Evaluation of Forest Features Determining GNSS Positioning Accuracy of a Novel Low-Cost, Mobile RTK System Using LiDAR and TreeNet

: Accurate positioning is one of the main components and challenges for precision forestry. This study was established to test the feasibility of a low-cost GNSS receiver, u-blox ZED-F9P, in movable RTK mode with features that determine its positioning accuracy following logging trails in the forest environment. The accuracy of the low-cost receiver was controlled via a geodetic-grade receiver and high-density LiDAR data. The features of nearby logging trails were extracted from the LiDAR data in three main categories: tree characteristics; ground-surface conditions; and crown-surface conditions. An object-based TreeNet approach was used to explore the inﬂuential features of the receiver’s positioning accuracy. The results of the TreeNet model indicated that tree height, ground elevation, aspect, canopy-surface elevation, and tree density were the top inﬂuencing features. The partial dependence plots showed that tree height above 14 m, ground elevation above 134 m, western direction, canopy-surface elevation above 138 m, and tree density above 30% signiﬁcantly increased positioning errors by the low-cost receiver over southern Finland. Overall, the low-cost receiver showed high performance in acquiring reliable and consistent positions, when integrated with LiDAR data. The system has a strong potential for navigating machinery in the pathway of precision harvesting in commercial forests.


