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G. Seeber, J. Campbell, L. Wanninger: Nuisance effects in precise GPS positi<strong>on</strong>ing 29<br />

to <str<strong>on</strong>g>the</str<strong>on</strong>g> tropospheric effect <strong>on</strong> vertical positi<strong>on</strong>ing (DEPENTHAL<br />

et al., 2000)<br />

I<strong>on</strong>ospheric propagati<strong>on</strong> delay<br />

Like <str<strong>on</strong>g>the</str<strong>on</strong>g> troposphere also <str<strong>on</strong>g>the</str<strong>on</strong>g> i<strong>on</strong>osphere can be modeled<br />

by <str<strong>on</strong>g>the</str<strong>on</strong>g> available wealth <str<strong>on</strong>g>of</str<strong>on</strong>g> data from ground tracking stati<strong>on</strong>s<br />

and LEO occultati<strong>on</strong>s (KLEUSBERG, 1998). Severe i<strong>on</strong>ospheric<br />

c<strong>on</strong>diti<strong>on</strong>s were experienced during <str<strong>on</strong>g>the</str<strong>on</strong>g> recent years<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> solar maximum. Various studies have been performed<br />

<strong>on</strong> how <str<strong>on</strong>g>the</str<strong>on</strong>g>se effects can be mitigated by <str<strong>on</strong>g>the</str<strong>on</strong>g> use <str<strong>on</strong>g>of</str<strong>on</strong>g> permanent<br />

reference stati<strong>on</strong> networks (WANNINGER, 1999). New aspects<br />

arise with <str<strong>on</strong>g>the</str<strong>on</strong>g> availability <str<strong>on</strong>g>of</str<strong>on</strong>g> additi<strong>on</strong>al frequencies using<br />

<str<strong>on</strong>g>the</str<strong>on</strong>g> forthcoming Galileo system (PANY et al., 2002).<br />

Ambiguity resoluti<strong>on</strong> techniques<br />

Significant progress has been achieved in ambiguity resoluti<strong>on</strong><br />

techniques by a more complete modeling <str<strong>on</strong>g>of</str<strong>on</strong>g> GPS<br />

observati<strong>on</strong>s (WÜBBENA, 2001). Particular investigati<strong>on</strong><br />

improves <str<strong>on</strong>g>the</str<strong>on</strong>g> techniques (GRAFAREND, 2000). Emphasis<br />

is given to near real-time soluti<strong>on</strong>s (KUTTERER, 2000). A<br />

powerful procedure uses data from permanent reference<br />

stati<strong>on</strong>s for an error modelling in real-time (WANNINGER,<br />

2000). This technique reduces distance dependent errors<br />

(orbit, troposphere, i<strong>on</strong>osphere) and at <str<strong>on</strong>g>the</str<strong>on</strong>g> same time it<br />

reduces <str<strong>on</strong>g>the</str<strong>on</strong>g> time to fix ambiguities and increases <str<strong>on</strong>g>the</str<strong>on</strong>g> success<br />

rate <str<strong>on</strong>g>of</str<strong>on</strong>g> ambiguity fixing. In Germany this c<strong>on</strong>cept is widely<br />

used in <str<strong>on</strong>g>the</str<strong>on</strong>g> SAPOS service (AdV, 2002). A modern approach<br />

is <str<strong>on</strong>g>the</str<strong>on</strong>g> modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> error state within a regi<strong>on</strong>al network<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> reference stati<strong>on</strong>s (WÜBBENA et al., 2001) and <str<strong>on</strong>g>the</str<strong>on</strong>g> integrati<strong>on</strong><br />

with c<strong>on</strong>tinental and global networks (WÜBBENA,<br />

2002b). Fur<str<strong>on</strong>g>the</str<strong>on</strong>g>r advantages are expected by <str<strong>on</strong>g>the</str<strong>on</strong>g> inclusi<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> additi<strong>on</strong>al GPS signals (VOLLATH et al., 1999) or Galileo<br />

data (TIBERIUS et al., 2002).<br />

Integrated modelling <str<strong>on</strong>g>of</str<strong>on</strong>g> effects<br />

