Impacts of forest spatial structure on variation of the multipath phenomenon of navigation satellite signals

Abstract

The GNSS (Global Navigation Satellite System) receivers are commonly used in forest management in order to determine objects coordinates, area or length assessment and many other tasks which need accurate positioning. Unfortunately, the forest structure strongly limits access to satellite signals, which makes the positioning accuracy much weak comparing to the open areas. The main reason for this issue is the multipath phenomenon of satellite signal. It causes radio waves reflections from surrounding obstacles so the signal do not reach directly to the GNSS receiver's antenna. Around 50% of error in GNSS positioning in the forest is because of multipath effect. In this research study, an attempt was made to quantify the forest stand features that may influence the multipath variability. The ground truth data was collected in six Forest Districts located in different part of Poland. The total amount of data was processed for over 2,700 study inventory plots with performed GNSS measurements. On every plot over 25 forest metrics were calculated and over 25 minutes of raw GNSS observations (1500 epochs) were captured. The main goal of this study was to find the way of multipath quan-tification and search the relationship between multipath variability and forest structure. It was reported that forest stand merchantable volume is the most important factor which influence the multipath phenomenon. Even though the similar geodetic class GNSS receivers were used it was observed significant difference of multipath values in similar conditions.

Full text

Folia Forestalia Polonica, Series A – Forestry, 2019, Vol. 61 (1), 3–21
ORIGINAL ARTICLE
© 2019 by the Committee on Forestry Sciences and Wood
Technology of the Polish Academy of Sciences
and the Forest Research Institute in S´kocin Stary Received 27 December 2018 / Accepted 29 January 2019
DOI: 10.2478/ffp-2019-0001
Impacts of forest spatial structure on variation of the
multipath phenomenon of navigation satellite signals
Michał Brach1 , Krzysztof Stereńczak2, Leszek Bolibok3, Łukasz Kwaśny1,
Grzegorz Krok2, Michał Laszkowski2
1 Warsaw University of Life Sciences – SGGW, Faculty of Forestr y, Department of Geomatics and Land Management,
Nowoursynowska 159, 02-776 Warsaw, Poland, phone: +48 602487647, fax: +48225938239,
e-mail: michal.brach@wl.sggw.pl
2 Forest Research Institute, Department of Geomatics, Sękocin Stary, Braci Leśnej 3, 05-090 Raszyn, Poland
3 Warsaw University of Life Sciences – SGGW, Faculty of Forestr y, Department of Silviculture, Nowoursy nowska 159,
02-776 Warsaw, Poland
AbstrAct
The GNSS (Global Navigation Satellite System) receivers are commonly used in forest management in order to determine
objects coordinates, area or length assessment and many other tasks which need accurate positioning. Unfortunately, the
forest structure strongly limits access to satellite signals, which makes the positioning accuracy much weak comparing
to the open areas. The main reason for this issue is the multipath phenomenon of satellite signal. It causes radio waves
reections from surrounding obstacles so the signal do not reach directly to the GNSS receiver’s antenna. Around 50%
of error in GNSS positioning in the forest is because of multipath effect. In this research study, an attempt was made to
quantify the forest stand features that may inuence the multipath variability. The ground truth data was collected in six
Forest Districts located in different part of Poland. The total amount of data was processed for over 2,700 study inventory
plots with performed GNSS measurements. On every plot over 25 forest metrics were calculated and over 25 minutes of
raw GNSS observations (1500 epochs) were captured. The main goal of this study was to nd the way of multipath quan-
tication and search the relationship between multipath variability and forest structure. It was reported that forest stand
merchantable volume is the most important factor which inuence the multipath phenomenon. Even though the similar
geodetic class GNSS receivers were used it was observed signicant difference of multipath values in similar conditions.
Key words
GNSS, multipath, random forest, Borut, forest structure, LiDAR
IntroductIon
The availability of satellite navigation has become
a permanent fact of life and exercises a practical im-
pact on the effective functioning of many aspects of the
economy (Closas et al. 2009). The concept of the linear
intersection technique introduced in the 1960s – real-
ized through a measurement of distances from a mini-
mum of four satellites (Teng et al. 2016) – has undergone
continual improvement. The Global Positioning System

Folia Forestalia Polonica, Series A – Forestry, 2019, Vol. 61 (1), 3–21
Michał Brach, Krz ysztof Stereńc zak, Leszek Bolibok, Łukasz Kwaśny, Grzegorz Krok, Michał Laszkowski
4
(GPS – the original name NAVSTAR-GPS) launched by
the United States Department of Defense provided the
foundations for the dynamic development of such tech-
nology by other countries. The best example of this is
the Russian GLONASS (GLObalnaja NAvigatsionnaja
Sputnikovaja Sistema) that reached full operational ca-
pacity in 2011 (Kaartinen et al. 2015). Although it is sig-
nicantly weaker than the US American system (Blum
et al. 2016), it meaningfully complements it by increas-
ing the possibilities for precise positioning in places of
limited accessibility to a satellite signal (Al-Shaery et
al. 2013). The existence of two independent navigation
systems enabled the creation of GNSS (Global Navi-
gation Satellite System) devices, characterized by re-
ceivers capable of registering signals from more than
one system. Dynamic development of the technologies
and the economic growth of developing countries have
caused GNSS to undergo a major transformation in re-
cent years. The Chinese system BeiDou-2 and the Eu-
ropean system Galileo (26 satellites on the space in De-
cember 2018 were reported on European Space Agency
web page) will soon achieve operational capacity, which
in practice translates into access to over 70 satellites to-
day and roughly 120 within the next few years (Li et
al. 2015). The benets for potential users are clear and
will be manifested primarily through an increase in ac-
curacy and stability of positioning, as well as through
a reduction in registration time and an increase in the
distances allowable between a receiver and reference
stations (Paziewski and Wielgosz 2014). This means
that researchers and engineers face signicant new
challenges related to improving receivers and further
developing navigation systems.
GNSS has eliminated traditional navigation and
become an everyday practice in surveying, as well as in
elds connected with the monitoring of environmental
resources. The system’s abilities have also been noted
in forestry, because of its high capacity and simplic-
ity in the effective collection of spatial data (Liu et al.
2017). The precise measurement of a forest is one of the
key elements in accurately estimating forest resources
(Liu et al. 2016). GNSS technology ts perfectly with
the concept of precision forestry that requires detailed
measurement of a forest and whose effects are seen in
the accurate estimation of forest resources (Holopain-
en et al. 2014). The ability to use navigational devices
has become a necessity and is one of the criteria for
evaluating prospective employees applying for jobs
in organizations performing forest management (Bet-
tinger and Merry 2018). The basic tasks executed with
this method still include the measuring of lengths and
areas, which in practice is achieved by use of the sim-
plest consumer-grade receivers. Problems relating to
the precision of the receivers deployed and the selection
of appropriate measuring techniques remain open and
require further study (Unger et al. 2013). The increased
need for spatial data causes navigational receivers to
be used for ever more varied tasks with varying levels
of expected accuracy, in areas such as re prevention,
forest utilization, forest conservation, spraying, and
boundary determination (Pirti 2016). The populariza-
tion of laser scanning technologies has made it possible
to obtain forest descriptions of previously unmatched
detail like vegetation height, crown cover, amount of
trees, biomass and general stand structure (Luo et al.
2017; Stereńczak et al. 2017; Kamińska et al. 2018;
Szostak et al. 2018), which has opened new possibilities
for precision forest utilization (Stereńczak and Moska-
lik 2015; Erfanifard et al. 2018; Mielcarek et al. 2018).
In this context, accuracy of positioning becomes key,
because it impacts the functioning of systems used for
estimating the mass of harvested timber (Frank and
Wing 2014), and GNSS receivers are deployed in the
steering of forestry machines and in semiautomated
tree-felling (Holden et al. 2001). Unfortunately, a satel-
lite signal traveling a distance of ca. 20,000 kilometers
undergoes multiple deformations, and the forest envi-
ronment (Closas et al. 2009) and even cosmic weather
(Hapgood 2017) can constitute obstacles that prevent
any measurement altogether. In spite of continuous
technological development and the millimeter preci-
sion achieved by GNSS receivers, it is only possible to
eliminate a portion of the factors degrading the signal,
including clock biases, ephemeris errors, and iono-
spheric and tropospheric delay (Suski 2012). In practice,
the surrounding forest structure (of which a forest is an
especially structurally complex type) offers decidedly
more factors that may affect triangulation. Rain and the
elevated humidity accumulated amidst trees weakens
access to satellite signals, which results in a decreased
number of visible satellites and worsening of the con-
stellation dened by a rise in the PDOP (Position Di-
lution of Precision) coefcient and the need for a dif-
ferent conguration of the GNSS receiver (Frank and

