GNSS PERMANENT NETWORKS MONITORING: PROBLEMS AND SOLUTIONS

Stefano Caldera

Politecnico di Milano, Polo Regionale di Como, via Valleggio 11, 22100 Como - stefano@geomatica.como.polimi.it

KEY WORDS: GNSS permanent networks, reference frames, GNSS network adjustment, national densification

ABSTRACT:This paper summarizes the three years research carried out within my Ph.D: the full manuscript comprises more than 200 pages, orga-nized in an introduction, 5 main chapters and a conclusion. Chapter 1 describes and recalls succinctly the definition and realizationsof reference systems, Chapter 2 details GNSS permanent networks establishment and the processing of their data using Bernese GNSSSoftware, with numerical applications to the new official Italian zero order network (RDN: Rete Dinamica Nazionale). Chapter 3presents the design and development of a Software package called “RegNet” that allows to automatically process GNSS data, performthe network adjustment and critically analyse the results via quality indicators, with the aim to improving the results at the final stage ofthe network adjustment. Chapter 4 is dedicated to the application of RegNet to two permanent networks in Italy, operating at two differ-ent scales (Regional and National), for the purpose of positioning services: in this Chapter the transformation from ITRF2005/IGS05to the old and new Italian reference frames is deeply analysed. Chapter 5 addresses a critical issue related to the processing of large net-works (exceeding e.g. 200 stations) that cannot easily be processed in one run using GPS Software packages and therefore necessitatesplitting the network on sub-networks.

1 INTRODUCTIONPermanent networks for positioning services (afterwards calledsimply positioning services) facilitate the use of GNSS methodsin all the applications related to survey, territory monitoring andpositioning in general (Euler et al., 2001, Wubbena, 2001, Chenet al., 2003). In general, positioning services carry out at least thefollowing tasks (Biagi and Sanso, 2007):

• estimate, monitor and distribute the permanent station coor-dinates in the global reference frame;

• check, in near real time, the continuity and the quality of thepermanent stations data;

• distribute the permanent stations raw data, for the post pro-cessing elaborations;

• estimate and distribute the transformation parameters be-tween the global reference frame to the frames typically re-quired by the users;

• estimate and model the correlated in time and space phe-nomena, inside the network area, in order to provide realtime services and post processing services.

This thesis concerns the problems related to station coordinatesmonitoring and to the transformation to the user frame estima-tion.By means of a continuous adjustment, a positioning service con-tinuously monitors its station coordinates and dynamically mate-rializes the reference frame, considering not only the smooth longterm trends but also the possible sharp discontinuities. Consider-ing that the most of its users need national cartographic coordi-nates, it should also estimate and distribute the transformation be-tween the global and the national cartographic reference frames.To guarantee maximum reliability and accuracy, a permanent net-work monitors its station coordinates by a continuous adjustmentand quality check. The network final adjustment, finalized to theestimation of its permanent station coordinates, is generally com-puted by daily adjustments of the network using the final IGSproducts, available with two weeks of latency. Permanent net-works for positioning services need at least two other monitoringprocesses, at two different latency levels: the first check is di-rectly managed by the software that acquires data streams fromstations to compute real time network products, the second is anadjustment in near real time performed to check both data qualityand coordinates stability.The final adjustment requires a large number of operations, from

data download to coordinates estimation; obviously, for the con-tinuous monitoring purpose, a software able to automate the wholeprocess is useful. Beyond the continuous technical execution ofthe adjustment, its should also provide a series of quality indexesand relevant statistics to check the quality of the data and to im-prove the results; moreover, the time series should be analysed toidentify discontinuities and long term trends.Strictly connected to the network adjustment is the fact that, ifthe network is composed of a large number of stations, their ad-justment cannot be performed in a unique elaboration, even witha powerful computation resource. In literature this problem hasbeen already handled by splitting the network in sub-clusters thatare independently adjusted and then re-combined, but the proce-dure, that is usually adopted, introduces false redundancies thatsignificantly depress the estimated covariances of station coordi-nates.This thesis is a dissertation on problems and possible solutionsencountered, starting from the design of the network and its ad-justment to the choices in its subclustering.

2 THE REGIONAL NETWORK ADJUSTMENTAll the network adjustments described in the thesis are performedwith the BPE processing engine of the scientific software BerneseGPS Software 5.0 of Astronomical Institute, University of Bern(BSW5.0) (Dach et al., 2007), following the international guide-lines for a regional network adjustment (Ferland et al., 2003) andthe strategies described in (Benciolini et al., 2008). In particular,the processes are performed with the strategy:• orbits interpolation;• code single point positioning (the receiver clocks modelling);• creation of single differences (baselines definition);• detection and removing of cycle slips;• preliminary ionospheric free float solution;• ambiguity fixing, by the QIF, in single base approach;• ionospheric free fixed solution, in multibase approach, com-

puted constricting the barycentre of the reference coordi-nates to their apriori values (minimal constraints).

After the data processing, the extraction of reports and indexesfrom the huge number of BSW5.0 output is needed to check thequality of data and results (Biagi et al., 2007a, Biagi et al., 2008);moreover, the coordinate time series should be analysed to iden-tify discontinuities and long term trends.

To automate the adjustment process, a package called RegNet hasbeen developed: it consists in a flow of procedures that performsall the operation needed by the network adjustment, from dataacquisition to the quality analysis; RegNet is technically summa-rized in Section 3. The quality indexes analysed follow broadlythe adjustment line; in particular, the most useful regard:

• dynamic modelling of satellite orbits from IGS ephemeris:for each satellite, the RMS of the residuals;

• data conversion from RINEX to BSW5.0 format: for eachstation, data presence, completeness and gaps;

• receiver clocks modelling: for each station, the RMS of sin-gle station ionospheric free code elaboration;

• cycle slips detection: for each baseline, the RMS of tripledifferences residuals;

• preliminary ionospheric free float solution: for each base-line, the number of initial ambiguities and RMS;

• ambiguity fixing: for each baseline, the percentage of fixedambiguities and RMS;

• final multibase solution: the final RMS.

3 THE AUTOMATION OF THE ADJUSTMENT:REGNET

RegNet is a set of routines, mainly written in MatLab (The Math-Works) and C, governed by a DOS batch file that permits the au-tomatic periodic network adjustment and quality check. From apractical point of view, in fact, the automation of the adjustmentas well as the handling of errors (reprocessing due to missingfiles or bad data quality, . . . ) is fundamental in order to minimizethe manual intervention by the operator. The network adjustment,following the IGS guidelines, requires the use of the final interna-tional products, generally available with 11−18 days of latency;some of these products are updated on a weekly basis and there-fore are used in the elaboration of all the days belonging to thesame week. For these reasons, the final network adjustment iscarried out once a week, performing seven separate daily elabo-rations of all the days of the week.All the operations performed by RegNet, summarized in Fig-ure 1, can be executed by launching the same main batch fileREGNET.BAT, once a week.

Figure 1: RegNet workflow.

3.1 RegNet data structureConsidering that elaborations are performed on the weekly basis,a reasonable choice is to group the elaborations by weekly cam-paigns. The configuration files are stored in a fictitious BSW5.0campaign, named DATA; these, stored in the \STA subfolder, con-tain information on reference stations, their apriori coordinates,the hardware changes on the network, the thresholds of the qual-ity indexes. The RegNet main programs, not here discussed indetail, are:

• SESSDEF.EXE: sets the elaboration session and some envi-ronment variables;

• IGSDOWNLOAD.EXE: downloads international data;

• NETWORKDOWNLOAD.EXE: downloads the adjusted networkdata;

• CHECKDATA.m: checks the presence of all the input files;

• SNX2APR.EXE: computes the apriori coordinates for the ref-erence stations starting from the IGS weekly solutions;

• BPELAUNCH.EXE: executes the network adjustment by sev-eral calls of the BSW5.0 BPE;

• BERNEXTR.EXE: extracts and organizes the main results fromthe BSW5.0 outputs;

• SERIES.m: analyzes the coordinate time series;

• INDEXES.m: analyzes the quality indexes;

• BASELINES.EXE: creates a map of the adjusted baselines;

• HEADERS.EXE: identifies instrumental changes and checkthe coherence between RINEX and station information;

• VELOCITIES.m: creates a map with the velocity field.