Introduction
The combination of low-cost global navigation satellite system (GNSS) with real-time kinematic (RTK) has streamlined determining centimeter-level positioning accuracy of vehicles feasible for precise practices [1,2]. However, the feasibility of this system is little known in forestry, where precision forestry is growing due to its advantages in reducing operational costs and ecological impacts.
Accurate positioning is one of the main components of precision forestry, along with remote sensing data and geospatial information systems. As forest operations become more autonomous, the demand for highly accurate positioning increases [3,4]. Machine navigation and control rely on reliable and accurate positioning to perform forest operations. On the other hand, any inaccuracy in positioning increases the costs of operations and our carbon footprint. It also decreases machine operational robustness and safety, with huge implications on the quality of production and environment [5]. Furthermore, in commercial forests, harvesters collect a huge amount of data from the processed single trees over large areas and forest stands. The data are economically valuable and include the bucking information and positions, which can be used for mapping and predicting forest attributes [4,6]. However, any positioning errors of the data significantly degrade the performance of the models used to estimate the merchantable timber volume collected by harvesters [7,8].
Various metrics are introduced to measure the performance of GNSS positioning, such as the availability of sufficient signals, the continuity and integrity of the signals, and most importantly, the accuracy of positioning [9]. The environmental factors have an undeniable impact on the quality of signals. For example, signal blockage and multipath errors result from site-specific conditions or atmospheric factors. The poor visibility of satellites due to trees' occlusion or terrain conditions is one of the main sources of single blockage, which hampers the geometry of the GNSS and increases the optimal time for the initialization of the system [10].
Earlier studies have focused on the impact of forest type or forest cover density [11][12][13][14] in the positioning accuracy of GNSS receivers in forest environments. For example, Feng et al. (2021) [14] explored the effect of forest types and crown size on the accuracy of positioning for individual trees through GNSS receivers. They found that the error of positioning in broadleaved forests is higher than in coniferous forests, while the size of crown did show no significant impact on the increasing the error of positioning. Likewise, Murgaš et al. [13] tested the accuracy of a mapping-grade device for the positioning of inventory plots under open sky and forest canopy conditions. They reported the increase of positioning errors under canopy condition, while the coniferous forests and young stands showed lower impacts on the positioning errors of the GNSS receiver. Moreover, few studies have considered the influence of GNSS receivers' factors along with the forest-related factors. Ordóñez Galán et al. [15] tested the influence of various forest cover features and GPS-related factors on the positioning accuracy of a DGPS receiver. They reported that the influence of forest cover features on the positioning accuracy is significant in comparison with the GPS factors. However, they concluded that there is no priority between different forest variables on the accuracy of the positions. Piedallu and Gégout [16] evaluated the accuracy of GPS positioning based on the type of receiver, forest cover type, the components of GPS survey, and the season. They reported the impacts of all factors on the positioning accuracy of GPS, except the season of data recording. The influence of high density of forest cover on the accuracy of positioning is higher than other variables. However, the consideration of other factors, such as terrain variables, which may affect the positioning accuracy of GNSS receivers in a forest environment, has been somewhat diminished in earlier studies. Valbuena et al. [17] explored both terrain and forest variables. However, they excluded the terrain variables in the final modelling and concluded that the leaf area index, the relative spacing index between trees, and the wood volume can express the positioning accuracy of a GNSS receiver in a pine forest. Meanwhile, Pini et al. [1] concluded that terrain conditions are not only significant for the accuracy of positions, but are also effective for the accurate heading of vehicles. Kabir et al. [18] reported a significant decrease in in the accuracy of GNSS receivers in the mountainous areas relative to orchards or open fields. Many of these studies were developed to introduce an appropriate GNSS receiver for measuring the accurate locations of individual trees or inventory plots under forest canopy. Hence, the measurements were carried out as static, with several minutes to record an accurate position. Although positioning accuracy through mapping-grade or geodetic-grade GNSS receivers is reliable, their high cost, the difficulty in carrying them in forest conditions, and the complexity of using them have led to a degradation of their efficiency for cost-sensitive and small size applications, such as operations in precision agriculture or precision forestry. Therefore, the need for a new generation of cost-effective GNSS receivers with high positioning accuracy and simplicity of usage under forest conditions, such as u-blox modules, is inevitable.
In modern forestry, the use of high-density LiDAR data is growing for mapping the forest environment, such as individual tree characteristics [7,19,20], aboveground biomass estimation [21,22], forest disturbances [23], and logging trail detection [24,25]. Mapping forest features depends on reliable and accurate field measurements for both attributes and positions. For this purpose, we need receivers that are able to acquire positions at centimetre-level accuracy, such as geodetic-grade GNSS receivers, to be compromised with LiDAR-derived forest metrics. However, there has also been some research that introduced the relatively expensive approaches by integrating GNSS, IMU, and mobile laser scanning (MLS) to improve the positioning accuracy for solving the simultaneous localization and mapping (SLAM) problem under forest canopy [26,27].
Despite the high positioning accuracy, the cost of establishment a traditional RTKrelated receiver, e.g., a geodetic-grade receiver, is approximately 10 times higher than a low-cost RTK receiver [28], which has made it inappropriate for cost-sensitive and small size applications, e.g., in forestry or agriculture applications. The reliable accuracy and continuity of low-cost GNSS receivers are reported for a variety of applications, mostly in non-forest environments, such as surveying and mapping [29,30], monitoring [28,31], Android smartphone positioning [32], precision agriculture [2], and urban environments [33]. Many of the earlier studies reported reliable positioning of the low-cos receivers, such as u-blox modules [28][29][30][34][35][36] in a desirable environment condition, for example, an open sky with a wide range in availability of satellites. However, their efficiency might be degraded in an obstructed environment or in the dynamic mode of positioning RTK. Jackson et al. [37] evaluated the positioning accuracy of five low-cost GNSS receivers for RTK positioning under different environments, in both static and dynamic conditions. The results indicated that the positioning errors of the low-cost receivers, in static tests, was less than 10 cm in less complex areas, such as rural environments. However, the error reached over 1 m in complex areas, such as urban and suburban environments. The positioning accuracy of the receivers was different in dynamic tests, and the optimal accuracy is reported 1.5 cm to 1.8 m for the suitable receiver. Likewise, Kadeřábek et al. [2] tested the performance of various types of RTK receivers in horizontal positioning under the modes of static or dynamic. They concluded that the accuracy of positioning is significantly lower in a dynamic mode rather than a static mode. They emphasised that accelerating the speed increases the error of positioning. Janos and Kuras 2021 [35] tested the positioning accuracy of a low-cost GNSS receiver, u-blox ZED-F9P, in the RTK mode under different environment conditions. They found that the type of antenna has a significant impact on the increase of positioning errors in a complex environment, such as urban canyons.
Although a variety of studies have explored the feasibility of traditional GNSS receivers in the forest environment, our understanding concerning the efficiency of newly low-cost receivers and the factors that affect their positioning accuracy is limited, particularly in commercial forests, where the monitoring of machines or recording of the position of processed single trees by harvesters [27,38,39] has become widespread in forest operations. Hence, this research was designed to test the feasibility of using low-cost GNSS receivers and RTK correction signal to determine precise positions in forests under the rotation forest management (RFM) system in southern Finland. Specifically, we want to evaluate the positioning accuracy of the u-blox ZED-F9P in combination with high-density LiDAR data. Moreover, we will explore features that affect the accuracy of a low-cost GNSS receiver in the forest using the TreeNet algorithm.

