Mitigation of the ionospheric and tropospheric errors

It is carried out a cycle of researches on estimation of the ionospheric delays spatial and temporal features (their single and double differences) with the purpose of determination of opportunities of using single-frequency GNSS equipment for centimeter accuracy positioning on middle baselines up to ~100 km.

It is developed the algorithmic and software toolset of estimation of the current integral zenith tropospheric delays (ZTD) with centimeter accuracy level by use of carrier-phase GNSS measurements of the network of permanent reference stations. In their turn, ZTD estimations are used for their interpolation (in conditions when it is possible and expedient) to the current GNSS user position with the purpose of positioning accuracy increase.

A number of the research results on the ionospheric delays features and realizing the methods of their compensation are given in the publications:


  1. Жалило, А.А., Е.А. Бессонов О проблеме учета ионосферной задержки навигационных сигналов в задачах точного ГНСС-позиционирования// 4-й Международный радиоэлектронный форум «Прикладная радиоэлектроника. Состояние и перспективы развития»: Харьков, ХНУРЭ. - 2011. - т. 1, №2. - C. 62 – 65;
  2. Жалило А.А., Бессонов Е.А. Повышение точности дифференциального одночастотного ГНСС-позиционирования путём сетевой коррекции ионосферных погрешностей// Всеукраинский межведомственный научно-технический сборник «Радиотехника». - № 169. - 2012 г. - С. 302-314;
  3. Желанов А.А. Бессонов Е.А. Использование глобальных ионосферных карт IGS в задачах высокоточного ГНСС-позиционирования// журнал "Прикладная радиоэлектроника". - 2011 г. - Т.10 №3.- С. 302-306;
  4. Бессонов Е.А. Аппроксимация гладкими функциями расчетных ионосферных коррекций в задачах точного ГНСС-позиционирования// Всеукраинский межведомственный научно-технический сборник «Радиотехника». - 2011 г. - №165.- С. 69-74;

Brief results on mitigation of ionospheric and tropospheric errors on positioning accuracy are given in the abridged form in the report «Estimation and mitigation of GNSS positioning ionospheric and tropospheric errors by use of season daily samples of GNSS permanent stations observations in Kharkov region» (the given work is carried out by partial financing according to the Agreement №ДЗ/467-2011 with Derzhinformnauka of Ukraine).

The detailed results of the researches carried out in 2011-2012 are at the stage of publication and will be posted on the Web-page later together with the results of the current researches of 2013.

One of the tasks of the current stage (2013) is assessment of spatial and temporal changes of the Total Electron Content (TEC) over the territory of Ukraine using GNSS observations of the ground network of permanent (continuously operating) reference stations (~60 stations). This scientific project is executed by financing of the National Academy of Sciences (NAS) of Ukraine with the purpose of creating the system (hardware and software means) of gathering, processing and analysis of GNSS observations of ground stations of Ukraine to support the project «Ionosat-Micro».

map_gnss_station

Fig. 1 - GNSS reference stations network located in the territory of Kiev, Cherkassy, Chernigov regions of Ukraine

It is supposed that as a result of the development it will be created and researched the regional spatial-temporary 2D TEC model of high resolution. This model will also allow improving the accuracy of ionospheric errors compensation (in comparison with Klobuchar ionospheric model, GIM IONEX and SBAS grid models, etc.) for navigation and positioning.

Below are given some illustrations of research results (2010-2012 [1]) of spatial-temporal features of the ionospheric delays and the ionospheric variations effect on differential single L1 GNSS positioning reliability and accuracy.

For the purposes of researching there are used dual frequency observations (2008) of the network of dual-frequency permanent reference GNSS stations in Kiev, Cherkassy and Chernigov regions of Ukraine (see Figure 1). In order to select the ionosphere delay variation component by use of the ionospheric «Geometry-Free» (GF) combination of carrier-phase observations the procedure of «detrending» is applied. For each of the station of the network there are obtained the absolute values of the ionospheric delays variations. The examples of non-differential variations of the ionospheric delays for several GPS satellites of the working constellation are presented in Fig. 2. The ionospheric variations dependence of time are shown in the pictures for several pairs of stations with baselines: «BOBR» – «GLSV» (~75 km), «SHDA» - «GLSV» (~97 km),» – «PRYL» - «GLSV» (137 km), «SMLA» – «GLSV» (~162 km). This allowed comparing and assessing the spatial-temporal correlations as well as the effectiveness of mutual compensation of variations on various baselines.

