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I.V. Bez zmenov, S.L. Pasynok
e - mail: bezmenov@vniiftri.ru, pasynok@vniiftri.ru
1. INTRODUCTION Some Analysis Centers in Russian Federation such as Information-Analytical centre of positioning, navigation, and timing (IAC PNT) TSNIIMASH, Mission Control Centre (MCC), High-precision ephemeris and time correction estimation system (HETCES/SVOEVP) as well as a number of Analysis Centers of the International GPS Service for Geodynamics (IGS) are producing daily precise orbits and time corrections of GLONASS satellites. These individual products are based on measurement data received from GLONASS globally distributed ground stations and available at several IGS Data Centers (e.g. CDDIS, IGN, etc.). For the reason that the application models as well as software systems and the data sets used by individual Centers are not identical the satellite orbit/clock solutions represented b by individual Centers can differ a little from each other. On the one hand, due to the absence of priori information regarding exact satellite orbit/clock solutions the preference can't be given to orbits of any of the Centers. On the other hand, the increasing role of GLONASS satellite orbit/clock products used in many applications of space geodesy necessitates having such combined products created by the authorized Russian organization which could serve as official data over the whole Russian Federation territory. A general scheme of combined orbits producing by the Coordinating Center on the base of information provided by the Analysis Centers is given in Fig. 1. 4. MATHEMATICAL TOOLS TECHNIQUE USED IN ORBIT/CLOCK COMBINATION Helmert transformation

H

P

:

x =
where

p = ( x0 , y 0 , z 0 , , , , )

(1+ ) RZ ( ) RY ( )R X ( ) (

x + x0

) = HP x

­ transformation parameters used in adjusting one orbital system 1to another 2:

FP =
FP =



j ,k

HPx
HPx

j 2, k

- x1j,
- x1j,
k

2 k
2

min
P
P

(without satellite's weights)


j ,k

j 2, k

W j min (with satellite's weights)

­ Euclidean norm in

R
j 2, k

Analysis Centers
Center #1 Center #2 Center #N

3 and x j x j ­ known vectors. 1, k 2 , k

The principle of clock combination is based on alignment of time scales for different time data sets in L1-norm principle combination on lignment of time scales for

.............

G , =


j ,k

t

+ + t - t

j 1, k

min ,

, - shift and drift parameters and parameters

Sp3-file

Sp3-file

Sp3-file

5. GLONASS ORBIT/CLOCK COMBINATION ACTIVITY IN MAIN METROLOGICAL CENTRE OF THE STATE SERVICE FOR TIME AND FREQUENCY (MMC SSTF), VNIIFTRI
By now an algorithm and software were developed in MMC SSTF for production of the combined orbits and clock corrections for GLONASS satellites. Main functions of the software are as follows:

Coordinating Center

Production of combined GLONASS orbits and clock corrections on base of data sets provided by individual Centers Outliers detection in satellite orbit/clock data sets as they determined by each Center and elimination if needed appropriate tli th b ti if epochs for each satellite and for each Center from further combination process The detection and elimination of "bad" satellites from combination process Applicatio orbital dynamics with calculatio of long ar Application orbital dynamics with calculation of long arc (1,3,5,7 days) orbits to obtain some statistical characteristics of orbits to obtai some statistical characteristics of combined orbits Producing report files of two types: 1) Sp3-files with combined orbits and clock corrections for GLONASS satellites (daily) 2) Sum-files of reports for the 8th day period with transformation parameters, statistical, accuracy and orbital characteristics files of reports the day period with parameters accuracy orbital for each satellites and each Center (weekly)

