 70 80 90
impa
ct (t
o ra
nge,
to Z
TD)
zenith distance
Single-diff: Impact of tangential orbit error
Jan
Dou
ša -
ZTD
erro
rs.g
pt 2
008-
04-2
5
Baseline SAB = 1000 km
δLABi [case: equal zeniths]
δLABi [case: equal azimuths]
δZTDA = - δZTDB [case: equal zeniths]δZTDA = - δZTDB [case: equal azimuths]
In case of equal zeniths (ziA = zi
B, RiA = Ri
B, ΨiA = Ψi
B), the impact is always
canceled out for the radial orbit error. Tangential orbit error has maximal
impact when the satellite is above the baseline and the error is parallel
with baseline (±0.027 for ZTDA, ZTDB). It is cancelled out when the error
is perpendicular to the baseline and reduced to the horizon. In case of
equal azimuths, the impact of the radial orbit error is maximal at ziA = 38 deg
(±0.0023 for ZTDA, ZTDB respectively). Tangential error impact is the largest
again above the baseline (the same as in equal zenith case) and slightly
faster reduces to the horizon. The impact is reduced with decreasing the
baseline length (approx. half for baseline 500km).
Simulation in network analysisBOGO
BRUS
BUCU
CHIZ
GLSVGOPE
HELG
HERS
LLIV
MATE
ONSA
OROS
POTS
SULP
VIS0
ZIMM
We used a network solution processed with the Bernese GPS soft-
ware to simulate the Radial/Along-track/Cross-track (RAC) orbit
errors. The ZTDs were estimated using ’star’ and ’circle’ networks
with the longest baseline of 1300km (’star’). The precise IGS final
orbits were used for data pre-processing, ambiguity fixing, for estimating the refer-
ence coordinates and ZTDs. The synthetic biases (1cm − 100cm) were introduced into
the IGS final orbits successively for G01, G03, G05 and G25 satellite in the RAC
components independently. Two ZTD solutions were provided and compared to the
reference ZTDs – ambiguity fixed (top Figs) and ambiguity free (bottom Figs). The
ZTD map differences are plotted for radial, along-track and cross-track components
in a 3-hr interval when satellite is above the region (Figs below).
-40
-30
-20
-10
0
10
20
30
40
00 02 04 06 08 10 12 14 16 18 20 22 00
ZTD
diff
eren
ce [m
m]
hours
ZTD difference due to satellite shift in Radial position
Satellite G03 (’Star’ network, 16 stations)- ambiguity fix
+100cm+25cm+10cm
+5cm+1cm -40
-30
-20
-10
0
10
20
30
40
00 02 04 06 08 10 12 14 16 18 20 22 00
ZTD
diff
eren
ce [m
m]
hours
ZTD difference due to satellite shift in Along-track position
Satellite G03 (’Star’ network, 16 stations)- ambiguity fix
+100cm+25cm+10cm+5cm+1cm -40
-30
-20
-10
0
10
20
30
40
00 02 04 06 08 10 12 14 16 18 20 22 00
ZTD
diff
eren
ce [m
m]
hours
ZTD difference due to satellite shift in Cross-track position
Satellite G03 (’Star’ network, 16 stations)- ambiguity fix
+100cm+25cm+10cm
+5cm+1cm
-40
-30
-20
-10
0
10
20
30
40
00 02 04 06 08 10 12 14 16 18 20 22 00
ZTD
diff
eren
ce [m
m]
hours
ZTD difference due to satellite shift in Radial position
Satellite G03 (’Star’ network, 16 stations)- ambiguity free
+100cm+25cm+10cm+5cm+1cm -40
-30
-20
-10
0
10
20
30
40
00 02 04 06 08 10 12 14 16 18 20 22 00
ZTD
diff
eren
ce [m
m]
hours
ZTD difference due to satellite shift in Along-track position
Satellite G03 (’Star’ network, 16 stations)- ambiguity free
+100cm+25cm+10cm+5cm+1cm -40
-30
-20
-10
0
10
20
30
40
00 02 04 06 08 10 12 14 16 18 20 22 00
ZTD
diff
eren
ce [m
m]
hours
ZTD difference due to satellite shift in Cross-track position
Satellite G03 (’Star’ network, 16 stations)- ambiguity free
+100cm+25cm+10cm
+5cm+1cm
Radial Along-track Cross-track
5
−45 −35 −25 −15 −5 5 15 25 35 45
ZTD−err [mm]
1m radial error star solutionDec 10, 2002 [18:30]
18
19
20 Satellite G03
20 25 30 35
40
−45 −35 −25 −15 −5 5 15 25 35 45
ZTD−err [mm]
1m along−track errorstar solutionDec 10, 2002 [18:30]
18
19
20 Satellite G03
5
10
−45 −35 −25 −15 −5 5 15 25 35 45
ZTD−err [mm]
1m cross−track errorstar solutionDec 10, 2002 [18:30]
18
19
20 Satellite G03
0
−45 −35 −25 −15 −5 5 15 25 35 45ZTD−err [mm]
1m radial error star solutionDec 10, 2002 [19:30]
18
19
20 Satellite G03
−15
−10
−50510
15
20
25
30
35
−45 −35 −25 −15 −5 5 15 25 35 45ZTD−err [mm]
1m along−track errorstar solutionDec 10, 2002 [19:30]
18
19
20 Satellite G03
−20
−15
−10
−5
0
5
10
15
−45 −35 −25 −15 −5 5 15 25 35 45ZTD−err [mm]
1m cross−track errorstar solutionDec 10, 2002 [19:30]
18
19
20 Satellite G03
0
−45 −35 −25 −15 −5 5 15 25 35 45
ZTD−err [mm]
1m radial error star solutionDec 10, 2002 [20:30]
18
19
20 Satellite G03
−30
−25
−20
−15
−10
−5
0
5
−45 −35 −25 −15 −5 5 15 25 35 45
ZTD−err [mm]
1m along−track errorstar solutionDec 10, 2002 [20:30]
18
19
20 Satellite G03
−15
−10−5
05
10
−45 −35 −25 −15 −5 5 15 25 35 45
ZTD−err [mm]
1m cross−track errorstar solutionDec 10, 2002 [20:30]
18
19
20 Satellite G03
Monitoring the quality of the IGS ultra-rapids
The overall accuracy of the precise IGS ultra-rapid orbit product is usually presented
by means of weighted rms. We present a detail evaluation with respect to each
individual satellite and with respect to every hour of 0-24h interval prediction. The
aim is to evaluate the individual satellite orbit quality and assigned accuracy codes
separately.