On the whole, the variation ionospheric component is characterized by periods of variations ~5-20 min and levels of variations ~5-50 cm. On medium (~50-75 km) and large (~150-200 km) baselines the ionospheric delays variations are characterized by low spatial-temporal correlation and cannot be compensated with reasonable (centimeter) accuracy by use of the differential method and/or conventional «trend» ionospheric models. On small baselines (up to ~10-15 km) the residual differential ionospheric variations are comparable with carrier-phase observations noise and multipath level.

Much greater effectiveness of user observations ionospheric error compensation is achieved by using the additional network ionospheric corrections (see more detail in work [2]).

To analyze the effectiveness of the method of the additional network ionospheric correction on baselines up to ~100 km there were used the observations of the network with baselines up to ~160 km. «GLSV» station is chosen as a leading reference station. The examples of interpolation/extrapolation results of the ionospheric delays formed on the baselines «SMLA»- «GLSV» and «PRYL» – «GLSV» on the baselines «SHDA»–«GLSV» (~97 km) and «BOBR»–«GLSV» (~75 km) are presented in Fig. 3–6.

On the whole, the additional ionospheric delays network correction allows practically full eliminating of the ionospheric delay trend component (maximum errors do not exceed ~1–2 cm) and considerably (on average up to ~40%) reducing the differential ionospheric variations level.


iono_variations_BOBR-GLSV iono_variations_SHDA-GLSV iono_variations_BOBR-PRYL iono_variations_SHDA-PRYL iono_variations_BOBR-SMLA iono_variations_SHDA-SMLA iono_variations_GLSV-SMLA iono_variations_GLSV-PRYL
Fig. 2 – Examples of «non-differential» ionospheric variations for different pairs of stations and for several GPS satellites

iono_extrapolation_BOBR-GLSV_SV10-SV21 iono_extrapolation_BOBR-GLSV_SV18-SV21
Before entering the network corrections, RSS=3,5 cm.
After entering the network corrections RSS decreased by 31%
Before entering the network corrections, RSS=5,1 cm.
After entering the network corrections RSS decreased by 15%

Fig. 3 – Initial («true») and extrapolated double differences of ionospheric delays on baseline «BOBR»-«GLSV»
a) for SV10-SV21 satellites,
b) for SV18-SV21 satellites


iono_extrapolation_BOBR-GLSV_SV22-SV21 iono_extrapolation_BOBR-GLSV_SV30-SV21
Before entering the network corrections, RSS=4,8 cm.
After entering the network corrections RSS decreased by 10%
Before entering the network corrections, RSS=6,55 cm.
After entering the network corrections RSS decreased by 21%

Fig. 4 - Initial («true») and extrapolated double differences of ionospheric delays on baseline «BOBR»- «GLSV»
a) for SV22-SV21 satellites,
b) for SV30-SV21 satellites,


iono_interpolation_SHDA-GLSV_SV18-SV21 iono_interpolation_SHDA-GLSV_SV6-SV21
Before entering the network corrections, RSS=6,26 cm.
After entering the network corrections RSS decreased by 47%
Before entering the network corrections, RSS=10,2 cm.
After entering the network corrections RSS decreased by 39%

Fig. 5 - Initial («true») and interpolated double differences of ionospheric delays on baseline «SHDA»-«GLSV»
a) for SV6-SV21 satellites,
b) for SV18-SV21 satellites


iono_interpolation_SHDA-GLSV_SV15-SV21 iono_interpolation_SHDA-GLSV_SV22-SV21
Before entering the network corrections, RSS=13 cm.
After entering the network corrections RSS decreased by 23%
Before entering the network corrections, RSS=6,18 cm.
After entering the network corrections RSS decreased by 39%

Fig. 6 – Initial («true») and interpolated double differences of ionospheric delays on baseline «SHDA»-«GLSV»
a) for SV15-SV21 satellites,
b) for SV22-SV21 satellites