All the .EXE programs are standalone applications which inputarguments are configurable by a specific DOS call in a way thatallows a completely automated call by some schedule command.At the end of each main subroutine a log file is written and sentby mail to the network responsible, which is thus able to follow inreal time the adjustment progress; an example of IGSDOWNLOAD.EXEreport is shown in Figure 2.

===============================================================================

IGSdownload v.2.0

Author: Stefano Caldera 27-APR-10 13:18

===============================================================================

General options:

----------------

-> GPSWEEK : 1578

-> Campaign : $(P)\DATA

-> Get Final Orbits : Yes

-> Get Rapid Orbits : No

-> Get RINEX : Yes

PS list file : DATA.LST

-> Get SINEX : No

# of weeks : 52 (1527 -> 1578)

-> Get UPDATES : Yes

-> Keep compressed files: Yes

Sessions summary:

----------------

GPSWEEK 0 1 2 3 4 5 6

----------------------------------------------------------------

1578 10-094 10-095 10-096 10-097 10-098 10-099 10-100

Final Orbits download

---------------------

--> IGS Pole File

-------------

# of files requested : 1

# of files downloaded : 1

# of files already downloaded : 0

# of files not found : 0

--> Ephemeris Files

---------------

# of files requested : 7

# of files downloaded : 7

# of files already downloaded : 0

# of files not found : 0

--> RINEX Files

-----------

# of files requested : 63

# of files downloaded (P) : 63

# of files already downloaded (*) : 0

# of files not found (-) : 0

C G G I M N P W Z

A R R E A O A T I

G A A N T T D Z M

L S Z G E 1 O R M

---------------------------------

1578-0 10-094 P P P P P P P P P

1578-1 10-095 P P P P P P P P P

1578-2 10-096 P P P P P P P P P

1578-3 10-097 P P P P P P P P P

1578-4 10-098 P P P P P P P P P

1578-5 10-099 P P P P P P P P P

1578-6 10-100 P P P P P P P P P

Figure 2: Excerpt of IGSSDOWNLOAD.EXE log file.

3.2 RegNet output structureBSW5.0 output files already contain all the essential informationfor a quality analysis of the results; however, they are often dis-persive, and the most significant information for a quick qualitycheck generally get lost in the large amount of reports; the aimof RegNet is then the extraction and analysis of targeted qualityindexes from the BSW5.0 output files, that should allow a easyidentification of problems and bad results. Each quality index isin fact compared with a threshold to automatically signal warn-ings; the thresholds have been tuned to optimal values investi-gating the correlations between quality indexes and coordinatesrepeatability of some networks adjusted during the last years.The extracted results, already mentioned and presented in Section2, are presented in different groups:

• weekly elaboration report;• coordinate time series database;• textual quality indexes databases, derived from the analysis

of the historical results;• graphics of index and coordinate time series.

3.2.1 Weekly elaboration report At the end of the weeklyadjustment, RegNet generates a final report file that lists a sum-mary of all the extracted index information and eventually high-lights problems. Moreover, in order to identify coordinates prob-lems, a first simple weekly coordinates comparison is performed:

• concerning the reference stations, the differences of the dailyestimates with respect to the apriori coordinates;

• concerning the adjusted stations, the differences between theaverage weekly estimated coordinates with respect to theapriori coordinates;

• the daily repeatability.

Even in this case, stations having index values greater than thethreshold are marked in order to be quickly identified. The reportis then automatically sent to the network supervisor via email.Due to its size, that could be very long, a complete example isnot reported here.

3.2.2 Coordinate time series Each station is separately an-alyzed and interpreted, in order to exclude the daily results thatpresent high residuals with respect to a specific data fitting model.Let define time span the difference between the last and the firstday with a valid coordinates solution: the fitting model is chosenaccording to the following criterion:

• linear trend + annual period, if the time span is greater thanone year (Blewitt and Lavallee, 2002):

x (t) = x0 + vx · t+ αx cos (ωt) + βx sin (ωt) (1)

• linear trend: if the time span is longer than 30 days butshorter than one year:

x (t) = x0 + vx · t (2)

• constant model: if the time span is shorter than 30 days:

x (t) = x0 (3)

where x0 is the coordinate at the mean epoch of the time span,vx is the velocity, αx and βx are the cosine and sine compo-nents of the annual signal. The signal amplitude is computed as:px =

√α2x + β2

x. The parameters are then estimated by LeastSquares. Note that the estimation either of annual signals or ve-locities for time series shorter than three years is not significant;in any case the complete modelling allows a better interpolationof the daily coordinates. It should be noted that if the station

presents interruptions, the daily coordinates are separately inter-polated between the interruptions. In future, a significance anal-ysis will be implemented on the differences between the interpo-lated parameters relevant to the different intervals.Once the parameters of the specific fitting model have been esti-mated by least squares, the daily coordinates residuals are com-pared to the threshold values (from the usual RegNet thresholdfile) in order to obtain the cleaned station solutions. Data fittingresults are stored in several specific weekly files; two of them, forexample, are:

• CRDMODEL XYZ.OUT, which contains statistics regarding theoutliers detection and the estimates (at the central epoch ofthe processed GPSWeek) in geocentric cartesian coordinatesbefore and after the outliers removal (Figure 3);

• PARMODEL ENU.OUT, which contains the estimated veloci-ties and period amplitudes (if estimated) of all the stationsin ENU coordinates (Figure 4).

EPOCH: 2009/336 A L L S O L U T I O N S

+--------------------------------------------------------------+

# STAZ Valid Out X (m) Y (m) Z (m) sX(mm) sY(mm) sZ(mm)

+---+-----+------+----+-------------+-------------+-------------+------+------+------+

1 GRAS 1011 7 4581690.8423 556114.9297 4389360.8576 4.2 1.9 3.8

2 GRAZ 1068 0 4194423.7395 1162702.7846 4647245.4683 2.8 1.4 2.5

3 MATE 364 0 4641949.4691 1393045.5156 4133287.5371 3.5 1.9 2.8

4 MEDI 946 12 4461400.6615 919593.6729 4449504.8293 4.2 4.4 3.3

5 PADO 707 0 4388881.9504 924567.5549 4519588.7970 2.3 1.5 2.1

6 WTZR 314 0 4075580.4764 931853.8809 4801568.1866 3.1 1.6 3.1

7 ZIMM 1119 2 4331296.9992 567555.9716 4633133.9950 3.0 1.7 2.7

C L E A N E D

+--------------------------------------------------------------+

# STAZ X (m) Y (m) Z (m) sX(mm) sY(mm) sZ(mm)

+---+-----+-------------+-------------+-------------+------+------+------+

1 GRAS 4581690.8417 556114.9300 4389360.8571 2.8 1.3 2.5

2 GRAZ 4194423.7395 1162702.7846 4647245.4683 2.8 1.4 2.5

3 MATE 4641949.4691 1393045.5156 4133287.5371 3.5 1.9 2.8

4 MEDI 4461400.6613 919593.6732 4449504.8292 4.1 4.1 3.3

5 PADO 4388881.9504 924567.5549 4519588.7970 2.3 1.5 2.1

6 WTZR 4075580.4764 931853.8809 4801568.1866 3.1 1.6 3.1

7 ZIMM 4331296.9993 567555.9714 4633133.9949 2.9 1.2 2.7

Figure 3: Example of RegNet CRDMODEL XYZ.OUT output file.Column Valid reports the number of daily coordinates ac-cepted, while column Out indicates the number of outlier found.CLEANED section shows the station coordinates and their RMSevaluated at the instant EPOCH of the cleaned solution; ALL