Folia Forestalia Polonica, Series A – Forestry, 2019, Vol. 61 (1), 3–21
Impacts of forest spat ial str ucture on variat ion of the multipath phenomenon of navigation satellite signals 5
Wing 2014). The concealing of the sky by nearby plants
and trees is a key factor (Weaver et al. 2015). The pres-
ence of trees can also impact the precision of position-
ing by affecting the state of foliage (Dogan et al. 2014;
Ucar et al. 2014), temperature, cloud cover (Danskin et
al. 2009b), and the occurrence of forest roads or aspect
which cause number of satellite limitation (Zimbelman
and Keefe 2018). The complexity of forest spatial struc-
tures, combined with a continuously growing need for
accurate positioning, provides the justication for fur-
ther – and more detailed – research into the problem of
the functioning of satellite navigation in forest envi-
ronments. Contributors to GNSS positing errors have
been identied in the number of trees, their diameter at
breast height (Sigrist et al. 1999; Kaartinen et al. 2015),
and the biomass and volume of trees, which have a di-
rect inuence on increasing signal noise and changing
the polarization of the carrier wave (Liu et al. 2016).
Wright (2018) has proposed the index of absorption of
the navigational signal by the tree stand. Liang et al.
(2014) was unable to obtain a centimeter precision even
when using a modern terrestrial laser scanner equipped
with an advanced IMU (Inertial Measurement Unit)
module and performing differential correction. One of
the best method to improve accuracy in the forest base
on differential correction technique which can be real-
ized in real time on in post-processing mode. The re-
search conducted by Szostak and Wężyk (2013) suggest
differential correction and extended epochs acquisition
usage in forest condition. The results have showed the
twofold increase of positioning accuracy however the
limitation of Internet coverage in the forest is one of the
key problem of this method.
MultIpAth sAtellIte sIgnAl ph enoMenon
A prevailing majority of similar studies have focused on
discovering the spatial characteristics of forest stands
that affect the nal accuracy of GNSS positioning. In
fact, about 50% of the error results from a phenomenon
of the satellite signal reection, which is referred in lit-
erature to as the “multipath effect” (Akbulut et al. 2017)
and causes deviations that can exceed 100 meters (Gire-
mus et al. 2007). The main factor impacting the varia-
tion in the signal’s reection is the immediate surround-
ings of the GNSS receiver, which is particularly signi-
cant in a forest environment (Cheng et al. 2016a), as well
in the vicinity of pools of water, mountains, or buildings
(Titouni et al. 2017) or, more generally, of any smooth
surfaces (Strode and Groves 2016). In order to analyze
the essence of the multipath phenomenon (MP) in forest
environment, it is rst necessary to distinguish the part
of the GNSS signal that reaches the receiver antenna di-
rectly, from that reaches it as reected off of surround-
ing objects. A partial loss of satellite signal in the forest
is also often explained by the Lambert-Beer law which,
in its basic form, describes the absorption of light by an
absorbing medium (Wright et al. 2017). The reected
signal has lower power and is delayed, the amplitude of
the carrier wave is diminished, the angle of its arrival at
the receiver is reduced, and it has an altered polarization
(Pirsiavash et al. 2017). The factors described primarily
have an effect on interference in the correct correlation
of code and phase between the GNSS receiver and the
GNSS satellite, thereby introducing signicant errors in
the measurement of distance between them (Groves et
al. 2013). Since the geometry of satellites repeats with
the cycle of the sidereal day, the value of reection at the
same measurement point and given the same observa-
tion conditions should be the same, with a systemic er-
ror of up to a few seconds (Wang et al. 2018a). Determi-
nation of the value of reection of signals MP1 and MP2
is possible through a combination of code and phase
observation for frequencies L1 (GPS: 1575.42 MHz,
GLONASS: 1602 MHz) and L2 (GPS: 1227.60 MHz,
GLONASS: 1246 MHz) emitted independently by the
GPS and GLONASS systems, which can be described
by the following formula (Bakula et al. 2015):
αα
αα
≡−+∝−




+∝−




=
=+−+
∝−




+∝−





≡−
∝−




+∝− −




=
=+−∝−




+∝− −





MP PLL
MB
mm
MP PL L
MB
mm
1 12
1
12
1
2
12
1
2
1
2 2
1
12
1
12
2
1
2
1
1
1
11
12
2
22
12
where:
λλ
αλαλ
α
≡− +∝−




+∝−





≡− ∝−




+∝− −





≡
Bnn
Bn n
f
f
1 2
1
2
1
2
1
2
1
1
11
12
2
21122
1
2
2
2

Folia Forestalia Polonica, Series A – Forestry, 2019, Vol. 61 (1), 3–21
Michał Brach, Krz ysztof Stereńc zak, Leszek Bolibok, Łukasz Kwaśny, Grzegorz Krok, Michał Laszkowski
6
λλ
αλαλ
α
≡− +∝−




