<p>Phase Center Corrections (PCC) are essential for precise GNSS positioning, yet differences between calibration sets (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Delta \)</EquationSource> </InlineEquation>PCC) are often evaluated at the pattern level, which complicates an assessment of their practical relevance for estimated geodetic parameters. We present <Emphasis FontCategory="NonProportional">PCC</Emphasis>-Explorer, an open-source tool written in Python that standardizes the forward propagation of PCC and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Delta \)</EquationSource> </InlineEquation>PCC into the parameter domain without requiring GNSS observation data. The approach combines a linearized observation model in a topocentric frame (North, East, Up, receiver clock error, tropospheric part), an elevation-dependent stochastic model, and a second weighting matrix that reflects the local satellite distribution as a function of geographic location, time span, and sampling rate. A least-squares adjustment yields parameter deviations averaged over user-defined output intervals and supports multi-GNSS single frequencies and ionosphere-free linear combinations (IF-LC). Using <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\Delta \)</EquationSource> </InlineEquation>PCC between chamber and robot calibrations of a LEIAR25.R4 LEIT antenna, we show that daily parameter deviations are dominated by the Up component and the receiver clock error, while horizontal and tropospheric effects remain within ±1&#xa0;mm. The impact varies mainly with latitude, reflecting the constellation geometry: for GPS IF-LC the Up component rises from <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\approx \)</EquationSource> </InlineEquation>1–3.5&#xa0;mm between <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\pm 55^\circ \)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\approx \)</EquationSource> </InlineEquation>14&#xa0;mm near the poles. GLONASS impacts are smaller (<InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\approx \)</EquationSource> </InlineEquation>0.5–4.5&#xa0;mm) and show stronger longitudinal variability. Shorter parameter output intervals (e.g., 3&#xa0;h) yields pronounced variability driven by changing satellite geometry. Over three years, the GPS mean 3D impact is 2.72&#xa0;mm (range 7.35&#xa0;mm), with periods consistent with sidereal repeats. Validation with differential PPP results at two EUREF Permanent Network (EPN) sites shows agreement at the sub-millimeter to millimeter level. The results underline that large pattern-level <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\Delta \)</EquationSource> </InlineEquation>PCC may map into the receiver clock or remain unsensed, motivating parameter-domain assessments. <Emphasis FontCategory="NonProportional">PCC-Explorer</Emphasis> enables transparent, comparable studies across sites, intervals, and processing settings, and will be open source for the user community.</p>

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PCC-Explorer: An open-source software tool to assess the impact of GNSS antenna phase center corrections on geodetic parameters

  • Johannes Kröger,
  • Tobias Kersten,
  • Steffen Schön

摘要

Phase Center Corrections (PCC) are essential for precise GNSS positioning, yet differences between calibration sets ( \(\Delta \) PCC) are often evaluated at the pattern level, which complicates an assessment of their practical relevance for estimated geodetic parameters. We present PCC-Explorer, an open-source tool written in Python that standardizes the forward propagation of PCC and \(\Delta \) PCC into the parameter domain without requiring GNSS observation data. The approach combines a linearized observation model in a topocentric frame (North, East, Up, receiver clock error, tropospheric part), an elevation-dependent stochastic model, and a second weighting matrix that reflects the local satellite distribution as a function of geographic location, time span, and sampling rate. A least-squares adjustment yields parameter deviations averaged over user-defined output intervals and supports multi-GNSS single frequencies and ionosphere-free linear combinations (IF-LC). Using \(\Delta \) PCC between chamber and robot calibrations of a LEIAR25.R4 LEIT antenna, we show that daily parameter deviations are dominated by the Up component and the receiver clock error, while horizontal and tropospheric effects remain within ±1 mm. The impact varies mainly with latitude, reflecting the constellation geometry: for GPS IF-LC the Up component rises from \(\approx \) 1–3.5 mm between \(\pm 55^\circ \) and \(\approx \) 14 mm near the poles. GLONASS impacts are smaller ( \(\approx \) 0.5–4.5 mm) and show stronger longitudinal variability. Shorter parameter output intervals (e.g., 3 h) yields pronounced variability driven by changing satellite geometry. Over three years, the GPS mean 3D impact is 2.72 mm (range 7.35 mm), with periods consistent with sidereal repeats. Validation with differential PPP results at two EUREF Permanent Network (EPN) sites shows agreement at the sub-millimeter to millimeter level. The results underline that large pattern-level \(\Delta \) PCC may map into the receiver clock or remain unsensed, motivating parameter-domain assessments. PCC-Explorer enables transparent, comparable studies across sites, intervals, and processing settings, and will be open source for the user community.