SOLUTIONS section reports the same values obtained by a no-outlier removal approach.Interpolation (with outlier rejection of 1.5cm in E,N and 2.5cm in H)

--------------------------------------------------------------------------------

LOCAL GEODETIC DATUM: IGS05 EPOCH: 1560/3 - 2009/336

NUM STATION NAME vE (M/Y) vN (M/Y) vU (M/Y) FLAG

1 GRAS 0.0211 +- 0.0001 0.0154 +- 0.0001 0.0004 +- 0.0001 S

2 GRAZ 0.0214 +- 0.0001 0.0158 +- 0.0001 0.0010 +- 0.0001 S

3 MATE 0.0199 +- 0.0001 0.0175 +- 0.0001 -0.0012 +- 0.0001 L

4 MEDI 0.0223 +- 0.0002 0.0189 +- 0.0001 -0.0014 +- 0.0002 S

5 PADO 0.0201 +- 0.0002 0.0179 +- 0.0001 -0.0002 +- 0.0002 L

6 WTZR 0.0214 +- 0.0002 0.0153 +- 0.0001 0.0092 +- 0.0002 L

7 ZIMM 0.0203 +- 0.0001 0.0159 +- 0.0001 0.0012 +- 0.0001 S

NUM STATION NAME pE (M) pN (M) pU (M) FLAG

1 GRAS 0.0013 +- 0.0001 0.0013 +- 0.0001 0.0018 +- 0.0002 S

2 GRAZ 0.0007 +- 0.0001 0.0011 +- 0.0001 0.0020 +- 0.0002 S

3 MATE L

4 MEDI 0.0025 +- 0.0002 0.0013 +- 0.0001 0.0028 +- 0.0002 S

5 PADO L

6 WTZR L

7 ZIMM 0.0009 +- 0.0001 0.0005 +- 0.0001 0.0017 +- 0.0002 S

Figure 4: Example of RegNet 11 PARMODEL ENU.OUT outputfile. vE,vN and vh are the estimated station velocities; pE,pN andpU, represent the amplitudes of the annual signal.

Figure 5 shows an example of a station coordinate time seriesgraphical file: the blue dots represent the accepted daily coordi-nates, the red crosses are the removed outliers and the red lineis the estimated model; the green and red lines are the interrup-tions. The big jump in correspondence of the GPSWeek 1400 isdue to the reference frame transition from IGb00 and IGS05. Theresiduals of the least square fitting are then combined in order toobtain two repeatability indexes: defining the residual of stationi, for component j (East, North, Up) and for day d, as:

δj (d, PSi) =∣∣jPSi (d)− jPSi (d)

∣∣ (4)

Figure 5: Example of RegNet graphic index: modelled time se-ries of station ZIMM (Zimmerwald).

where jPSi is the coordinate estimated for the permanent stationi in day d and jPSi is the corresponding coordinates obtained bythe model, the indexes are:

• a daily synthetic index, computed as:

σj (d) =

√√√√ 1

NPS(d)

NPS(d)∑i=1

(δj (d, PSi)

)2(5)

whereNPS is the number of stations estimated in the day d;

• a station synthetic index:

σj (PSi) =

√√√√ 1

ND(PSi)

ND(PSi)∑i=1

(δj (d, PSi)

)2(6)

where ND is the number of days in which the station i hasbeen estimated.

3.2.3 Quality indexes time series In order to create time se-ries of each index, the weekly results are incrementally stored intheir respective global database; the databases are afterwards ar-ranged, in order to group the result time series by station, baselineand day. Starting from this large set of indexes files, several spe-cific graphs are then generated, in order to represent the results intheir temporal succession.For example, Figure 6 shows a typical not ordered results file(number of observed epochs), and Figure 7 a station summary.

*************************

NUMBER OF OBSERVED EPOCHS

*************************

Threshold: 1440

wwww-d yy-ddd yyyy-mm-dd STAT F EPOCHS

------+------+----------+---------+------+

1495-0 08-244 2008-08-31 PADO R 2760

1495-0 08-244 2008-08-31 WTZR R 2880

1495-0 08-244 2008-08-31 ZIMM R 2880

1495-1 08-245 2008-09-01 CAGL R 1439 *

1495-1 08-245 2008-09-01 GRAS R 1440

1495-1 08-245 2008-09-01 GRAZ R 1440

1495-1 08-245 2008-09-01 IENG R 609 *

1495-1 08-245 2008-09-01 MATE R 1440

1495-1 08-245 2008-09-01 NOT1 R 1440

Figure 6: Example of RegNet database output file.

Concerning the graphical outputs, the daily and the station / base-lines indexes graphs are created (example in Figure 8); concern-ing the second, for each day, the red circle represents the averagevalue over all the stations/baselines and the blue bar indicates therange between the minimum and the maximum station/baselinevalue.

*********************************************

NUMBER OF OBSERVED EPOCHS: STATION STATISTICS

*********************************************

STAT F AVG MIN MAX DEV.ST DAYS

-----+-+---------+------------------+------------------+---------+-------+

CAGL R 2824.6 478 (1528-6) 2880 (+ DAYS) 270.8 623

GRAS R 2873.0 1440 (+ DAYS) 2880 (+ DAYS) 99.3 629

GRAZ R 2847.1 82 (1537-2) 2880 (+ DAYS) 272.7 620

IENG R 2813.2 9 (1576-2) 2880 (+ DAYS) 326.1 577

MATE R 2837.4 360 (1584-0) 2880 (+ DAYS) 223.4 636

WTZR R 2855.0 360 (1584-0) 2880 (+ DAYS) 159.6 634

ZIMM R 2872.7 1440 (+ DAYS) 2880 (+ DAYS) 86.2 633

...

-------+---------+------------------+------------------+---------+-------+

TOT 2773.2 1 (+ STNS) 2880 (+ STNS) 333.9 85899

Figure 7: Example of RegNet index station summary file.

Figure 8: Example of RegNet graphic index: station graphs.

4 A NATIONAL DENSIFICATION EXAMPLE: THENEW ITALIAN REFERENCE FRAME

4.1 ETRS89 and its realizationsThe local reference system suggested for mapping applicationsin Europe is the European Terrestrial Reference System 1989 -ETRS89 (Boucher and Altamimi, 1992), based on a densificationof the global frame ITRF. The ETRS89 definition has its rise inthe cartographic requirements: an European site generally movesof about 2-3 cm/y with respect to the global system ITRS; this,even at the scale of only ten years, produces a displacement thatis significant at least for the large scale cartography: one purposeof ETRS89, therefore, is to reduce this issue in order to obtainreference frame as crystallized as possible. ETRS89 is then de-fined as coincident with ITRS at 1989.0 epoch, but it moves androtates with the so called stable part of Europe.At the continental scale, ETRS is realized and monitored by theEUREF Permanent Network (EPN) and is updated in line withITRF. An exception is the realization 2005: for complex tech-nicalities, not discussed here, the ETRF2000 is still the currentEuropean frame. ETRFyy is distributed with the estimated coor-dinates and velocities of the EPN permanent stations, at the refer-ence epoch and the transformation parameters between ITRFxxand ETRFyy (Boucher and Altamimi, 2007).