+∝−





≡− ∝−




+∝− −





≡
Bnn
Bn n
f
f
1 2
1
2
1
2
1
2
1
1
11122
21
12
2
1
2
2
2
f1 – frequency L1 for GPS or GLONASS satellites,
f2 – frequency L2 for GPS or GLONASS satellites,
ni λi – full value of uncertainty for a phase cycle at fre-
quency i,
Pi – pseudo-distances for frequency i,
Li – wavelength for frequency i,
Mi – multipath value for code measurement at fre-
quency i,
mi – multipath value for phase measurement at fre-
quency i.
The values of MP1 and MP2 have a sinusoidal
character (Fig. 1) and depend on the satellites’ location
in the sky and on the observational smoothing model
implemented in the receiver, which typically remains
a secret of the manufacturer (Irsigler 2010). Knowledge
about MP variability allows for a partial elimination
of receiver and satellite clock errors and compensation
for tropospheric and ionospheric delay (Hilla and Cline
2004). The multipath phenomenon has, for many years,
been a subject of numerous studies whose main goal
was the greatest possible elimination of the occurrence
of oscillations (Weill 2003; Ragheb et al. 2007; Ziedan
2011; Rabaoui et al. 2012; Jgouta and Nsiri 2015). Pro-
posed solutions nd practical applications in new GNSS
receivers, in both the structure of their electronics and
construction of their antennas (Danskin et al. 2009a;
Cheng et al. 2016b). Despite that fact, there is still no
effective method for solving the problem of multipath
GNSS navigational signals in the forest environment
(Wang et al. 2018b).
This study evaluates the impact of selected ele-
ments of the forest environment on modeling the MP1
and MP2 values. Forest stand characteristics are rela-
tively simple to determine in the eld and on the basis
of data given in forest appraisal descriptions. On that
basis, it is possible to estimate the conditions for satel-
lite signal observation in a given forest unit.
object of study
GNSS signals were recorded in 2015 in the forest dis-
tricts of Milicz, Pieńsk, Gorlice and Supraśl. In 2016
in the district of Herby and the sub-district Katrynka.
Only the Gorlice forest district was of mountainous
character (minimum elevation 300 meters, maximum
elevation 830 meters above sea level), the others possess
local elevations that do not have a signicant impact
on the canopy or forest management. The resources of
a decided majority of objects are based on a coniferous
–3
–2
–1
0
1
2
3
0
120 240 360 480 600 720 840 960 1080 1200 1320 1440
Multipath Eect
Time [s]
Figure 1. Juxtaposition of multipath values in an open area (black line) and on a study plot (grey line)

Folia Forestalia Polonica, Series A – Forestry, 2019, Vol. 61 (1), 3–21
Impacts of forest spat ial str ucture on variat ion of the multipath phenomenon of navigation satellite signals 7
tree stand with prevalence of Scots pine (70%). A dom-
inant share of broadleaf species occurs in the Pieńsk
forest district located in the western part of Poland and
in Gorlice, where nearly 45% of the stand area was cov-
ered by beech. Due to a diversity in aggregation of for-
est objects, study plots were located in areas of between
10,000 and 40,000 hectares. In total, 2,704 points were
used for investigation of the GNSS signal multipath ef-
fect ongoing under the canopy (Fig. 2).
For each survey GNSS point, a forest stand inven-
tory was carried out to a diameter of 12.62 m, which
encompassed an area of 500 square meter. The inven-
tory included, among other things, determination of
tree species, age, height of trees with diameter at breast
height (DBH) bigger than 0.07 meter, DBH, and situa-
tion of the trunk with regard to the center of the plot and
with regard to the center of the crown, for trees lean-
ing more than 10 degrees. These inventory data were
used to determine a number of tree stand characteris-
tics (Tab. 1). Tree stand resources per object were de-
termined with regressive methods based on data from
ALS (Airborne Laser Scanning) point clouds and eld
measurements done at the study circle plots. Based on
the digital terrain model (DTM) obtained from the ALS
data, the mean degrees slope and aspect (8 classes) were
indicated (Tab. 1).
study Method
Four different models of dual-frequency GNSS sur-
veyor-class receivers were used for registering raw
data in the RINEX (Receiver Independent Exchange
System) format (Gurtner and Estey 2007). These were
the Trimble R8 GNSS (used no May to November 2015
and March to July 2016), Stonex S9 (used on May to
December 2015 and on April to June 2016), Topcon
HiperPro (used on November 2015) and Leica Viva
GS08plus (used on august to November 2015). The an-
tennas were mounted on a mast with a variable length
of 2.5 to 5 m, depending on the technical abilities of
the measuring team. Twenty-ve minutes (1,500 ep-
ochs) of observations were recorded at each observation
point with the elevation cutoff set to 10 degrees, which
slightly exceeds norms used for open areas (Hofmann-
Wellenhof et al. 2008) and is standard for forest areas
(Hasegawa and Yoshimura 2003). Selected authors
claim that a navigational receiver reaches its maxi-
mum precision after about 10–15 minutes of operation
0 2 km
0 2 km0 2 km 0 2 km
0 2 km 0 2 km
AD
B
F
E C
A B C
D E F
Figure 2. Location of objects of study (A – Pieńsk, B – Herby, C – Supraśl, D – Milicz, E – Katrynka, F – Gorlice) and of study
plots