The dominati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> stati<strong>on</strong> dependent and distance dependent<br />

nuisance effects is intensively treated in permanent reference<br />

stati<strong>on</strong> networks. The procedures in use are stati<strong>on</strong> calibrati<strong>on</strong>,<br />

virtual reference stati<strong>on</strong>s (VRS) and area correcti<strong>on</strong><br />

parameters (ACP). Comprehensive publicati<strong>on</strong>s can be taken<br />

from <str<strong>on</strong>g>the</str<strong>on</strong>g> proceedings <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> annual SAPOS c<strong>on</strong>ferences,<br />

for example AdV (2002). Some key publicati<strong>on</strong>s in this area<br />

are BÖDER et al. (1999), WANNINGER (2000), WÜBBENA<br />

(2002a).<br />

The capacities and limits <str<strong>on</strong>g>of</str<strong>on</strong>g> nuisance effect modeling are<br />

dem<strong>on</strong>strated in a comprehensive intercomparis<strong>on</strong> study.<br />

The overall effect in a data analysis can be c<strong>on</strong>sidered as<br />

a process noise, including s<str<strong>on</strong>g>of</str<strong>on</strong>g>tware noise (selecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a<br />

particular s<str<strong>on</strong>g>of</str<strong>on</strong>g>tware package), operator noise (selecti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

particular opti<strong>on</strong>s), reference frame realizati<strong>on</strong> noise (selecti<strong>on</strong><br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> a set <str<strong>on</strong>g>of</str<strong>on</strong>g> fiducials). As a c<strong>on</strong>sequence, a given data<br />

set will lead to slightly different results, when different<br />

operators work with different s<str<strong>on</strong>g>of</str<strong>on</strong>g>tware packages. A 40-day<br />

l<strong>on</strong>g data set from about 50 stati<strong>on</strong>s <strong>on</strong> <str<strong>on</strong>g>the</str<strong>on</strong>g> sou<str<strong>on</strong>g>the</str<strong>on</strong>g>rn hemisphere<br />

have been analysed with 4 different s<str<strong>on</strong>g>of</str<strong>on</strong>g>tware packages<br />

in 7 laboratories. The mean differences between soluti<strong>on</strong>s<br />

are 1 cm in horiz<strong>on</strong>tal positi<strong>on</strong> and 2 cm in height (DIETRICH<br />

et al., 2001) .<br />

References<br />

AdV: Vorträge des 4. SAPOS Symposiums, 21.-23. Mai 2002<br />

in Hannover. Arbeitsgemeinschaft der Vermessungsverwaltungen<br />

der Länder der Bundesrepublik Deutschland, 2002<br />

AUGATH, W.: Signal and Stati<strong>on</strong> Validati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> GNSS Permanent<br />

Stati<strong>on</strong>s for Precise Positi<strong>on</strong>ing, Wea<str<strong>on</strong>g>the</str<strong>on</strong>g>r Forecast and<br />

Navigati<strong>on</strong>. 5th Setmana Geomatica, Cartography, Telematics<br />

and Navigati<strong>on</strong>. Barcel<strong>on</strong>a. 11.-14.02.2003.<br />

AUGATH, W., BLUMENBACH, TH., WILDT, ST.: SAPOS 2002 Symposium:<br />

Qualitätssicherung bei Referenzstati<strong>on</strong>en und in<br />

Referenzstati<strong>on</strong>snetzen. SAPOS-Symposium 2002,<br />

Hannover, 21.-23.05.2002.<br />

BECKER M., HAEFELE P., PESEC P.: First Results <str<strong>on</strong>g>of</str<strong>on</strong>g> WVR1100<br />

Water Vapor Radiometer Measurements in Graz and <str<strong>on</strong>g>the</str<strong>on</strong>g><br />

CERGOP-2 Project; Proceedings WEGENER 2002,<br />

A<str<strong>on</strong>g>the</str<strong>on</strong>g>ns, June 12-14, 2002, NTUA A<str<strong>on</strong>g>the</str<strong>on</strong>g>ns, Greece.<br />