4.1.1 The Italian national ETRS89 realizations Many na-tions have their own official ETRS89 realizations: in Italy, un-til the last year, it was materialized by the IGM95 network ofthe Istituto Geografico Militare Italiano, (IGMI); the network iscomposed of about 2000 markers, surveyed in the nineties andadjusted in ETRF89 (Surace, 1997); IGM95 is distributed by theIGM monographs. In Italy, differences of some decimetres ex-ist between IGS05 and ETRF2005, with an increasing rate of1-2 cm/y and deformations of some cm between the Northernand Southern regions, due to differential geodynamical deforma-tions a the national scale (Jimenez-Munt et al., 2006); moreover,due to surveying instrumentations, data analysis techniques andelapsed time, IGM95 presents additional, spatially correlated de-formations and randomly sparse errors, whit a RMS of 3 cm inplanimetry and 5 cm in altimetry.

4.2 RDN: RETE DINAMICA NAZIONALEAt the beginning of 2007 the author participated in a work (Biagiet al., 2007b) that stated the Italy need of a zero order permanent

network; furthermore it was stated that the establishment of azero order network would have implied minimal hardware costs,because enough and well distributed permanent stations, whosedata could be available to the users community for free, alreadyexisted in Italy. Also thanks to this work, in order to obviatethe IGM95 obsolescence, in 2007 IGMI has begun a new pro-cess that updates the national network from a static to a perma-nent reference frame: this is done by the institution of an officialnational GNSS permanent network (Rete Dinamica Nazionale,RDN) (Baroni et al., 2009), adjusted in ITRF2005 and distributedin ETRF2000 (t0 = 2008.0). In particular, the following opera-tions have been done (Baroni et al., 2009):

• definition of a national permanent network of GNSS per-manent stations, called Rete Dinamica Nazionale (DynamicNational Network, RDN);

• adjustment of the network, in ITRF2005 and in ETRF2000;

• connection and adjustment in RDN of IGM95, in order toupdate its benchmarks coordinates.

In details, RDN is composed of 100 permanent stations, selectedamong the Italian existing stations on the basis of an homoge-neous distribution and quality (Figure 9); all the stations are per-manent, but they do not still have an automatic and continuousdata link to IGMI. Four weeks of data have been collected and

Figure 9: RDN network. The red triangles represent IGS stationsconstrained in the adjustment.

processed, from DOY 357/2007 to DOY 019/2008 (GPSWeeksfrom 1459 to 1462), obtaining an estimate for epoch 2008.0. Inorder to guarantee a comparison and a cross validation of the re-sults, the network, processed by IGMI, has been re-elaboratedby other three independent centres: the Universities of Padua andBologna and the G3 Group, particularly by the Laboratorio di Ge-omatica of Politecnico di Milano-Polo Regionale di Como. TheITRF2005 2008.0 estimated coordinates have been transformedto ETRF2000 at the same epoch, by applying the official inter-national transformation. The new Italian official reference framehas been then realized updating the coordinates of the old IGM95benchmarks using the RDN ETRF2000 coordinates as reference.Note that the original IGM95 network has not been re-surveyedand re-adjusted: the old IGM95 set of baselines has been con-nected to RDN by surveying some baseline from 45 RDN perma-nent stations to at least three IGM95 nearest benchmarks. Afterthat, all the original surveyed IGM95 baselines have been ad-justed again using the RDN ETRF2000 coordinates as constraint.Therefore, ETRF2000−RDN is only a partial update of ETRF89− IGM95: although the reference frame obsolescence is fixed,ETRF2000 − RDN partially still suffers of the technical prob-lems described in Section 4.1.1.

4.2.1 RDN adjustment: results obtained by G3 Herewith,the results are just summarised; a more complete report is in [Bi-agi et al., 2009a]. The network adjustment has been performedfollowing the procedures described in Section 2; furthermore:• all the stations raw data have been acquired directly from

IGMI;• the elaborations and the results and quality indexes have

been extracted and analysed using the RegNet package;• starting from the indexes analysis, the problematic data have

been identified and rejected in order to reprocess the ac-cepted data.

Concerning the data presence, the 96% of files were actuallyacquired, the 5.5% of which were rejected following the epochcut-off threshold (at least 23 hours/day of data) and 1 file was ex-cluded because a high code single point positioning RMS (greaterthan 4 m). It should be noted that the data incompleteness is of-ten due to the practice of data reconstruction from the real timestream. About 3% of the files have been rejected because high co-ordinate residuals; most of them regards a single station, whichshown a bad observation quality on the second frequency due toradio interferences. Regarding the final number of initial am-biguities, for a network like RDN values smaller than 150 aretypically expected: the minima for complete 24 hours sessionsare in the range 80-90 and values greater than 200 could indicateserious problem in the data. On this respect, only one baselinepresents sometimes critical statistics, due to combined problemof both the stations. The statistics of the percentages of suc-cess in the ambiguities fixing presents an uniform percentagedistribution ranging from 60 to 100% through the days: this is anindicator that the data quality varies station from station but thatis consistent in all the period, no highlighting clear outliers. Thedaily RMS of the final multibase solution, that represents anoverall final quality index, assumes acceptable values for all thedays, with values in the 1.1−1.3 mm range.The shortness of the time series impedes the estimation of mean-ingful station velocities; however, in order to decorrelate the resid-uals, the position of each station has been computed with a lineartrend estimation evaluated in the central epoch of the month ofdata (2008.0). An empiric covariance estimation, as in (Amiri-Simkooei, 2009), has not been attempted simply due to the short-ness of the time series. The global residual statistics (Table 1)are satisfactory, with standard deviations lower than 2 mm inplanimetry and 4 mm in Up.

(mm) East North Upσ 1.4 1.2 3.3

Min -6.3 -12.3 -13.9Max 8.0 6.0 14.5

Table 1: Global statistics of the time series. E: average, Min:minimum, Max: maximum.

Transformation from IGS05 to ETRF2000 (t = 2008.0) Thetransformation of the IGS05 coordinates to the ETRF2000 framehas been performed using the international formula starting fromthe IGS05 solution; the procedure is in fact still appropriate alsostarting from IGS05 instead of ITRF2005, since IGS05 and ITRF-2005 are consistency at some millimetres level.

Differences between G3 and IGMI Since the role of G3 in theRDN adjustment was to validate IGM results, our estimated co-ordinates have been summarized and published by IGMI in theofficial technical report. In order to investigate biases betweenthe solutions, a deeper analysis has been carried out: Table 2shows the statistics of the differences between the station coor-dinates of the official catalogue and the G3 solution: a bias of 3mm is visible in the Up component, probably due to the differentelaboration approaches and, most of all, to the rejection criteria

adopted. In the same table the distribution of the differences arealso reported; the four classes have been chosen in such a mannerthat every class reasonably represents different possible causes:

• class 1: numerical rounding;• class 2: differences reasonably contained within the estima-

tion accuracy, due to different elaboration approach;• classes 3 and 4: significant differences, due to different elab-

oration approaches and different rejection criteria.(mm) East North Up Class Range (mm) # PS

E -0.6 -0.4 2.8 1 [0−2) 28σ 0.8 0.5 2.4 2 [2−5) 55

Min -1.7 -1.5 -3.9 3 [5−10) 15Max 6.7 1.5 11.3 4 [10−15] 1

Table 2: Comparisons of IGMI−G3 coordinates and differencedistribution. E: mean difference, σ: standard deviation of all thedifferences, Min: minimum difference; Max: maximum differ-ence.The comparison of the station synthetic index (6) between IGMIand G3 solutions is shown in Table 3: IGMI solutions presenta standard deviation higher than the G3; probably these differ-ences are due to the the presence in IGMI solution of problematicsessions that have been removed by G3 according to the RegNetquality check. For the RDN purpose these differences are notsignificant.