Folia Forestalia Polonica, Series A – Forestry, 2019, Vol. 61 (1), 3–21
Michał Brach, Krz ysztof Stereńc zak, Leszek Bolibok, Łukasz Kwaśny, Grzegorz Krok, Michał Laszkowski
8
(Bastos and Hasegawa 2013; McGaughey et al. 2017).
In practice, the time used for forest inventory the plots
was much longer, which allowed authors for gathering
surplus data and was compatible with the assertion that
any additional time for the registration of signals in-
creases the accuracy of static positioning (Bettinger and
Merry 2012). Raw observation data were subjected to
a post-processing differential correction process based
on reference data obtained from the three nearest base
stations of the ASG-EUPOS network (Bosy et al. 2007).
This allowed the calculation of coordinates indicating
the center of the inventory plot and estimation of the
precision of measurement described by the standard de-
viation value for the north axis (std.n), east axis (std.e),
shift vector (std.hz), and height (std.n). Calculations
were performed with the Magnet Tools (Topcon Inc.
2013) software, which also allows determination of ba-
sic satellite signal observation parameters (Tab.2). The
Table 1. List of canopy characteristics gathered in study plots
Characteristic Description of characteristic
tree.account Number of trees in circular plot
h.max Maximum tree height in circular plot
h.mean Mean height calculated from all tree heights in circular plot
h.100 Maximum height in circular plot
h.mean.t Mean height weighted by the breast height cross-sectional trunk area
h.100.t Maximum height weighted by the breast height cross-sectional trunk area
w1.tree.account Number of trees in the rst canopy layer
w1.h.max Maximum tree height in the rst layer in circular plot area
w1.h.mean Mean height of the rst layer
w1.h.100 Maximum height of the rst layer
w1.h.mean.t Mean height of the rst layer weighted by the breast height cross-sectional trunk area
w1.h.100.t Maximum height of the rst layer weighted by the breast height cross-sectional trunk area
v.bul Reference tree stand resource from BULiGL measurements
v.lidar Tree stand resource global model for each object
main.species Main species attributed to each division
prec.main.species Share of main species
age.main.species Age of main species
class.age 20 year age class; 6 indicates sixth class or higher
species.typ Canopy type based on main species: coniferous/broadleaf
species.typ.2
Species group calculated on the basis of the share of main species
PURE CONIFEROUS share of dominant coniferous species ≥ 7%
PURE BROADLEAF share of dominant broadleaf species ≥ 7%
MIXED CONIFEROUS share of dominant coniferous species < 7%
MIXED BROADLEAF share of dominant broadleaf species < 7%
prec.conif Share of coniferous species based on LMN from divisions
structure Structure attributed from LMN
slope Mean terrain slope
aspect Mean terrain aspect
aspect.class
Aspect with a division into 8 directional classes: 1 (337.5°–22.5°), 2 (22.5°–67.5°), 3
(67.5°–112.5°), 4 (112.5°–157.5°), 5 (157.5°–202.5°), 6 (202.5°–247.5°), 7 (247.5°–292.5°),
8 (292.5°–337.5°)

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Impacts of forest spat ial str ucture on variat ion of the multipath phenomenon of navigation satellite signals 9
set of data was divided into leaf-off and leaf-on periods
on the basis of photographic documentation of the sky.
Reection of the satellite signal expressed by the
MP1 and MP2 values was obtained with the TEQC
software (Estey and Meertens 1999), which provides
advanced processing of RINEX les. The GPS satel-
lites in RINEX les are recognized with G abbreviation
and GLONASS with R respectively. Multipath statistics
were determined in two groups:
1. for all satellite signals recorded on a study plot with
division into MP1, MP2, and GPS and GLONASS
systems,
2. satellite signals received from the single satellite
characterized by the longest continuous observa-
tion time, with division into MP1 and MP2.
The statistics for both groups were calculated with
the R program (R Core Team 2013). Additionally, the
percentage share of registered signals (prec.positive.sig)
obtained from all satellites with relation to the signals
blocked by the specic forest environment (Tab. 3) was
calculated.
In order to compare the impacts of different param-
eters of the forest complex environment on the digital
value capturing the GNSS signal’s multipath phenome-
non, the Borut algorithm was used (Kursa and Rudnicki
2010, 2015). This algorithm, based on the random for-
ests (RF) model (Breiman et al. 1999), creates a ranking
of analyzed independent variables arranged with regard
Table 2. List of navigational characteristics obtained by
processing raw satellite data in the Magnet Tools program
Charac-
teristic Description of characteristic
xX axis
y Y axis
zHeight
std.n X precision
std.e Y precision
std.hz HZ shift vector
std.z Height precision
time Measurement time
g.sat Number of GPS satellites
r.sat Number of GLONASS satellites
pdop Dimensionless coefcient of three-dimensional
Position Dilution of Precision
hdop Dimensionless coefcient of Horizontal Dilution
of Precision
vdop Dimensionless coefcient of Vertical Dilution of
Precision
antenna.H Height of antenna mounting
receiver Model of GNSS navigational receiver
month Month of measurement
District Object of study
Table 3. List of statistics for the multipath satellite signal effect
Characteristics
group Characteristic Description of characteristic
All satellite signals
mean.12.g, median.12.g,
max.12.g, min.12.g, std.12.g
Mean, median, maximum, minimum, and standard deviation for MP1
multipath effect for the GPS system
mean.12.r, median.12.r, max.12.r,
min.12.r, std.12.r
Mean, median, maximum, minimum, and standard deviation for MP1
multipath effect for the GLONASS system
mean.21.g, median.21.g,
max.21.g, min.21.g, std.21.g
Mean, median, maximum, minimum, and standard deviation for MP2
multipath effect for the GPS system
mean.21.r, median.21.r, max.21.r,
min.21.r, std.21.r
Mean, median, maximum, minimum, and standard deviation for MP2
multipath effect for the GLONASS system
prec.positive.sig.12, prec.positive.
sig.21
Percentage share of signals registered at the point in relation to
signals blocked by the forest environment for MP1 and MP2 values
Satellite signals
for single satellite
mean.sat.12, median.sat.12, max.
sat.12, min.sat.12, std.sat.12
Mean, median, maximum, minimum, and standard deviation for MP1
multipath effect
mean.sat.21, median.sat.21, max.
sat.21, min.sat.21, std.sat.21
Mean, median, maximum, minimum, and standard deviation for MP2
multipath effect

Folia Forestalia Polonica, Series A – Forestry, 2019, Vol. 61 (1), 3–21
Michał Brach, Krz ysztof Stereńc zak, Leszek Bolibok, Łukasz Kwaśny, Grzegorz Krok, Michał Laszkowski
10
to their capacity for explaining the indicated dependent
variable. Results from the calculations make it possible
to determine the Importance of a given characteristic
that represents the number of selections of the given
independent variable by particular decision trees gen-
erated by the RF algorithm (Strobl et al. 2007). This
algorithm allows comparison of variables of differing
characters (quantitative and qualitative), as well as indi-
cating variables that do not have an impact on the value
of the dependent variable. Independent variables are
divided into three main categories: signicant (marked
in green in Fig. 3), uncertain (yellow), and insignicant
(red) (Rai 2017). In the case of each analysis conducted,
the algorithm delivered results after 10,000 iterations,
unless it unequivocally attributed all uncertain vari-
ables to the signicant or insignicant category earlier.
In addition, the RF model (Liaw et al. 2018) was used
for estimating the percentage share of variation of the
numerical value for the multipath phenomenon that is
explicable with information gathered in the studied in-
dependent variables.
results
A set of scripts written in the R language was created
as part of the study. They allow fast processing of data
obtained from the TEQC program created for the in-
terpretation of RINEX les. These scripts facilitated
the rapid processing of over 30,000 text les of a total
volume exceeding 5GB. The possibility of calculating
basic statistics for MP1 and MP2 values for all satel-
lites registered on each study plot and for the single
satellite signal characterized by the longest registra-
tion time is the main result of this procedure. Separate
visual interpretations of the results of the multipath
value for the GPS or GLONASS satellites are an ad-
ditional element (Fig. 4). Due to the standard formats
of RINEX les and results of the TEQC program’s op-
eration, the scripts developed can be successfully used
for further studies in the open environment of the R
program.
The amount of leaves and needles in tree crowns
has key signicance for interpreting the results of the
Figure 3. Example of a result of application of the Borut algorithm with signals from one satellite and MP2 multipath values
that characterizes the Importance of independent variables in leaf-off season