Description of the Study Area
We selected three forest stands for our experiment from Karpanmaa forests in southern Finland ( Figure 1). One stand is young and had undergone its first commercial thinning. Two other stands are mature and are waiting for their second/third commercial thinning operations. The tree species compositions are pine, spruce, and birch, with a predominance of pine in the three stands. The age of stands is distributed from 34 to 72 years. The height of trees is between 5 and 29 m. The ground elevation of the forest ranges between 127 and 149 m.

Data
We used the high-density LiDAR data, under the license of the National Land Survey of Finland (NLS), recorded in 2020 for the selected stands. The data have a density of greater than 5 points/m 2 along with horizontal and altimetric errors of less than 45 and 10 cm [40], respectively. The features affecting the positioning accuracy of the u-blox ZED-F9P were mapped from the LiDAR-derived metrics such as the digital terrain model (DTM), digital surface model (DSM), point density, and signal intensity. Logging trails were detected from the high-density LiDAR data based on the U-Net convolutional neural network approach developed by Abdi et al. [25]. In addition, we obtained orthophotos from the databases of NLS [41]. The attributes of the forest stands were collected from the databases of Finsilva Oy.

Data
We used the high-density LiDAR data, under the license of the National Land Survey of Finland (NLS), recorded in 2020 for the selected stands. The data have a density of greater than 5 points/m 2 along with horizontal and altimetric errors of less than 45 and 10 cm [40], respectively. The features affecting the positioning accuracy of the u-blox ZED-F9P were mapped from the LiDAR-derived metrics such as the digital terrain model (DTM), digital surface model (DSM), point density, and signal intensity. Logging trails were detected from the high-density LiDAR data based on the U-Net convolutional neural network approach developed by Abdi et al. [25]. In addition, we obtained orthophotos from the databases of NLS [41]. The attributes of the forest stands were collected from the databases of Finsilva Oy.
The Oregon ® 750t receiver was used for navigating the approximate locations of the selected logging trails.
We used the u-blox ZED-F9P to identify features affecting the positioning accuracy of the low-cost GNSS receivers in the forest. The u-blox ZED-F9P is a multi-band GNSS receiver that can measure positions at centimetre-level accuracies in RTK mode. This receiver obtains signals from multiple bands (L1, L2/E5b/B21) of all four global GNSS constellations including GPS, Galileo, BeiDou, and GLONASS via a Multi band GNSS antenna ANN-MB-00 (SMA) (u-blox, Thalwil, Switzerland) [42]. The antenna is designed in a small, compact size. It can be easily mounted on different machinery due to its magnetic fixed installation base and a long cable of 5 m [43]. The GNSS and RTK integration has accelerated its convergence time (down to less than 10 sec) [42]. Moreover, performance with the application for conducting unmanned autonomous vehicles (UAV), automatic and semi-automatic machinery, and robotic machines has improved [44]. The u-blox F9P was equipped with advanced anti-spoofing and anti-jamming algorithms that guarantee highly accurate positioning and navigation information. The receiver and antenna are both waterproof and can also operate under extreme temperatures (−40 • C to +85 • C) [45].
We used the Trimble R2 receiver, paired with Trimble TSC7 (Trimble Inc., Sunnyvale, CA, USA), for collecting accurate control points during recording data through u-blox F9P. The Trimble R2 can acquire high positioning accuracy in RTK mode both horizontally (1 cm to 1 ppm RMS) and vertically (2 cm to 1 ppm RMS).