IGMI solution G3 solution(mm) East North Up East North Up

E 1.3 1.1 4.5 1.4 1.2 3.3σ 1.3 1.1 3.2 0.3 0.5 0.8

min 0.4 0.3 1.3 0.6 0.7 1.6max 9.2 7.8 13.1 2.9 3.9 5.9

Table 3: Statistics of the station synthetic index.

5 PERMANENT NETWORKS FOR POSITIONINGSERVICES

5.1 The positioning services reference frameReal time users need of coordinates in the national cartographicreference frame can be fulfilled in two different modalities:

(A) 1) the Positioning Service estimates and distributes coordi-nates and products in the current IGSyy;

2) the Positioning Service estimates and publishes the trans-formation to the national reference frame;

3) the users estimate IGSyy coordinates and afterwards trans-form them into the national reference frame.

(B) 1) The Positioning Service estimates and distributes coor-dinates and products in the current IGSyy and in the na-tional reference frame;

2) the Positioning Service distributes both the global (forthe post processing applications) and the national (for thereal time applications) coordinates;

3) the real time users estimate their position directly in thenational reference frame.

As stated in Section 4.1.1, ETRF89-IGM95 was spatially dis-torted and presented sparse errors; technically, modality (B) wouldhad introduced significant approximations in the network compu-tation and then a significant degradation of the real time productsaccuracy: therefore, while ETRF89-IGM95 was in force, the onlypossible approach was (A).The current Italian reference frame ETRF2000-RDN is charac-terized by an accuracy higher than that of ETRF89-IGM95; it isreasonable to expect that (B) approach does not determine effec-tive problems in the network management and in the productsquality; instead, it could permit a concrete simplification on theusers side. On this regards, some investigation at the nationallevel have been performed.

During the last years, the author has been involved in the net-work adjustment, coordinates monitoring, transformation estima-tion and experimentation of two positioning services in Italy: thelocal service of Lombardia Region and the national network ofLeica Geosystems Italia, named ItalPoS. Because of their extend,the two networks represent two different case studies with differ-ent problems related to the network adjustment and the estima-tion of the transformation to the cartographic frame; in the fol-lowing Sections, the monitoring of the two networks are brieflydiscussed. Moreover the transformation between the global andthe national reference frames are tested.

5.2 GPSLombardia positioning serviceLombardia Region is located in Northern Italy; its population isabout 9.000.000 people and its surface is of about 24.000 km2.In 2003 an agreement was subscribed by Lombardia Region, Is-tituto di Ricerca per l’Ecologia e l’Economia applicate alle AreeAlpine (IREALP, a research institute funded by Lombardia Re-gion) and Politecnico di Milano for the realization of a regionalpositioning service. The network (Figure 10) is now composedby 16 permanent stations with a mean reciprocal distance of 50km. The control center is operated by IREALP technicians; FKPand VRS are the network phase real time products provided tothe users, while single station code corrections (DGPS), stationRINEX and VRS RINEX data are also available. Network man-agement and data and products distribution are now completelyunder IREALP responsibility; beside a general role of scientificconsultant, the Politecnico di Milano-Polo Regionale di Comoruns the final monitoring of the network and the transformationto the national cartographic reference frame.

Figure 10: GPSLombardia network.

5.2.1 The network adjustment and monitoring The finaladjustment strategy adopted in the GPSLombardia network pro-cessing is the same described in Section 2; this strategy has beendefined after several re-adjustments of the GPSLombardia net-work aimed to improve the results on the basis of quality indexesvalues and coordinates repeatability (Biagi et al., 2007a).The IGS stations used in the adjustment have been chosen accord-ingly to homogeneous distribution and minimum distance princi-ples, with the following compromises: some southern stations,although quite far, have been included to be shared with the net-works located in southern Italy. The adjustment is automaticallyperformed with BSW5.0 using RegNet.The network is being continuously monitored from January, 1stof 2006: at present, more than four years of data are availableand have been analyzed (from GPSWeek 1356 to 1560). As it iswell known, in the passage from GPS Week 1399 to GPS Week1400 (2006, 5th November, 00:00) the reference frame changedfrom IGb00 to IGS05, that implied also significant discontinuitiesin the time series of IGS coordinates; transformation parametersfrom IGb00 to IGS05 have been published (Ferland, 2006), how-ever, the discontinuity is due to significant improvements in thedata elaboration standards and a merging of old and new stan-dards in the results analysis does not seem appropriate.

Elaboration success GPSLombardia stations show very goodstatistics with the exceptions of PORA, which presented somemissing periods due to communication problems. Globally, about98% of the GPSLombardia expected files is correctly processed.

Code Single Point Positioning RMS COMO shows a particu-lar behaviour: generally the statistics are acceptable, but the ini-tial time series is unusual (Figure 11) due to multipath, caused bya jib crane mounted near the station and left free to rotate with thewind; in March 2007 the crane has been removed; this could havebeen a critical situation but, fortunately, the interference was notso high on phase observations.

Figure 11: COMO daily ionospheric free code RMS.

Ambiguities Concerning the initial number of ambiguities, thereare worrying maxima due to the baselines involving MATE; sinceMATE receiver was replaced (GPSWeek 1506), the maxima low-ered. The percentages of success in the ambiguities fixing isshown in Figure 12; the minima values jump after GPSWeek1400 are due to a change in the elaboration parameters: in thatweek, in fact, the threshold on the number of observed epochhas been introduced; that caused the exclusion of short sessionsthat obviously contained a number of initial ambiguities lowerthan an almost complete session. After GPSWeek 1400, the per-centages are always greater than 70%, except for some isolateddays. The time series presents a periodic behaviour correlatedwith seasons: generally, in fact, the worse results are obtainedin summers; probably, this is due to some residual atmosphericeffect, either ionospheric or tropospheric, but a final explanationneeds more specific analyses.

Figure 12: Daily number of fixed ambiguities.

Coordinates modelling All the station time series have beeninterpolated by the models described in Section 3.2.2: globally,only 21 of 16777 daily results (0.12%) have been excluded be-cause of bad interpolation residuals (15 mm in planimetry or 25mm in Up). All these sessions concern heavy snow days wherethe stations antenna is covered by a snow layer that interfereswith the signal reception; anyway, on the long term, the exclu-sion of so few sessions does not entail significant differences inthe coordinates interpolation with respect to the RAW time seriesmodelling. On the contrary, the residuals RMS improves, espe-cially in the Up component (Table 4).

RAW CLEANEDE N U E N U

σ (mm) 1.3 1.4 4.2 1.3 1.4 3.9min (mm) -24.0 -15.3 -74.3 -12.5 -14.7 -24.9max (mm) 10.4 20.1 21.5 10.4 14.8 21.5

Table 4: Raw and cleaned statistics of all the residuals.The time series are sufficiently long to consider the estimated ve-locities representative of the mean geodynamic movements. Any-way the velocities of COMO (belonging to EUREF) have beencompared with the EPN catalogue and the coherence is at thesub-millimeter level (Table 5).

VX (m/y) VY (m/y) VZ (m/y)GPSLombardia

-0.0143 +- 0.0001 0.0180 +- 0.0001 0.0106 +- 0.0001EPN

-0.0139 +- 0.0002 0.0180 +- 0.0001 0.0107 +- 0.0002

Table 5: COMO velocities: comparison between GPSLombardiaand EPN solutions; note that the standard deviations of our resultsare empirically computed by the residual time series.