Folia Forestalia Polonica, Series A – Forestry, 2019, Vol. 61 (1), 3–21
Impacts of forest spat ial str ucture on variat ion of the multipath phenomenon of navigation satellite signals 11
multipath effect, because it determines the strength and
number of signals registered by receiver the antenna.
This phenomenon can be expressed more simply by the
amount of light reaching the forest oor, it allows a bet-
ter understanding of the complexity of the canopy struc-
ture (Olpenda et al. 2018). On this basis, the obtained
results have been analyzed in two groups with regard
to the state of the leaf cover (leaf-on and leaf-off). Mul-
tipath oscillations are demonstrated quite well by the
sets of readings registered in open areas and under can-
opy (Fig. 1). Both mean as well as minimum and maxi-
mum values are multiple times greater in cases where
the receiver is surrounded by numerous obstacles. It is
also noticeable that multipath variation is signicantly
less dynamic in cases of a lack of cover.
Based on the obtained percentage share of variation
that explains the studied characteristics, those statistics
from Table 3 were selected whose value exceeded 20
for at least one of the vegetation periods (Tab. 4 and 5).
Table 5. Comparison of the percentage share of variation
explaining the multipath phenomenon for selected statistics
registered by a single satellite
Wave L1 L2
System GNSS
Charac-
teristic
min.
sat.
12
max.
sat.
12
std.sat.
12
min.
sat.
21
max.
sat.
21
std.sat.
21
Leaf-off 6.29 2.82 19.35 19.19 8.89 13.67
Leaf-on 26.66 27.21 33.2 24.24 26.56 32.47
In the case of the initially selected 22 statistics
for all satellites, the percentage share of variation al-
G18
G20
G05
G25
G21
G25
G28
G31
0 2 4 6 8 10 12 14 16 18 20 22 24 26
Satellite
Time
R08
R15
R24
R07
R22
R13
R06
R14
R23
20
15
10
5
0
–5
–10
0 2 4 6 8 10 12 14 16 18 20 22 24 26
Time
Figure 4. Example of results of the functioning of the script written in R to interpret the signal’s multipath effect for the rst
frequency (L1) for the GPS (left) and GLONASS (right) systems
Table 4. Comparison of the percentage share of variation explaining the multipath phenomenon for selected statistics registered
by all available satellites
Wave L1 L2
System GPS GLONASS GNSS GPS GLONASS GNSS
Characteristic median.
12.g
std.
12.r
prec.positive.
sig.12
min.
21.g
min.
21.r
max
21.r
mean.
21.r
std.
21.r
prec.positive.
sig.21
Leaf-off 31.5 28.06 69.11 14.79 37.98 35.92 28.57 59.34 68.95
Leaf-on 18.74 41.13 48.62 38.03 8.29 10.71 2.14 30.52 48.46

Folia Forestalia Polonica, Series A – Forestry, 2019, Vol. 61 (1), 3–21
Michał Brach, Krz ysztof Stereńc zak, Leszek Bolibok, Łukasz Kwaśny, Grzegorz Krok, Michał Laszkowski
12
lowed elimination of 13 characteristics that indicated
very weak correlation. A greater number of character-
istics available for detailed analyses occurs at the L2
frequency and for the GLONASS system. The leaf-off
season is difcult to characterize, if all registered satel-
lites are taken into account. The opposite is observed in
all cases when only one satellite registering data con-
tinuously through over 97% of the operating time on the
study plot is taken into account. Selected characteristics
in this case display an average share of variation of ca.
30% distributed evenly between frequency L1 and L2.
In all analyzed cases, the GLONASS system’s stand-
ard deviation displays decidedly better results for both
frequencies. The total capacity for registering signals is
higher in the leaf-off season by ca. 20% in comparison
to the height of the vegetation period.
The results of the Borut algorithm enabled identi-
cation of the independent variables that can impact the
selected 15 statistical characteristics. The independent
variables were classied into two thematic groups de-
lineating tree stand characteristics (Tab. 1) and navi-
gational characteristics (Tab. 2). The presented results
take into account these characteristics, which were not
registered for a maximum of two of the multipath ef-
fect statistics. The remaining characteristics occurred
signicantly less frequently or were not selected by the
algorithm at all. For the leaf-off season, a total of 12 tree
stand characteristics and 12 navigational characteristics
were selected (Tab. 6), and for the leaf-on season 16 and
14, respectively (Tab. 7). For both types of vegetation
seasons, tree volume and maximum height (h100) are
characterized by a high value of importance. In the case
of navigational characteristics, independent variables
such as the antenna height (antenna.h) and model of
navigational receiver (receiver) are signicant. In com-
parison to other statistics, the standard deviation of the
GLONASS system for both frequencies is characterized
by higher capacities for explaining variation through in-
dependent variables. The values of Importance of one
analyzed satellite and of all observed signals span simi-
lar levels for the analyzed statistics. Only in the case
of the leaf-on season and navigational characteristics
was a doubly high value of Importance observed for all
satellite signals in comparison to the data from a single
satellite. The highest values of Importance (29) were
observed in the case of the type of navigational receiver
(receiver) for statistics dening the percentage share of
signals registered in the leaf-off season. In the case of
this statistic, a strong correlation with time occurs for
all vegetation states of the tree stand. A strong corre-
lation was noted between the percentage share of the
number of registered signals (prec.positive.sig) and the
time of operation of a receiver (time). These values of
Importance are at the level of 23 for the leaf-off season
and 24 for the height of vegetation season.
Among characteristics related to terrain relief,
a small impact was noted for the hill slope. The varia-
tion in standard deviation for L1 and L2 is almost half
as great for the object located in the Gorlice District,
where mean slopes are three times larger than at other
objects of study (Fig. 5).
Multipath eect value
Object of study
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Gorlice Herby Katrynka Milicz Pieńsk Supraśl
mean of std.sat.12
mean of std.sat.21
Figure 5. Values of standard deviation for a single satellite
and L1 and L2 frequencies with respect to the object of study
The impact of the tree stand on the maximum val-
ues of the multipath signal effect is presented for six
dominant species whose prevalence within the tree
population of the study plots was the biggest. Broad-
leaf species maintain a reection index of 14 during the
leaf-off season, regardless of the navigational system or
studied frequency, while during the height of the veg-
etation season these values are twice as high and exceed
30. Birch canopies are particularly worth mentioning,
as they create conditions for a strong multipath signal
effect, which is manifested in their maximum values
(94) and the highest (over 7) standard deviation (Fig. 6
and Tab. 8).