Sp3-file (daily) with combined GLONASS satellite orbit/clock solutions

Sum-file (weekly) with results of data processing

Fig. 1. A general scheme of combined orbits producing

An idea of the weighted average orbit/clock combination for GPS and GLONASS satellite constellations by mathematical processing of calculation results obtained by individual Analytic Centers goes back to IGS. Since 1993 and to the present IGS issues Sp3-files with official values of coordinates and clock corrections of GPS satellites. Since 2004 up to now the combined orbits and clock corrections of GLONASS satellites are formed under the auspices of IGS by the Data-processing center of National administration of oceanic and atmospheric researches and National geodetic service of the USA (NOAA/NGS). ti ti 2. INTERNATIONAL GLONASS PILOT PROJECT (IGLOS-PP) Originally the combined orbits of GLONASS were formed in the framework of the international IGLOS-PP. IGLOS-PP was a Pi ot il Project initiated in 2000 to track and analyze data from the Russian GLONASS satellite constellation. It also served as an important demonstration of integrating new constellations and signals into the IGS framework. The IGLOS-PP was terminated at the request of the Project Chair at the end of 2005, because GLONASS data and products had been successfully integrated into the standard operations of the IGS. Now 9 Centers are involved in the activities on production of the combined GLONASS orbits (see Fig. 2). The Coordinating Center of the IGLOS project on orbits/clock combination of GLONASS satellites : IGL IGLOS Combine Orbits, NOAA/NGS Operational Data Center, USA Combine Operational

The centers participating in the IGLOS project on orbits/clock combination of GLONASS satellites: BKG COD COD COF EMR ESA GFZ GRG IAC MCC Bundesamt fuer Kartographie und Geodaesie, Germany Center for Orbit Determination in Europe, AIUB, Switzerland Center for Orbit Determination in Europe, AIUB, Switzerland Natural Resources Canada European Space Agency, Germany GeoForschungsZentrum Potsdam, Germany Groupe de Recherche en Geodesie Spatiale /CNES, France Information-Analytical Centre, RF Mission Control Centre , RF Fig. 3. Main dialog window of the software for producing GLONASS satellite combined orbits and clock corrections Comparison results of GLONASS orbits defined by the Centers with the IGL combined orbits for the period from 2011.01.29 to 2011.02.05 are presented on Fig. 4.

The time diagram of participation of the Centers in the IGLOS project since 2004 up to date.

Fig. 4. RMS of GLONASS satellite positions for individual Centers in comparison with IGL combined orbits Fig. 2. The time diagram of participation of different Centers in GLONASS orbit/clock combination. Remark: VNF ­ final combined orbits of MMC SSTF, VNIIFTRI; VNF* ­ preliminary combined orbits of MMC SSTF, VNIIFTRI (before elimination of "bad" sitellites) SVO ­ abbreviature of High-precision ephemeris and time correction estimation system (HETCES/SVOEVP), RF High and estimation system (HETCES/SV RF

3. ORBIT/CLOCK COMBINATION STRATEGY The principles of orbits/clock combination were proposed by Beutler G., Springer T., Kouba J., Mireault Y., Lahaye F. It is based on iterative process of creation of satellite orbital systems. First orbital system. ·Each Center's ephemeris is rotated to establish a common orientation to account for possible systematic pole offsets between individual Analysis Center solution and to make the GLONASS combined orbits compatible with the IERS EOP. ·Calculation of averages (over all Centers) values of coordinates of all satellites. Second orbital system. ·Align of all Center's ephemeris to the 1-st orbital system. of all ephemeris to the system. ·Calculation of weights of both the Centers and the satellites. ·Calculation of the average values of coordinates of satellites taking into account weights of all Centers. Combined orbital system. orbital system ·Align of all Center's ephemeris to the 1-st orbital system taking into account satellite's weights. ·Calculation of the average values of satellite positions taking into account weights of all Centers.

6. ASYMPTOTIC THEOREM
N
N

Denote: ­ number of Centers, Cent
Epo

N Sat

­ number of satellites, ­ number of epochs in a day, position as it wa at ­ position of j-th satellite as it was estimated by i-th Center in k-th day at n-th epoch. ­ residual vector:

xij k , n , xijk ,n ,

j xijk ,n = xexect,k ,n - xijk ,n , ,

where

j xexect,k ,n

­ exact solution (unknown).

Theorem. Let the following conditions be satisfied 1. RMS calculated for the period in N days for each of the Centers, asymptotically (at N sufficiently large) are equal to each other. 2. In k-th day and n-th epoch the position vector for combined orbit of j-th satellite represents a weighted average N Cent j (with weights W ) of satellite's positions as determined by the Centers: x = x ij k , n W comb,k ,n , i ,k i ,k i =1


1

3. The weights W

i,k by monotonely decreasing dependence.

are related for each k with residual mean squared RMS

i,k

=

j xi,k ,n 3N Epo N Sat j =1 n=1

N

Sat

N

Epo

2

Then RMS for the combined orbit calculated for the period in N days is no greater then RMS for each of the Centers.