Stations located in mountain region present an annual signal inheight more evident than the other stations. Concerning the plani-metric components, only station BREA shows a clear annual sig-nal: the relevant powers is of about 4 mm in North component(Figure 13).

Figure 13: BREA time series.

The service coordinates update According to Section 5.1, GP-SLombardia station coordinates and transformation to the nationalcartographic frame have been updated on a periodic basis; thepermanent station coordinates of each update are computed by alinear regression of all the available time series, evaluated at theupdating epoch.

5.2.2 IGSyy-ETRS89 local transformation history The dif-ferent methodologies adopted in the years for the computation ofthe transformation between the global and the cartographic refer-ence frames, for the Lombardy area, are detailed in (Biagi et al.,2009b) and summarized in the following sections.

1) 2005: IGb00→ETRF89-IGM95 For the first estimation itwas supposed that the transformation between IGb00 and IGM95could be implemented by a local adaptation of the internationalformula between ITRF2000 (IGb00 approximately) and ETRF2000at epoch 1989.0, where:• the starting ITRF2000 coordinates were the GPSLombardia

IGb00 station coordinates at epoch t = 2005.445;• the official parameters between IGb00 and ETRF2000 att = 2005.445 were used;

• the station velocities for the back-propagation in time weresupposed equal to the regional mean velocities, computedby a weighted mean (inverse distance weights with respectto the Lombardy barycenter) of the velocities published byEPN of the 8 IGS stations constrained in the network adjust-ment.

A comparison between the results obtained by the applicationof the transformation on 140 surveyed reference points and theirETRF89-IGM95 monographed coordinates shown excellent plani-metric differences and a local Up IGM95 deformation; consider-ing that the main transformation goal is the cartographic support,also the altimetric results were acceptable.

2) 2006: IGb00→ETRF89-IGM95 A new adaptation for thisepoch provided bad results: it was considered that this bias wasdue to an instability in the computation of the mean region annualvelocity, obtained by a weighted mean of the ETRS89 velocitiesand propagated by a multiplication for 20 years; in order to solvethis problem, a different transformation approach was tried andadopted in the successive years. The transformation was com-puted with the following steps:

• selection of set of permanent stations, located around theLombardy Region, whose IGb00 and ETRF2000 estimateswere available;

• estimation of a similarity transformation (IGb00-ETRF2000(1989.0)), by means of the known coordinates of the afore-said stations;

• application of the estimated transformation to IGb00 coor-dinates in order to obtain the corresponding ETRF2000(t =1989.0).

3) and 4) 2007, 2008: IGS05→ETRF89-IGM95 The trans-formations for epochs 31 March 2007 and 1 January 2008 werecarried out with the same approach used in the 2006 transforma-tion, but introducing the new IGS05 reference frame instead ofthe old realization IGb00.

5) from 2009: IGS05→ETRF2000-RDN Considering that GP-SLombardia and RDN share 12 permanent stations, the similar-ity transformation can be estimated directly starting from theirestimated IGS05 and official RDN catalogue coordinates. Thetransformation residuals on the permanent stations (update 2009,Table 6) show excellent statistics, with a standard deviation ofabout 2 mm in all the components.

∆E (mm) ∆N (mm) ∆U (mm)σ 2.1 1.4 2.9

min -2.1 -2.5 -5.4max 6.0 3.0 4.0

Table 6: IGS05→ETRF2000-RDN transformation residualsstatistics.In order to evaluate the quality of the transformation, the analysismust be carried out not on the residuals of the permanent stationsused in the transformation computation (for which a good resultis expected) but on the ETRF2000-RDN benchmarks new coordi-nates. Due to a lack of time, we could not test the transformationon all the 140 IGM95 benchmarks, but only on a subset of 28 ofthem. The statistics of the differences, shown in Table 7, are sub-stantially good; the greatest value in Up component concerns thepoint Stresa, located alongside the Maggiore Lake bank, which issubject to an high local subsidence effect.

∆E (cm) ∆N (cm) ∆U (cm)mean -1.0 -0.4 -2.1σ 1.5 1.5 3.0

min -4.0 -2.9 -11.0max 3.8 2.4 3.2

Table 7: Statistics of the comparison on the ETRF2000-RDN co-ordinates of the 23 reference points (transformed-monographed).

5.3 SmartNet ItalPoS positioning serviceLeica Geosystems Italia network, named SmartNet ItalPoS (fromnow, only ItalPoS), represents an example of a commercial GNSS

network for positioning services at the national scale. At thepresent (February 2010), ItalPoS is composed of about 170 GNSSpermanent stations distributed over all the Italian territory (Fig-ure 14). ItalPoS real time and post-processing services vary onthe basis of the kind of registration of the users; in particular,two kind of users are possible: SmartNet (free) and ItalPos (fee-paying).

5.3.1 ItalPoS adjustment and monitoring In 2008, with theformalization of an agreement, ItalPoS adjustment and monitor-ing started to be carried out by G3. In particular, the final networkadjustment is performed at Politecnico di Milano-Polo Regionaledi Como, while an experimental quasi-real time station coordi-nates monitoring is performed by Politecnico di Torino. Con-cerning the final adjustment, the network is continuously adjustedfrom September 2008 (GPSWeek 1495), using the RegNet pack-age, and now 62 weeks of data (up to GPSWeek 1556) have beenalready processed. The adjustment procedures are the same usedin the already presented networks; the IGS reference stations in-cluded in the network are shown in Figure 14.

Figure 14: ItalPoS network (as of December 2009). The red tri-angles represent the IGS reference stations.

Data presence At the present, the data stored in the post-proces-sing RINEX files are reconstructed from the real time data flowof each station to ItalPoS control center; for a network finalizedto post-processing applications this would be a disadvantage, butsince ItalPoS applications are pratically all in real time services,the post-processing of the same data that contributed to the realtime products generation represent also an a-posteriori verifica-tion of the distributed services quality. In mean, ItalPoS stationscollect 2755 epochs per day, with a RMS of 343 epochs; thismeans, on the average, that each station losses one hour of dataeach day. Obviously, if the exclusion criterion based on the min-imum number of observed epoch is strict, a large number of sta-tions would not be processed. In order to maximize the numberof processed files without deteriorate the elaborations quality, acompromise of 1440/2880 threshold (12 hours) have been im-posed.Globally, a considerable number of expected files (13.9%) is notfound on the server, while the 2.1% of downloaded data is ex-cluded by the already analysed epochs criterion: therefore, theexpected files correctly processed are the 84.3%.

Ambiguities In the average, 76.8 % of ambiguities are fixed(Figure 15), with a RMS of 9.6 %; the time series present somesmall, even null values but the index is globally acceptable. Even

the ItalPoS time series present the same seasonal effect describedfor GPSLombardia.

Figure 15: Daily percentage of fixed ambiguities.

Final RMS The daily final multibase RMS presents values alittle greater than those of GPSLombardia; anyway the worst val-ues are smaller than 2 mm (except for one day in the whole series)and do not present particular criticality.

Coordinates modelling The network configuration is continu-ously changing, so that, on a total of 163 stations, only 54 stationspresent time series with at least 365 valid estimates; for an homo-geneous estimation, therefore, all the coordinates have been mod-elled by a linear trend. On a total of 42096 daily estimates, 134(0.3%) are excluded because of their residuals (as usual limits of1.5 cm in planimetry and 2.5 cm in height are used); the globalresiduals statistics of the raw and cleaned solutions are reportedin Table 8.

RAW CLEANEDE N U E N U

σ (mm) 1.9 2.1 6.9 1.8 2.0 6.6min (mm) -29.2 -32.8 -70.4 -14.0 -14.8 -25.0max (mm) 32.6 26.4 86.0 14.5 14.9 24.6

Table 8: Raw and cleaned statistics of all the residuals.