Folia Forestalia Polonica, Series A – Forestry, 2019, Vol. 61 (1), 3–21
Impacts of forest spat ial str ucture on variat ion of the multipath phenomenon of navigation satellite signals 13
The vegetation season does not play a signicant
role for coniferous canopies, although a slightly higher
index was recorded for r. Mean MP1 and MP2 values
are lower by half for the GLONASS system in all cases
(Fig. 6).
The temporal distribution for operation of the
GNSS receivers used in the study was diverse. About
65% of measurements were carried out in the leaf-on
season, except in the case of the Topcon receiver, which
was only used in winter. Apart from the Leica model,
receivers registered lower multipath signal values dur-
ing the leaf-off season. The smallest range of standard
deviation was observed for the Trimble receiver, while
the greatest differences for L1 and L2 frequencies were
observed for the Leica and Stonex receiver models
(Fig. 7).
Table 6. List of the correlation of Importance values between selected statistics for the multipath effect and selected tree stand
and navigational characteristics in the leaf-off season
median.12.g
std.12.r
prec.positive.sig.12
min.21.g
min.21.r
max21.r
mean.21.r
std.21.r
prec.positive.sig.21
min.sat.12
max.sat.12
std.sat.12
min.sat.21
max.sat.21
std.sat.21
All satellites One Satellite
h.max 6.3 6.6 5 3.5 5.8 6.2 4.9 4.9 5 5.1 6 4.9 5.4 6.3 5.6
Tree stand characteristics
h.100 7.4 6.4 5 3.7 5.5 5.9 4.6 5.8 5 6.4 6 6.9 5.2 5.8 6.1
h.mean.t 5.9 7.1 5 3.6 5.9 6.8 5 6.2 5 5.8 6.1 6.2 5.7 6.7 6.9
h.100.t 7.2 6.9 5.1 3.4 5.5 5.9 4.6 5.6 5 6 5.9 6.4 5.5 5.4 6.5
w1.tree.account 4.8 5.1 3.5 2.4 4.3 6 5.2 4.8 3.7 7 7 5 4.6 6.8 2.6
w1.h.max 6.3 6.3 5 3.5 5.8 6.2 4.9 5 5 5.2 6 4.9 5.4 6.4 5.7
w1.h.mean 5.5 8.7 5.8 3.8 5.8 6.5 5.4 6.4 5.4 6.5 6.1 6.1 5.8 7.2 7.1
w1.h.100 7.5 6 5.1 3.3 6 6 4.4 6 5.1 5.6 5.1 5.8 5.1 5.9 5.5
w1.h.mean.t 5.8 7.2 5.3 3.6 5.4 6.4 6 5.3 5.3 6.6 5.3 5 6.5 6.4
w1.h.100.t 7.4 5.9 5.2 3 6 6.1 4.3 6 5.1 5.4 5.1 5.5 5.4 5.6 5.4
v.bul 5.4 8.5 6 5 6.3 7 4.5 7.9 6 12 11 10 7.5 11 11
v.lidar 6.2 9.9 6.9 5.6 6.2 7.2 4.4 7.2 6.8 12 11 11 8 10 10
x11 9.4 17 5.1 13 14 12 14 18 4.3 5.2 7 9.5 6.6 7.2
Navigational characteristics
y 15 8.1 21 4.3 14 15 11 16 21 6.8 5.8 8.8 11 8 8.3
z7 8.2 11 6.4 8.5 9.4 7 11 11 4 4.4 6.2 3 2.6
std.n 4.8 12 7.5 2.9 6.7 6.1 4.2 9.6 7.1 3.6 5.1 3.6 3.5 6.2
std.e 5.1 11 7 2.6 4.6 4.5 3.5 7 6.9 3.5 3.9 7.5 5.3 4.6 9.1
std.hz 5.1 11 7.2 2.9 6 5.8 3.9 8.6 7 2.4 3.2 6.4 4.2 4.3 7.7
std.z 4.5 10 5.6 3.3 7 6.5 4 8.5 5.5 3.3 4.4 4.8 5 7.1
time 6.5 4 23 4 3 4 7.5 6.8 23 6.6 2.8 4.3 7.8 2.8
pdop 4 6.5 8 5.2 4.1 3.8 6.1 8 2.9 3.8 4.5 3.3 4 2.8
antenna.h 16 13 25 7.5 18 17 9.5 21 25 4.3 3 12 13 4.2 6.6
receiver 23 3.2 29 5.9 21 21 22 26 29 8.7 13 3.8 5.1
district 9 5.4 12 5.4 9.7 9.5 5.5 10 12 3.1 3.4 6.5 2.2

