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The aim of the work was to analyze temporal changes of the impact of multipath propagation of GNSS pseudo-range signal used for positioning (determined via code pseudorange observations) during the calendar year, depending on weather conditions change (especially as a result of foliage of trees, changes in surfaces reflectance due to rain or snow, etc.). The analysis was performed on the sequences of one day data measured on a stationary point.



The experiment - long-term GNSS measurements to monitor changes in multipath propagation errors GNSS signal - was implemented at the field laboratory of the Research Institute of Geodesy, Topography and Cartography, v.v.i. - Geodetic Observatory Pecny in Ondrejov near Prague.

For measurements it was selected position, from which the view of the sky is limited by nearby buildings, structures, and particularly metal shed deciduous and coniferous woods. The following photos show the location of before-described obstacles in the area. The simple plan describes the distances to the biggest obstacle - the main building of the observatory.

Covering of the "sky plot" shows the Figure 2.

2.2. DATA

The Trimble SPS855 receiver with antenna Trimble Zephyr Model 2 was used for measurements in experiment to receive signals on two frequencies of GNSS navigation systems NAVSTAR GPS and GLONASS, however, only data from the NAVSTAR GPS were processed. The registration of meteorological data was concurrently performed (especially temperature, humidity and atmospheric pressure).

Basic measurement unit is one day (24 hours), which was determined with respect to maximizing the sky coverage data from the satellites from different directions. Because the NAVSTAR GPS satellites configuration is repeated with a period of 24 hours sidereal time, it makes no sense to extend the basic measurement unit for several days.

From the measured period (from winter to summer 2015) were selected measurement days, during which the situation in the surrounding obstacles is stable (e. g. permanent snow, rain etc.), and during which it was carried out photographic documentation of the state of the surface and the foliage of trees. Finally, it was selected 23 days for further analysis. The selected data including a description of the situation of surrounding obstacles summarized in the following Table 1 (DOY is the number of day in 2015).


Measured data from GNSS technology - daily files - were tested in terms of multipath signals (multipath) processed by software gNut-Anubis, which is being developed at Geodetic Observatory Pecny. Function of software is described in detail in (Vaclavovic and Dousa, 2016).

Program gNut-Anubis (see e.g. nubis-summary) calculated on the base of the GNSS RINEX set of measured data for a selected point in time: azimuth, elevation and multipath value for all satellites that were observed at this time. In our case, we focused on further processing only on GPS NAVSTAR satellites. In addition to the observation data file software still needs to calculate the appropriate navigation file.

Value multipath MC for frequencies i, j, k is

[mathematical expression not reproducible] (1)

Value multipath on [C.sub.1] code is calculated according to the expression

[mathematical expression not reproducible] (2)

and on the [C.sub.2] code

[mathematical expression not reproducible] (3)

where [P.sub.i] is the pseudorange, [L.sub.i] is a "phase of carrier frequency", expressed in meters, and [f.sub.i] is the corresponding frequency. Phase jumps ("cycle slips") for [L.sub.i] are computed using linear combinations of [L.sub.4] (Melbourn-Wubbena) or [L.sub.6] - see (Vaclavovic and Dousa, 2016).

Multipath calculation is as follows:

For a given number of epochs that are configured through parameters in gNut-Anubis software (in our case it was 20) is determined for a particular signal (e.g., M[C.sub.1]) via linear combination (1), which mainly contains multipath. The number of epochs must be continuous without phase jumps and follows a desired epoch, which is related to the resulting value. The resultant value of multipath is given by the dispersion of the results of the linear combination (1).

In the following text we encounter the term "quadratic mean value" (abbreviated RMS or graphic "root mean square"), which is defined as follows: the quadratic mean m of n values of v is defined by the expression:

[mathematical expression not reproducible] (4)

Data processing into the final result was then carried out by the software:

* Multi-anubis-GPS.for which processes the results of the program-gNut Anubis and for a selected azimuth and elevation (step one degree) searches the maximum value (if the same azimuth, and elevation observed more satellites) multipath on each of the codes C1 and C2.