The statistics of the station synthetic index (6) are reported in Ta-ble 9. The worst planimetric repeatability corresponds to stationSTUE, which presents a pronounced strange behaviour, undoubt-edly due to the fact that the station is located nearby a dam andtherefore its position is influenced by the seasonal pondage emp-tying/filling process. On the contrary, an example of station thatdoes not show particular problems is represented by TERA (Fig-ure 16); however, its time series has been interrupted becauseof the evident jump due to of the Abruzzo earthquake (TERA isabout 40 km from the epicentre).

E (mm) N (mm) U (mm)mean 1.7 1.8 5.8σ 0.5 0.4 1.0

min 1.4 1.3 3.7max 5.0 3.0 8.8

Table 9: Station synthetic index statistics.

5.3.2 IGSyy-ETRS89 local transformation history Consid-ering that ItalPoS operates from half 2008, at the moment threetransformations have been computed: the first (first half of 2008)was estimated in order to compute the coordinates in the ETRF89-IGM95 frame, while the target frame of the other two (beginningand late 2009) is ETRF2000-RDN. Each of the three estimateshas been carried out with a different approach, in order to takeadvantage of the best data available at the transformation epoch.

5.3.3 2008: IGS05→ETRF89-IGM95 Due to IGM95 defor-mation, it was noted that unique national transformation estima-tion did not provided sufficient accuracy to model the IGS05-ETRF89-IGM95 differences: the transformation has been then

Figure 16: TERA time series. The vertical green line correspondsto the Abruzzo earthquake.

computed subdividing the national territory into independent zones,with the estimation of independent 7 parameters transformations.A detailed description can be found in (Biagi et al., 2009a).

5.3.4 2009: IGS05→ETRF2000-RDN ItalPoS station IGS05coordinates were updated in the beginning of 2009 using the re-sults of the three months of data available (31 August (GPSWeek1495) - 30 November 2008 (GPSWeek 1508)); 27 of the 138 Ital-PoS stations belong also to the RDN network and therefore theycan be used in order to directly estimate the similarity parameters.Nevertheless, at the epoch of the transformation the RDN coordi-nate catalogue was not officially published yet so they cannot beused as reference points. Therefore, the method applied was thesame used in the 2), 3) and 4) GPSLombardia transformationscomputations (Section 5.2.2). After the official RDN cataloguepublication, an a-posteriori verification on the coordinates of the27 common stations between ItalPoS and RDN also produced co-herence at the sub-centimetre level.

5.3.5 2010: IGS05→ETRF2000-RDN The 2010 coordinatesand transformation reference epoch is 2009.8 (3 October 2009,DOY 277, GPSWeek 1552.0); considering that 31 ItalPoS sta-tions are in common with the official RDN network, which of-ficial ETRF2000-RDN catalogue of coordinates is available, thetransformation has been computed with the direct estimation ofthe similarity transformation parameters; the transformation resid-uals are summarized in Table 10. In the immediate future, the2010 transformation will be also checked on the 28 ETRF2000-RDN benchmarks.

∆E (mm) ∆N (mm) ∆U (mm)σ 2.6 2.7 8.4

min -6.1 -4.4 -13.5max 4.1 5.8 20.0

Table 10: ItalPoS IGS05(2009.8)→ETRF2000-RDN transforma-tion residuals statistics.

6 RIGOROUS COMBINATION OF SIMULTANEOUSGNSS NETWORKS

Raw data of GNSS permanent networks are typically processedby daily sessions in order to estimate daily coordinates, ancil-lary unknowns and their covariances. Typically an open baselinegraph is built and the relevant double differences are processed;as already described in Section 2, in the case of local networksthe international guidelines suggest to minimally constrain thereference frame by fixing the barycentre of a polyhedron of IGSfiducial stations included in the processing. The normal system tobe inverted in the least squares estimation requires memory occu-pation and computational effort that is proportional to the squareof the unknowns number, and this causes a limit to the number ofstations that can be simultaneously processed and an increasing

on the computational time. At the present, a standard Windowsserver can easily estimate a batch solution for about 170-190 sta-tions; very few networks in the world exceed these dimensionsand require a network distributed adjustment (Davies and Blewitt,2000), as IGS and some regional networks, for example EPN; inany case, the distributed adjustment is a popular choice also forsmaller networks.

6.1 The network distributed adjustment approachTo implement a distributed adjustment, at first the network is splitinto overlapping subnetworks, such that each station belongs toan assigned minimum number of subnetworks. The subnetworksare separately adjusted and the relevant normal equations (NEQ)are then stacked to obtain a final network solution. The problemis classical and has a rigorous solution, called Helmert block-ing, when the observations are typically uncorrelated. For theGNSS networks thought, where many times the phase double dif-ferences are treated as observations, the hypothesis of linear inde-pendence is by definition inconsistent: this could give to blundersin the solution. It is worth to note that in the GPS case, the subnet-works overlap is not strictly needed, because a consistent networksolution can be obtained also by joining separate solutions: linksand consistence are guaranteed by the raw observations to a com-mon GNSS constellation and by using the same IGS products inthe observations processing. In any case, the overlap is useful be-cause it guarantees the cross check of the results.As it is well known, this praxis builds artificial independent ob-servations, either false repeated baselines or false closed poly-gons, because the same files are processed by more ProcessingFacilities (PF) but the correlations of the relevant NEQs are ig-nored at the stacking level. In the following this distributed ap-proach will be called COnstant in time Distribution (COD).

6.2 VAD: an alternative approachAn alternative approach consists in distributing the adjustmentof a network into overlapping subnetworks that share just onestation: in this way, all the possible independent double differ-ences are processed and the resulting daily baselines graph is aconnected open graph, exactly as in a rigorous adjustment of thewhole network (Biagi and Sanso, 2009). Supposing to work ona weekly basis, at the end of the week the seven daily NEQs arestacked in a weekly solution. To guarantee overlaps and con-sidering that, generally, not all the stations are present all days,the daily subnetworks configuration can be forced to vary withdays: in this way, true closures and repetitions and cross checksfor all the stations are obtained. In the following this approachwill be called VAriable in time Distribution (VAD): with respectto COD, the VAD approach imposes a significant coordinationwork between the PFs, in order to define the configuration of thenetwork splitting for each day. In any case, despite the coordi-nation difficulties, the VAD approach allows a rigorous combina-tion of different overlapping subnetworks that, at the daily scale,is equivalent to the adjustment of the whole network: in the dailysubnetworks stacking, just the correlation due to the connectingstation is neglected.

6.3 A numerical testIn order to numerically compare the results provided by COD andVAD, a network of 102 stations has been analysed: it is composedof 24 IGS official Reference Frame stations and 78 stations be-longing to the EPN network; four weeks of data, GPSWeeks from1550 to 1553, have been processed. At first a unique adjustmentof the whole network (Batch adjustment) has been computed andthe relevant results represent the benchmark (BA); then COD andVAD approaches have been simulated and compared with BA. Allprocessing have been managed by RegNet and performed withthe usual strategy. Particularly, in BA a minimally constrained

NEQ has been produced for each daily data processing. For CODand VAD solutions, the processing schema is shown in Figure 17.

Figure 17: Chart of daily and weekly NEQs stacking used inCOD and VAD approaches. DOW: day of week; NEQ(LC):loosely constrained NEQ; NEQ(MC): minimally constrainedNEQ.

6.3.1 COD implementation To implement the COD approach,three PFs have been simulated imposing that each station belongsto two different PFs. The PFs subnetworks has been manuallydesigned in order to guarantee their quasi homogeneous distribu-tion, by assigning to each PF a total of 68 stations (16 referencestations and 52 stations to be estimated). Figure 18 shows an ex-ample of daily stacking of the three PFs NEQs: some baselinesare repeated and many polygons are created. Remember that inthe stacking, their correlation is not taken into account.