Folia Forestalia Polonica, Series A – Forestry, 2019, Vol. 61 (1), 3–21
Michał Brach, Krz ysztof Stereńc zak, Leszek Bolibok, Łukasz Kwaśny, Grzegorz Krok, Michał Laszkowski
14
Table 7. List of the correlation of Importance values between selected statistics for multipath effect and selected canopy and
navigational statistics in the leaf-on season
median.12.g
std.12r
prec.positive.sig.12
min.21.g
min.21.r
max21.r
mean.21.r
std.21r
prec.positive.sig.21
min.sat.12
max.sat.12
std.sat.12
max.sat.21
min.sat.21
std.sat.21
All satellites One satellite
tree.account 3 3 6.2 5.7 6.8 5.7 2.6 5.2 6.2 5.5 8.4 6.3 7.4 7.3 5.7
Tree stand characteristics
h.max 6.7 7.1 7.2 4.5 7.3 5.9 6.2 7.4 7.3 4.4 5.9 5 5.5 6.9 5.9
h.mean 4.8 9.1 8 5.9 11 8.9 7.2 14 7.6 5.8 7.6 8.7 9.4 9.9 10
h.100 7.8 7.1 6.8 5 7.4 7.4 6.4 10 7 5 6.3 7 6.4 8.4 7.1
h.mean.t 7.6 6.2 7.9 4.9 8.2 8.5 6 10 7.5 5.2 7.5 6.5 6.5 8.5 7.8
h.100.t 7 6.9 6.5 5.2 7.9 7.9 6.1 9.2 6.6 4.5 5.9 6.1 5.7 8 6.7
w1.tree.account 5.6 7.2 7 7.8 7.8 6.8 4.8 6.4 7.2 6.4 6.5 7.8 9.9 10 6
w1.h.max 6.8 7.4 7.3 4.5 7.4 6 6.3 7.3 7.4 4.5 6 5.1 5.5 7 6.2
w1.h.mean 7.3 7.5 7.5 5 7.5 8.4 7 10 7.5 5.3 7.1 7.2 7 8 7.4
w1.h.100 7.8 6.8 6.6 6.9 6.6 7.5 6.9 9.4 6.7 4.9 6.7 7 6.6 8.2 7.2
w1.h.mean.t 7.4 5.3 7 5.1 7.2 7.4 6.8 8.9 7 4.8 6.4 6.4 6 7.7 6.5
w1.h.100.t 7.4 7 6.7 6.4 6.8 6.8 6.5 8.9 6.9 4.6 6.2 6.5 5.8 7.5 6.9
v.bul 7 9.6 12 6.2 9.4 6.5 5.5 11 12 7.9 9.7 12 11 13 13
v.lidar 9 14 14 6 12 7.9 6.3 14 13 8 8.8 12 11 13 12
age.main.
species 6.2 8 5.2 4.4 4.7 3.6 3.3 4 5.2 5.7 3.5 4 9 10 7.7
slope 8.2 10 9 11 5.3 4 6.4 6.5 7.9 7 9 7.9 6.4 9.5 5.6
x14 20 13 13 8.3 6.1 8.5 14 13 12 13 15 16 11 15
Navigational characteristics
y14 13 13 8.9 8.3 8.8 11 15 12 6 8 8.5 7.5 6.8 7.6
z12 18 9.8 12 7.7 5.7 11 11 9.7 12 13 14 15 12 14
std.n 6.7 8.4 9 5.4 5.6 7.5 7.4 9.2 5.1 5.2 5.9 3.8 3.7 4
std.e 4.6 9 10 4 5.2 5.9 6.7 7.4 10 4 3.2 3.8 4.6 4.9 5.5
std.hz 6.2 9.5 10 6 5 7.1 7.8 10 5 5.1 5.2 4.4 4.8 5.2
std.z 7.4 9.4 9 5.3 5.8 8.2 11 9 4.3 4.1 7 5.9 7.8 11
time 8.9 6.6 24 6.7 7.9 6.1 11 24 6.7 4 8.6 4.3 6.6
pdop 5.9 6.1 15 5.8 7 5.1 5.9 7.6 15 6.2 7.6 8.7 8.1 5 5.2
hdop 6 8.4 19 7.1 7.6 5.4 5.4 9.8 18 6.5 7.7 9.5 8.6 6.7 8.8
vdop 6 5.4 14 4.8 6.5 4.7 6 7.6 13 6.7 8.1 9 8 5.5 5
antenna.h 13 15 13 8.4 8.6 6.8 8.3 10 13 9.5 9.8 10 9.6 9 9.8
receiver 12 14 11 11 4 4 6 8.1 11 911 11 11 9.7 11
district 10 15 10 11 8.2 6.4 6.2 9.9 10 9.7 12 11 11 9.8 12

Folia Forestalia Polonica, Series A – Forestry, 2019, Vol. 61 (1), 3–21
Impacts of forest spat ial str ucture on variat ion of the multipath phenomenon of navigation satellite signals 15
dIscussI on
The data presented in this text within the framework of
the REMBIOFOR project titled “Remote Sensing De-
termination of Timber Biomass and Coal Resource in
Forests” constitute an especially valuable set for analy-
ses of the variation of satellite signals in forest environ-
ments. First of all, it is based on a signicant number of
plots (2,704), for which a large (around 1,500 epochs)
collection of raw satellite data was made. It is a unique
pool, as in most cases navigational measurements car-
ried out in the forest are realized within short time in-
tervals, and available correction methods are applied in
real time or in post-processing. In the case of this pro-
ject, use of a data-collection time reaching 25 minutes
is congruent with standards for the registration of sat-
ellite signals (Hofmann-Wellenhof et al. 2008), which
allowed appropriate post-processing and the gathering
of surplus measurement data describing characteristics
of carrier waves.
An initial analysis of the multipath signal effect
drawing on the basic statistics and graphs obtained with
the application of R scripts made it possible to conclude
that the variation in this phenomenon is large and dif-
cult to interpret. Although this variation is characterized
by a certain cyclical temporal nature, the number of cy-
cles and their value is quite variable and hard to predict.
This state of affairs is a result not only of the forest en-
Multipath signal eect
Dominant species / Vegetation season
0
10
20
30
40
50
60
70
80
90
100
leaf-on leaf-o leaf-on leaf-o leaf-on leaf-o leaf-on leaf-o leaf-on leaf-o leaf-on leaf-o
Beech Birch Oak Fir Pine Spruce
mean from max.12.g
mean from max.21.g
mean from max.12.r
mean from max.21.r
Figure 6. Comparison of maximum MP1 and MP2 values for GPS (g) and GLONASS (r) systems with regard to dominant
species and vegetation season
Receiver model / Vegetation season
Multipath signal eect
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
leaf-on leaf-oleaf-o
mean from std.12.g
mean from std.21.g
mean from std.12.r
mean from std.21.r
Leica
leaf-on leaf-o
Trimble
leaf-on leaf-o
Stonex Topcon
Fi gure 7. Comparison of maximum MP1 and MP2 values for GPS (g) and GLONASS (r) systems with regard to dominant
species and GNSS receiver model