The IGS ultra-rapid orbits are epoch by epoch compared to the IGS rapid product
(3 rotations estimated for every epoch). From the differences, which are stored in
a database we generate the plots of
• the orbit accuracy dependency on the prediction interval (Fig 1),
• the evolution of the individual orbit accuracy in the time-series (Fig 2),
• to monitor the real orbit differences together with the triple of expected error
assigned to satellite (3 ∗ 2AccCode) (Fig 3).
The Figure 4 finally shows 1D RMS from the IGS ultra-rapid comparison to IGS
rapids provided by the IGS ACC, which display in yellow the eclipsing periods clearly
identifying the problems in specific satellite predictions.
��� "!$#%'&
0
10
20
30
40
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60
2005 2006 2007 2008 2009
RM
S [c
m]
IGU x IGR : orbit position differences
Satellite G03
Dou
sa -
plot
_Orb
Pre
dTS
.gpt
[2
008-
04-1
3]
prediction [h]22h19h16h13h10h 7h 4h 1h
fit
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2005 2006 2007 2008 2009
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3]
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fit
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2005 2006 2007 2008 2009
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Dou
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[2
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04-1
3]
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fit
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2005 2006 2007 2008 2009
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04-1
3]
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fit
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04-1
3]
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fit
��� (!$#%*)
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��� (!$#%,+
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Mar 07 Mar 11 Mar 15 Mar 19 Mar 23 Mar 27 Mar 31diffe
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3-s
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[cm
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Acc
.gpt
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Position error [cm]Compared accuracy [cm]
IGU accuracy [cm]temporary unhealthy
permanent unhealthy
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Mar 07 Mar 11 Mar 15 Mar 19 Mar 23 Mar 27 Mar 31diffe
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[cm
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Acc
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Position error [cm]Compared accuracy [cm]
IGU accuracy [cm]temporary unhealthy
permanent unhealthy
��� (!$#%*-
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012007
032007
052007
072007
092007
112007
012008
032008
1D o
rbit
RM
S [c
m]
(sat
ellit
e sh
ifted
+20
cm
)
Eclipting satellites and 1D orbit RMS (IGU/6h prediction w.r.t. IGR)
G01
G02
G03
G04
G05
G06
G07
G08
G09
G10
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Ecl
ips.
gpt
[200
8-04
-04]
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40
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120
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220
012007
032007
052007
072007
092007
112007
012008
032008
1D o
rbit
RM
S [c
m]
(sat
ellit
e sh
ifted
+20
cm
)
Eclipting satellites and 1D orbit RMS (IGU/6h prediction w.r.t. IGR)
G11
G12
G13
G14
G15
G16
G17
G18
G19
G20
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Ecl
ips.
gpt
[200
8-04
-04]
. �/ �� � � 0 1� � � �� � � � � �� � �2 � �� 3 � � � � � �� � �� 4 �� 0 � �� � 5 67 � 68 � 69 8 9 �
Summary Radial Tangent
PPP 1 cm 7 cm
Network 217 cm 19 cmThe table shows the example requirements for the
radial and tangential orbit position accuracy to ensure
that the ZTD contamination is lower than 1cm (when not absorbed by the ambiguities
or clock corrections). In a network, we consider 1000km baselines (the effects will reduce
to one-half in case of 500km baselines). Because the ambiguities are able to absorb
a significant portion of the ephemeris errors in both cases, they help to overcome
the current deficiencies in predicted orbit quality. To set up general requirements is
difficult - the satellite constellation, the network configuration and especially the pre-
processing (solving for ambiguities, clocks, coordinates) altogether differentiate the
situation in which the orbit errors can be absorbed into different model constituents.
The radial component errors are negligible in the network solution, but the most
inaccurate orbit along-track component can ocassional affect the ZTDs when the
satellite is flying in a baseline direction. Only some of the baselines are sensitive in
specific situations and, unfortunately, the averaging, with respect to other satellite
observables, is thus limited. The radial component is crucial in PPP ZTDs when
satellite is near the zenith, while the along-track component causes maximal error in
elevation of 45deg if the satellite is flying to or from the station. Fortunately, the error
averaging performs over all the satellites. Satellite clock corrections can additionally
absorb a significant part of the error in the regional solution. Usually, only a few
weakly estimated satellites occur in a single product, thus a robust satellite checking
strategy applied by the user will be satisfactory in many cases for the network solution.
A significantly different pattern of the orbit accuracy degradation, with respect to the
prediction time, is clearly identified for the GPS Block IIR and IIA satellites during an
eclipsing period. There are 14 (15) of IIA satellites from the whole GPS constellation
(including PRN32) and they still represent 44%. The accuracy codes are in most cases
relevant, but usually underestimated for the Block-IIA satellites during the eclipsing
periods and at the beginning of the maintenance periods.