* Multi-Anubis-GPS-10.for that functions like a multi-program Anubis-GPS.for only seeks maximum and RMS multipath in a spherical trapezoid 10 x 10 degrees due clearer graphical interpretation of the results.

* "Working software" for combination of results of above mentioned software, results of it is "RMS" and maximum values "max".

Given the observational campaign was organized so that the south side of the forest and on the north side of the horizon was overshadowed by the building of the observatory was to select the observations decisive moments foliage of trees, snow cover and relative humidity. The results were shown in addition spreadsheet processing and graphically examples of multipath values for C1 and C2 are for DOY 037 in Figure 3. The complete set of images is subject of the research report (Kostelecky Jr. and Kostelecky, 2015).


The following Table 2 shows the numerical values of multipath in its entirety observed azimuth and altitude satellites. This is the maximum and the mean-square value (see above) for each day.

The following Table 3 shows the mean square value between two multipath somewhat extreme "conditions" of weather. Mean-square value is calculated on the grounds of destination "mean-square value of the effects of uncertainty" in determining the position of the code measurements. To calculate the differences were therefore selected days with different weather conditions.


The analyzed differences of the multipath propagation (multipath) between two, somewhat extreme climatic conditions show, that can be stated: the significant differences in multipath propagation are only in a specific direction to the satellites. The average values vary considerably less. Dependence on changing conditions (seasons) does not significantly change the value of multipath.

Given the relatively very unfavorable configuration of the experiment, the mean square value of the multipath C1 is to about 60 cm and to 40 cm for C2. The dependence on the weather conditions varies between 10 and 20 cm.


The experiment was carried out in the framework of contract research tied to the project Technology Agency TB0200MD051, workplace NTIS in VUGTK, v.v.i. Processing of obtained observing data were computed in the frame of LO1506 (PUNTIS) and project LM2015079 CzechGeo / EPOS.


Kostelecky, J. Jr. and Kostelecky, J.: 2015, Processing long stationary measuring the impact of multipath propagation of GNSS signal at the Geodetic Observatory Pecny. Comprehensive Research Report 1241/2015. VUGTK, v.v.i., Zdiby, 127 pp, (in Czech).

Vaclavovic, P. and Dousa, J.: 2016, G-Nut/Anubis: Open-source tool for multi-GNSS data monitoring with a multipath detection for new signals, frequencies and constellations. In: IAG Symposia Series, Rizos, Ch. and Willis, P. (eds), Springer, 143, 775-782.

DOI: 10.1007/1345_2015_97

Jakub KOSTELECKY (1)), Jan KOSTELECKY (1,) (2)) (*) and Pavel VACLAVOVIC (1))

(1)) Research Institute of Geodesy, Topography and Cartography, GO Pecny - NTIS, 251 65 Ondrejov 244, Czech Republic

(2)) Faculty of Mining and Geology, VSB TU Ostrava, 17 listopadu 15, 708 33 Ostrava, Czech Republic

(*) Corresponding author's e-mail:


Article history:

Received 2 May 2017

Accepted 31 August 2017

Available online 25 September 2017

DOI: 10.13168/AGG.2017.0023

Cite this article as: Kostelecky J Jr, Kostelecky J, Vaclavovic P: Testing of GNSS multipath in different observational conditions at one stationary station. Acta Geodyn. Geomater., 14, No. 4 (188), 425-429, 2017. DOI: 10.13168/AGG.2017.0023
Table 1 Observation Conditions

DOY   Date        snow           leaves          message

037    6.2.2015   yes            no              part of
041   10.2.2015   yes, melting   no              day
043   12.2.2015   yes, partly    no
044   13.2.2015   very small     no
050   19.2.2015   very small     no
062    3.3.2015   no             no              wet
065    6.3.2015   no             no              dry
069   10.3.2015   no             no              dry
077   18.3.2015   no             no              dry
083   24.3.2015   no             no
086   27.3.2015   no             no              wet
089   30.3.2015   no             no
092    2.4.2015   yes            no
093    3.4.2015   yes            no
105   15.4.2015   no             weak sprouting
107   17.4.2015   no             leaves          wet
                                 small leave
110   20.4.2015   no             young leaves
114   24.4.2015   no             yes
124    4.5.2015   no             yes             wet
125    5.5.2015   no             yes             wet
126    6.5.2015   no             yes             wet
127    7.5.2015   no             yes             wet
133   13.5.2015   no             yes             wet