Folia Forestalia Polonica, Series A – Forestry, 2019, Vol. 61 (1), 3–21
Michał Brach, Krz ysztof Stereńc zak, Leszek Bolibok, Łukasz Kwaśny, Grzegorz Krok, Michał Laszkowski
16
vironment but also of the navigational receiver utilized,
the leaf state, and the height of mounting of the antenna.
Moreover, the dynamics of the satellite segment itself,
which is in constant motion, makes it impossible to pre-
sume constant and unchangeable conditions. It seems,
therefore, that the decision to seek correlations for the
main statistics like minimum, maximum, and mean val-
ues or standard deviation is a correct one, because the
multipath index constantly oscillates around a median
equal to 0. Results obtained from the RF algorithm al-
lowed a nal determination of statistics that can be eval-
uated for their inuence on the satellite signal. In most
cases, the mean and median values do not signicantly
characterize the multipath satellite signal phenomenon.
The case is different for minimum and maximum val-
ues and standard deviation. These characteristics have
a smaller impact on the phenomenon during the leaf-on
vegetation season, which is a logical consequence of the
strong impact of the leaves on increasing the signal’s
multipath effect. This state of affairs is also reected in
the differences in the number of factors and their values
between the leaf-on and leaf-off season (Tab. 6 and 7).
It is much more difcult to nd strong correlations be-
tween a chosen statistic and independent characteristics
at the height of the vegetation season than in winter. The
multipath effect is characterized by a greater variation,
hence there are more characteristics that can explain it,
but their Importance value is lower. The choice of one
satellite whose signal is registered throughout the entire
measurement process allows an easier demonstration of
tree stand characteristics that may inuence the mul-
tipath effect. It can be explained by the more frequent
occurrence of breaks in the signal from satellites locat-
ed closer to the horizon and by the necessity of a time-
consuming re-initiation of acquisition. Interruptions in
the recording of MP1 and MP2 values have a negative
impact on the measures that represent them. Despite the
large ranges of values, the Borut algorithm provided
a way of distinguishing these tree stand characteris-
tics that can contribute to an increase in the multipath
signal phenomenon. Both in the leaf-off season and at
the height of the vegetation season, these are the mean
height of the rst-layer trees (w1.h.mean) and tree stand
merchantable volume (v.lidar and v. bul). It is, however,
worth mentioning that the correlation for the volume is
slightly weaker in the leaf-off season. This is a valuable
conclusion, because by possessing knowledge about the
dominant species and tree stand volume, one is able to
partially reduce positioning errors through appropriate
planning of the date of measurement and its location. It
is clear that it is not the number of trees that determines
signal refraction but their height and stand merchanta-
ble volume, which is consistent with the ndings of oth-
er authors (Kaartinen et al. 2015; Liu et al. 2017). One
Table 8. Comparison of standard deviation of the multipath effect with regard to dominant species and vegetation season
L1 Frequency L2 Frequency
GPS System GLONASS System GPS System GLONASS System
season Species std.12.g std.12.r std.21.g std.21.r
leaf-off
Beech 1.61 2.39 2.13 2.05
Birch 1.45 1.96 1.46 2.01
Oak 1.56 2.50 1.52 2.13
Fir 2.76 1.35 2.82 1.68
Pine 2.31 2.24 1.76 1.93
Spruce 1.84 2.28 1.64 1.72
leaf-on
Beech 1.98 1.44 2.96 1.65
Birch 7.32 1.84 1.87 1.49
Oak 4.84 1.89 4.21 1.52
Fir 1.53 1.22 3.07 1.64
Pine 3.07 2.16 1.73 1.61
Spruce 1.86 2.13 1.48 1.64

Folia Forestalia Polonica, Series A – Forestry, 2019, Vol. 61 (1), 3–21
Impacts of forest spat ial str ucture on variat ion of the multipath phenomenon of navigation satellite signals 17
of the main undertakings of this study was to determine
these characteristics of tree stands that can strongly af-
fect the multipath effect and that are relatively easy to
determine directly in the eld. While tree height can be
presumed to be readily apparent, determining volume
requires much experience. It is a variable that encom-
passes many tree stand characteristics, such as the num-
ber of trees, their height, crown diameter, and the tree
species itself (Miścicki and Stereńczak 2013; Fassnacht
et al. 2018). Taking into account the accessibility of this
value in forest appraisal reports, it is possible to identify
objects where the multipath signal effect will be higher.
Among selected navigational characteristics, the impact
of the model of receiver used and the height of the an-
tenna are particularly notable. The impact of the height
is a well-known factor documented in studies of the
precision and accuracy of navigational receivers and is
consistent with the results obtained by other scholars
(Brach and Zasada 2014; Frank and Wing 2014). Infor-
mation about the variation caused by models of GNSS
receiver of the same class is, however, scarce. This
means that when conducting research into the accuracy
of a navigational receiver, it is worth carrying out an
initial analysis of the multipath signal value, as it deter-
mines the nal results of the research.
Even with the signicant share of Scots pine tree
stands (70%) in the study, taking the vegetation season
into account is still justied. In over half the objects of
study, stands comprised a main species with admixtures
of other species at the level of 30%. Among broadleaf
stands, the birch – as the species with the most ex-
ible structure with a high number of leaves – has the
greatest impact on the multipath signal phenomenon. In
spite of the high LAIs (Leaf Area Index) for oak and
beech (Gower et al. 1999; Le Dantec et al. 2000), their
maximum values are lower, which provides a basis for
obtaining better positioning results. The vegetation sea-
son does not signicantly affect the MP1 and MP2 val-
ues during the period of study for coniferous canopies.
Nevertheless, r canopies obtain visibly worse results,
which relates to the greater spatial density and build of
the needles of that species (Robakowski et al. 2004).
This causes greater obstruction of satellite signals.
Interestingly, signicantly lower multipath signal
effect values were recorded on areas with a high slope.
The reasons for this can be found in the smaller number
of satellites registered by the receiver. This especially
concerns satellites with a low elevation, which are those
that by rule generate the highest signal reection. More-
over, the structure of the forest itself is, from the point
of view of its three-dimensional space registered by the
antenna, less complicated in a situation where a larger
portion is lled with terrain and not sky.
The obtained results conrm the extraordinarily
complex and hard-to-interpret specicity of the satel-
lite signal multipath effect. In spite of signicant study
material, it is difcult to nd strong correlations, which
is due to the complexity of the study plots’ structure. In
practice, each of the areas, regardless of whether or not
it has the same appraised features, is characterized by
an entirely different state of spatial complexity. Add-
ing to that the variations in the geometry of the satel-
lite system, weather conditions, and the receiver model
creates a matrix of variables that is very difcult to
analyze. With all certainty, it has been conrmed that
the multipath effect is partially explicable by tree stand
volume, which is a characteristic dened in managed
forests. It has also been conrmed that the elevation of
the antenna at its maximum height, in combination with
extended measurement time, is a factor that can signi-
cantly improve positioning quality. Enabling registra-
tion in the GNSS receiver during the work of inventory-
ing study plots ensures the obtaining of at least 1500
epochs of raw observation data, which at a further stage
can help achieve qualitatively better results.
conclusIons
– Increase of tree stand merchantable volume contrib-
utes to increase in carrier wave reection and a de-
creased capacity for registering satellite signals.
– Selecting the model of GNSS receiver is one of the
signicant factors that impacts the accuracy of po-
sitioning.
– Forest stands with r and birch during leaf season
present difculties for carrying out navigational
measurements, but samples for both species were
purely represented, thats why this conclusion should
be future studied.
– Reducing the number of satellites on low horizontal
elevation by increasing the height of the antenna or
blocking access to a part of the sky improves the
general quality of the data obtained.

Folia Forestalia Polonica, Series A – Forestry, 2019, Vol. 61 (1), 3–21
Michał Brach, Krz ysztof Stereńc zak, Leszek Bolibok, Łukasz Kwaśny, Grzegorz Krok, Michał Laszkowski
18
– Taking into account knowledge about multipath
phenomenon it possible to compensate for poten-
tial positioning errors by appropriately selecting the
vegetation season and tree stand characteristics.
AcKnowledgeMents
This research was funded by REMBIOFOR project ti-
tled “Remote sensing estimation of tree biomass and
coal resource in forests” and co-nanced by resources
provided by the National Centre for Research and De-
velopment, as part of the program titled “Natural envi-
ronment, agriculture and forestry” BIOSTRATEG, as
stated in agreement number BIOSTRATEG1/267755/4/
NCBR/2015.
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