BECKER M., ZEIDLER C.: GPS Antenneneichung in der Absorberhalle<br />

des EMV Testzentrums Greding, Proc., 4. GPS-<br />

Antennenworkshop, Hannover, 21. Mai 2002, LGN 2002.<br />

BÖDER V., MENGE F.: Kalibrierung v<strong>on</strong> GPS-Referenzstati<strong>on</strong>en;<br />

2. SAPOS-Symposium, Berlin 1999<br />

BÖDER V., MENGE F., SEEBER G., WÜBBENA G., SCHMITZ M.:<br />

How to Deal With Stati<strong>on</strong> Dependent Errors – New<br />

Developments <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> Absolute Calibrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> PCV and<br />

Phase-Multipath With a Precise Robot; Proceedings <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>the</str<strong>on</strong>g> 14th Inter<str<strong>on</strong>g>nati<strong>on</strong>al</str<strong>on</strong>g> technical Meeting <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> Satellite<br />

Divisi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Navigati<strong>on</strong> ION GPS 2001,<br />

Salt Lake City 2001<br />

BÖDER V.: Zur hochpräzisen GPS-Positi<strong>on</strong>s- und Lagebestimmung<br />

unter bes<strong>on</strong>derer Berücksichtigung mariner Anwendungen.<br />

Wiss. Arbeiten der Fachrichtung Vermessungswesen<br />

der Universität Hannover, Nr. 245, 2002<br />

CAMPBELL J., SEEBER G.: 4. GPS-Antennenworkshop am 21.<br />

Mai 2002 im Rahmen des 4. SAPOS-Symposiums in<br />

Hannover. Zeitschrift für Geodäsie, Geoinformati<strong>on</strong> und<br />

Landmanagement (zfv) 128 (2002), 335, Proceedings <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

<str<strong>on</strong>g>the</str<strong>on</strong>g> Workshop available at www.lgn.de<br />

DEPENTHAL C., MAYER M., KUTTERER H., LINDNER K., HECK<br />

B.: Einfluss der Atmosphäre auf GPS-Beobachtungen im<br />

Bereich der Antarktis; in: Dietrich R. (Ed..): Deutsche Beiträge<br />

zu GPS-Kampagnen des Scientific Committee <strong>on</strong><br />

Antarctic Research (SCAR) 1995-1998. DGK B 310,<br />

München 2000, 195-199<br />

DIETRICH R., DACH R., ENGELHARDT G., IHDE J., KORTH W.,<br />

KUTTERER H.-J., LINDNER K., MAYER M., MENGE F.,<br />

MILLER H., MÜLLER C., NIEMEIER W., PERLT J., POHL M.,<br />

SALBACH H., SCHENKE H.-W., SCHÖNE T., SEEBER G., VEIT<br />

A., VÖLKSEN C.: ITRF coordinates and plate velocities<br />

from repeated GPS campaigns in Antarctica – an analysis<br />

based <strong>on</strong> different individual soluti<strong>on</strong>s; Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Geodesy,<br />

74, 756-766, 2001<br />

EISSFELLER B., TIBERIUS C., PANY T., BIBERGER R., SCHÜLER<br />

T., HEINRICHS G.: Instantaneous Ambiguity Resoluti<strong>on</strong><br />

for GPS/Galileo RTK Positi<strong>on</strong>ing; Proceedings <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> 9th<br />

Saint Petersburg Inter<str<strong>on</strong>g>nati<strong>on</strong>al</str<strong>on</strong>g> C<strong>on</strong>ference <strong>on</strong> Integrated<br />

Navigati<strong>on</strong> Systems, Russia, St. Petersburg, 27-29<br />

GÖRRES, B.: Kalibrierung v<strong>on</strong> GPS-Antennen. VDV-Schriftenreihe,<br />

Band 19 “GPS-Referenzstati<strong>on</strong>sdienste”, Verlag<br />

Chmielorz GmbH, Wiesbaden 2001, 31-46<br />

GRAFAREND E.W.: Mixed integer-real valued adjustment (IRA)<br />

problems: GPS initial cycle ambiguity resoluti<strong>on</strong> by means<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> LLL algorithm; GPS Soluti<strong>on</strong>s 4 (2000) 31-44

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