<p>As part of the ongoing system modernization, the Russian navigation satellite system GLONASS has specified a dedicated electron density model supporting ionospheric path delay corrections for single-frequency navigation users. Solar-geophysical parameters for use with this model are made available through the code division multiple access (CDMA) signals, transmitted by selected GLONASS-K1, -K2 and -M+ satellites on the L3 and L1 frequencies. As a notable feature, the GLONASS ionosphere model can be used to predict the slant total electron content (STEC) through numerical integration of the 3-dimensional electron density along the signal path or a single-layer approximation of the 2-dimensional vertical total electron content (VTEC). Based on reference TEC values provided by global ionosphere maps, the performance of the GLONASS ionosphere model is assessed over an 11-year period using measured solar flux and geomagnetic activity values and compared with correction models of the GPS and Galileo constellations. Furthermore, the quality of solar-geophysical parameters made available in the CDMA navigation message over 1 year after launch of the first GLONASS-K2 satellite is evaluated. Compared to global ionosphere maps of the International GNSS Service, the GLONASS model exhibits VTEC biases in the range of roughly <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10291_2025_1939_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="73" /> </InlineMediaObject> <EquationSource Format="TEX">${\pm 1}\,\textrm{TECU}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mo>±</mo> <mn>1</mn> </mrow> <mspace width="0.166667em" /> <mtext>TECU</mtext> </mrow> </math></EquationSource> </InlineEquation>. Mean absolute errors (MAE) range from about <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10291_2025_1939_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">${5}\,\textrm{TECU}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>5</mn> <mspace width="0.166667em" /> <mtext>TECU</mtext> </mrow> </math></EquationSource> </InlineEquation> in quiet years to 16 TECU at high solar activity. The corresponding mean absolute percentage errors (MAPE) range from roughly 50% (high activity) to 60% (low activity). Only minor performance differences were observed when comparing predictions based on broadcast values of solar flux and geomagnetic activity with observed values from space weather centers. On the other hand, a clear reduction of both the mean absolute (3–14 TECU) and mean absolute percentage errors (41–45%) is achieved when adjusting the adaptation coefficient of the GLONASS model based on the daily mean ratio of predicted and observed VTEC values. Irrespective of this, major VTEC modeling problems at very high solar activity could be identified. Overall, the GLONASS model outperforms the Klobuchar model but does not reach the prediction performance of the Galileo NeQuick-G and NTCM-G models, which exhibit errors of about 2–8 TECU (MAE) and 26–37% (MAPE).</p>

Characterization and performance assessment of the GLONASS ionosphere model

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2025年7月28日

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O. Montenbruck,
C. Price Gonzalez,
P. Steigenberger

摘要

As part of the ongoing system modernization, the Russian navigation satellite system GLONASS has specified a dedicated electron density model supporting ionospheric path delay corrections for single-frequency navigation users. Solar-geophysical parameters for use with this model are made available through the code division multiple access (CDMA) signals, transmitted by selected GLONASS-K1, -K2 and -M+ satellites on the L3 and L1 frequencies. As a notable feature, the GLONASS ionosphere model can be used to predict the slant total electron content (STEC) through numerical integration of the 3-dimensional electron density along the signal path or a single-layer approximation of the 2-dimensional vertical total electron content (VTEC). Based on reference TEC values provided by global ionosphere maps, the performance of the GLONASS ionosphere model is assessed over an 11-year period using measured solar flux and geomagnetic activity values and compared with correction models of the GPS and Galileo constellations. Furthermore, the quality of solar-geophysical parameters made available in the CDMA navigation message over 1 year after launch of the first GLONASS-K2 satellite is evaluated. Compared to global ionosphere maps of the International GNSS Service, the GLONASS model exhibits VTEC biases in the range of roughly ${\pm 1}\,\textrm{TECU}$ $\pm 1 TECU$ . Mean absolute errors (MAE) range from about ${5}\,\textrm{TECU}$ $5 TECU$ in quiet years to 16 TECU at high solar activity. The corresponding mean absolute percentage errors (MAPE) range from roughly 50% (high activity) to 60% (low activity). Only minor performance differences were observed when comparing predictions based on broadcast values of solar flux and geomagnetic activity with observed values from space weather centers. On the other hand, a clear reduction of both the mean absolute (3–14 TECU) and mean absolute percentage errors (41–45%) is achieved when adjusting the adaptation coefficient of the GLONASS model based on the daily mean ratio of predicted and observed VTEC values. Irrespective of this, major VTEC modeling problems at very high solar activity could be identified. Overall, the GLONASS model outperforms the Klobuchar model but does not reach the prediction performance of the Galileo NeQuick-G and NTCM-G models, which exhibit errors of about 2–8 TECU (MAE) and 26–37% (MAPE).