Research Sulky
We modified a sulky for transporting the u-blox and its compartment for recording positioning data in the forest. The sulky includes two bicycle wheels of 28 in width. The length, width, and height of the main body of the sulky are 1.2 m, 65 cm, and 87 cm, respectively. It was equipped with a veneer plate (103 cm × 53 cm) for holding the devices. A thin plate (50 cm × 40 cm) was installed on the veneer plate for fixing the magnetic antenna. The sulky was controlled by a draught pole (adjustable up to 1.3 m), which includes a trapezoid-shaped handle to make pulling easier for the user ( Figure 2).

Field Measurements
We established the local base stations to send corrected data to the rover receiver in the vicinity of our study site ( Figure 1a). The base and movable stations were developed using a SparkFun GPS-RTK2 Board (SparkFun Electronics, Boulder, CO, USA) with ublox-ZED-F9P module and the SMA. The receivers of the base stations were configured based on an NTRIP-protocol via the internet server (rtk2go.com) to provide RTCM V3.2 standard correction signals.
We selected a number of logging trails with about 2 km for our experiment (Figure 1c). The shapefiles of the logging trails were converted into GPS Exchange Format (GPX) and imported into the Garmin device for spotting out the logging trails in the field.
We started our measurement from 8:32 a.m. and ended at 12:37 p.m. (GMT). The routes were so designed to pass through different species with diversity in age, height, density, canopy cover, and topographic conditions. Our speed was close to the normal speed of harvesters and forwarders (i.e., 44 to 56 m/min) in the forest.
The u-blox ZED-F9P receiver and its compartments, including the SAM, 4G TP-LINK M7200 modem (TP-Link Technologies Co., Shenzhen, China), and Laptop computer, were mounted on a research sulky that was designed for this purpose ( Figure 2). The configuration period of the receiver was set to 1 Hz. All four GNSS constellations were selected to receive adequate and strong signals to acquire positions by the u-blox F9P in RTK mode. A Raspberry Pi minicomputer with RTK-LIB open-source program was used for operating the RTK-station. We used u-center evaluation software program to monitor and process all aspects of recorded data (e.g., horizontal and vertical positions, accuracies, time, tracking of GNSS constellations, etc.) during the operation of the u-blox GNSS receiver [46]. All recorded data were captured in ASCII format, imported into ArcGIS (Esri, Redlands, CA, USA), and integrated with the object features to be used for TreeNet analysis.

Field Measurements
We established the local base stations to send corrected data to the rover receiver in the vicinity of our study site ( Figure 1a). The base and movable stations were developed using a SparkFun GPS-RTK2 Board (SparkFun Electronics, Boulder, USA) with ublox-ZED-F9P module and the SMA. The receivers of the base stations were configured based on an NTRIP-protocol via the internet server (rtk2go.com) to provide RTCM V3.2 standard correction signals.
We selected a number of logging trails with about 2 km for our experiment ( Figure  1c). The shapefiles of the logging trails were converted into GPS Exchange Format (GPX) and imported into the Garmin device for spotting out the logging trails in the field.
We started our measurement from 8:32 a.m. and ended at 12:37 p.m. (GMT). The routes were so designed to pass through different species with diversity in age, height, density, canopy cover, and topographic conditions. Our speed was close to the normal speed of harvesters and forwarders (i.e., 44 to 56 m/min) in the forest.
The u-blox ZED-F9P receiver and its compartments, including the SAM, 4G TP-LINK M7200 modem (TP-Link Technologies Co., Shenzhen, China), and Laptop computer, were mounted on a research sulky that was designed for this purpose (Figure 2). The configuration period of the receiver was set to 1 Hz. All four GNSS constellations were selected to receive adequate and strong signals to acquire positions by the u-blox F9P in RTK mode. A Raspberry Pi minicomputer with RTK-LIB open-source program was used for operating the RTK-station. We used u-center evaluation software program to monitor and process all aspects of recorded data (e.g., horizontal and vertical positions, accuracies, time, tracking of GNSS constellations, etc.) during the operation of the u-blox GNSS receiver [46]. All recorded data were captured in ASCII format, imported into ArcGIS (Esri, Redlands, USA), and integrated with the object features to be used for TreeNet analysis.
We recorded the positions of 64 control points on the logging trails with an accuracy We recorded the positions of 64 control points on the logging trails with an accuracy of less than 1 cm by the Trimble R2, as references, in RTK mode. The absolute errors were calculated between the measured positions by the u-blox F9P and the positions of the control points. The one-sample t-test was used to determine whether the mean of errors exceeded the optimal directions of an image pixel (i.e., 50 cm) derived from the high-density LiDAR data at a significance level of 0.05.