Figure 18: COD approach: daily NEQs stacking of DOY 09-263. Red triangles: reference IGS stations, blue circles: stationsto be adjusted, red baselines: PF1, blue baselines: PF2, greenbaselines: PF3.

6.3.2 VAD implementation The simulation of VAD approachis more complicated than the COD: contrary to the COD ap-proach, in fact, the VAD configuration must change each day inorder to guarantee overlaps; furthermore, the daily connectingstation cannot be held fixed, because if in some day its data are

not available, the subnetworks would be unconnected. For thesereasons, in order to automatically create the daily configuration,a VAD routine has been developed and embedded in RegNet; inparticular, the processing of each day is structured as follow:• data download;• data pre-processing with BSW5.0;• rejection of files that do not satisfy quality criteria;• design of the subnetworks:

– connecting station (RC ) choice: the selected station isthe nearest to the daily network barycentre;

– stations assignment: the stations are randomly assignedto one of the subnetworks, in such a manner that thestation numerousness of subnetworks is as much ho-mogeneous as possible. The reference and the to-be-adjusted stations are separately treated, in order toguarantee a minimum number of reference stations toeach subnetwork;

• distribution of each station data to its appropriate PF; obvi-ously, RC is assigned to all the subnetworks;

• independent PFs adjustments, such as COD approach.The random criterion used in the subnetworks creation has beenused only for a test purpose and clearly does not represent anoptimum method; anyway it provides network configurations asarbitrary as possible, that are useful in this testing phase; a morereasonable criterion will be implemented in future. In order tobe compared with COD, even the VAD approach has been sim-ulated on three PFs: despite the random generation of the con-figurations, RegNet indexes statistics of VAD approach are verysimilar to BA and COD.Figure 19 shows the example of daily stacking of the three PFsNEQs; in VAD approach, no baselines are repeated and no falseclosures are generated.

Figure 19: VAD approach: daily NEQs stacking of DOY 09-263.Red triangles: reference IGS stations, blue circles: stations to beadjusted, black diamond: connecting station, red baselines: PF1,blue baselines: PF2, green baselines: PF3.

6.3.3 Results comparison In order to evaluate COD and VADapproaches, their results have been compared with BA as refer-ence; in particular, for each station, the following comparisonshave been carried out:• differences in the weekly solution station coordinates and

covariances;• repeatability of the coordinate time series;• differences in the daily estimates.

The comparison of the weekly estimates has been carried outby computing the differences, with respect to the weekly BA re-sults, of the four sets of VAD and COD weekly station coordi-nates. The highest differences concern 2-3 stations that are iso-lated from the others (for example the two Icelandic stations) orthat shown problems even in the BA adjustment. Globally, thethree approaches produce similar results and the differences arenegligible.In order to evaluate how COD and VAD approaches correctlyestimate the coordinates covariances, the coordinates standarddeviations obtained by the approaches have been compared withthose of BA approach, which, although not realistic (Barzaghi etal., 2004), are rigorously estimated: COD false redundancies fur-ther depress the estimated covariances for all the stations, whileVAD provides correct estimates (Table 11): only the values of theconnecting station (which is the same in all the days) are under-estimated, as their correlations in the subnetworks are not takeninto account.

GPSWeek 1550 COD/BA VAD/BAX Y Z X Y Z

mean 0.7 0.7 0.7 1.0 1.0 1.0min 0.6 0.6 0.6 0.5 0.6 0.6max 0.8 0.8 0.8 1.2 1.1 1.2

Table 11: Ratio of estimated standard deviations of COD andVAD with respect to BA for GPSweek 1550. The ratios of theother three GPSweeks are exactly the same.

Coordinate time series repeatability of the three approachesshows that VAD approach reproduces nearly perfectly the BA re-sults, while COD repeatability in Up component is slightly better;anyway, the results are comparable. Concerning the differencesin the daily estimates between COD and VAD with respect toBA, minimum and maximum of BA-VAD differences in up seemworrying, but these values represent only few bad sessions; infact, about 91% of the differences in height are lower than 0.5mm. VAD statistics are quite worse than that of COD, but it isworth to remember that the daily VAD subnetworks configura-tions are randomly generated and not optimized. More analyseswill be performed on some optimality criterion in the VAD sub-networks generation.

7 CONCLUSIONS

In the Italian framework, the establishment of a zero order perma-nent network was necessary to allow a common adjustment of lo-cal permanent networks and the transition from the previous staticIGM95 reference frame to a new permanent frame. In 2007 it wasdemonstrated with a numerical test that this would be feasiblewith minimal hardware costs, because enough, well distributedand freely distributing data permanent stations already existedin Italy. Also thanks to this contribution, in 2008 Istituto Ge-ografico Militare, the Italian geographic authority, started a mod-ernization phase by the institution of the new ETRF2000-RDN(Rete Dinamica Nazionale, National Dynamic Network) frame,based on a permanent network, whose estimates allowed to re-move the deformations accumulated by the old IGM95. The au-thor has been significantly involved into the RDN realization as amember of one of the three independent cross-validation centres.The adjustment and the quality monitoring of RDN was automat-ically performed by RegNet software, whose development andimprovement required a large part of the Ph.D. activities. Partic-ularly, RegNet is tuned to manage all the processing by BerneseGPS Software and to extract quality indexes by the relevant out-puts. Obviously RegNet is not the first package to automate theprocessing of a permanent network; nevertheless, its interest is inthe computation of quality indexes and in the creation of relevantstatistics that allow to identify the main station problems and to

enhance the adjustment results.Our group is involved in the monitoring of two permanent net-works aimed at positioning services: GPSLombardia, at the Ital-ian Regional scale and composed of 16 permanent stations, andItalPoS, at the national scale and composed of about 150 stations.The experience matured in these collaborations permitted to testand tune RegNet software and to analyse the strategies for theadjustment of local networks. Moreover, the need of position-ing services to compute and distribute the transformation betweenITRS (at present ITRF2005) and ETRS89 (in the past ETRF89-IGM95 and at the present ETRF2000-RDN) permitted the studyof the problems related to this transformation at the regional andthe national scale providing alternative solutions depending onthe type of data available.The last analysed problem is relevant to the network splitting andrecombining in the daily/weekly adjustment: the quick growthof the number of stations of ItalPoS raised the problem relatedto the technical impossibility to perform a Batch adjustment of anetwork composed of more than 200 stations; normally, in thiscase the network is split into significantly overlapping subnet-works, that are separately processed on the daily basis and finallyrecombined (COD approach): in this way the correlations due tothe overlaps are ignored and false independent redundancies areintroduced; this error does not affect the coordinate estimationsbut involves a significant underestimation of the covariances. Analternative approach (VAD) has been discussed: a test performedon a network of about 100 permanent stations belonging to theEuropean EPN network demonstrates that VAD provides accu-racies and estimates very similar to those obtained by a Batchrigorous adjustment: this is true also if the daily VAD subnet-work configurations are randomly generated and not optimized.More analyses on some optimality criterion will be performed inthe next future.

ACKNOWLEDGEMENTS

RDN, ItalPoS and GPSLombardia data have been provided re-spectively by Istituto Geografico Militare, Leica Geosystems Italiaand IREALP-Istituto di Ricerca per l’Ecologia e l’Economia Ap-plicate alle Aree Alpine. The present work has been partiallysupported by the the “Galileo and the modernized satellite posi-tioning” Italian PRIN 2006 project funded by the Italian Ministryof University (MIUR).

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