Table 2 Average of multipath in the whole range of azimuths and
elevations, mean square values (RMS) and the maximum of multipath for
each day.

DOY  date       snow     leaves          message      mean  RMS
                                                      [cm]  [cm]

 37   6.2.2015  yes      no              part of day  52    61.5
 41  10.2.2015  melting  no                           53.3  61.7
 43  12.2.2015  partly   no                           52.3  62.2
 44  13.2.2015  small    no                           52.1  61.3
 50  19.2.2015  small    no                           51.9  60.4
 62   3.3.2015  no       no              wet          55    62.5
 65   6.3.2015  no       no              dry          53.6  63.9
 69  10.3.2015  no       no              dry          53.6  62.5
 77  18.3.2015  no       no              dry          54.3  62.8
 83  24.3.2015  no       no                           53.3  61.1
 86  27.3.2015  no       no              rain         54.8  63.6
 89  30.3.2015  no       no                           56.9  65
 92   2.4.2015  yes      no                           55.5  63
 93   3.4.2015  yes      no                           54.5  62.8
105  15.4.2015  no       weak sprouting               55.2  62.9
107  17.4.2015  no       small leaves    wet          53.4  61.4
110  20.4.2015  no       young leaves                 54.6  62.8
114  24.4.2015  no       yes                          51.8  59.5
124   4.5.2015  no       yes             wet          50.9  59.2
125   5.5.2015  no       yes             wet          50.6  57.8
126   6.5.2015  no       yes             rain         51.9  59.2
127   7.5.2015  no       yes             wet          52    58.4
133  13.5.2015  no       yes             wet          49.7  56.5

     C1          C2
DOY  max   mean  RMS   max
     [cm]  [cm]  [cm]  [cm]

 37  501   35.1  39.8  465
 41  299   36.4  41.1  349
 43  447   36    41.8  504
 44  503   35.7  40.6  331
 50  373   35.9  40    303
 62  323   38.1  42.9  461
 65  553   36.9  41.3  305
 69  515   37.1  42.2  317
 77  308   37.5  41.8  403
 83  359   37.1  41.8  389
 86  365   37.7  41.8  242
 89  395   37.9  41.4  301
 92  412   37.6  41.6  278
 93  329   36.7  40.2  233
105  362   37.5  42.3  240

107  280   35.6  39.2  292
110  363   37.8  43    435
114  346   35.5  38.4  181
124  443   35.3  38.1  235
125  410   35.4  39.5  363
126  511   35.2  37.2  262
127  268   35.3  38.3  227
133  467   36.1  39.8  263

Table 3 Mean square value of difference (dRMS) in its entirety azimuths
and elevations and the maximum mean values of the difference between
two multipath periods (DOY1 minus DOY2).

                              C1                   C2
DOY1-DOY2  difference of      dRMS [cm]  max [cm]  dRMS [cm]  max [cm]

037-038    no                 11.4       100       10.5        95
037-065    snow/without snow  22.6       191       16.4       127
069-071    no                 14.5       116        8.7        74
069-086    dry/wet            17.6       111       12.6        97
083-133    trees              13.4       104       15.3       112
           plane /leafed
104-105    no                 11.0        64       15.3       156
124-125    no                 11.0        47       12.3       131
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Article Details
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Title Annotation:ORIGINAL PAPER
Author:Kostelecky, Jakub; Kostelecky, Jan; Vaclavovic, Pavel
Publication:Acta Geodynamica et Geromaterialia
Article Type:Report
Date:Oct 1, 2017

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