High-Density Laser Scanning Features
We applied the binning interpolation method based on the maximum cell-assignment method to generate a digital surface model (DSM) from the high-density LiDAR points. The linear interpolation method was used to fill void areas in the DSM. The digital terrain model (DTM) was created based on the interpolation from ground points as well [47]. The features representing the surface topography and canopy conditions, such as slope gradient, aspect, topography/canopy position, plan curvature, profile curvature, and mean curvature [48,49], were derived from the DTM and DSM (Figure 3).
We subtracted the DTM from the DSM to reach the canopy height model (CHM) [50]. The canopy density was generated based on the ratio of the number of nonground points to the total number of points in an object [51]. The tree canopy was delineated from the CHM and used for measuring the canopy cover within an object [52]. The intensity image was created from the range of pulse-intensity values of the laser points [53]. It was applied in combination with orthophotos to determine species types within the objects. assignment method to generate a digital surface model (DSM) from the high-density LiDAR points. The linear interpolation method was used to fill void areas in the DSM. The digital terrain model (DTM) was created based on the interpolation from ground points as well [47]. The features representing the surface topography and canopy conditions, such as slope gradient, aspect, topography/ canopy position, plan curvature, profile curvature, and mean curvature [48,49], were derived from the DTM and DSM ( Figure 3). We subtracted the DTM from the DSM to reach the canopy height model (CHM) [50]. The canopy density was generated based on the ratio of the number of nonground points to the total number of points in an object [51]. The tree canopy was delineated from the CHM and used for measuring the canopy cover within an object [52]. The intensity image was created from the range of pulse-intensity values of the laser points [53]. It was applied in combination with orthophotos to determine species types within the objects.

Object Features
A buffer of 10 m was delineated around the logging trails, and then the area was segmented into the homogenous units (objects) based on the similarity in the spectral properties of the adjacent cells in the high-resolution orthophotos. The average size of the objects was obtained around 18 sq.m. The values of the derived features from the LiDAR data (Table 1) and the accuracy of positioning by u-blox ZED-F9P were summarized

Object Features
A buffer of 10 m was delineated around the logging trails, and then the area was segmented into the homogenous units (objects) based on the similarity in the spectral properties of the adjacent cells in the high-resolution orthophotos. The average size of the objects was obtained around 18 sq.m. The values of the derived features from the LiDAR data (Table 1) and the accuracy of positioning by u-blox ZED-F9P were summarized within the objects. This single database was used for analyzing the relationship between the target and the features using TreeNet.

TreeNet Regression
We used the TreeNet regression algorithm to determine influential features on the positioning accuracy of the u-blox ZED-F9P. Numerous advantages have been reported for TreeNet, in comparison with other machine learning based approaches. In addition to its highly accurate predictions, TreeNet is not sensitive to errors in data or missing data. No data pre-processing (e.g., transformation, normalisation, or reduction) or preselection of the variables is required. TreeNet is strong against overfitting, and the process of growing trees is extraordinarily fast [54,55].
TreeNet begins with an initial model, which consists of a very small tree. This simple model is deliberately weak. The residuals are computed for each data in the first model and are used to grow the second tree. The residuals of the second tree are then computed and used to grow the third tree. Likewise, this process repeats to generate a sequence of hundreds or thousands of trees, in order to achieve an optimal tree. All trees contribute to the optimal model. The final model prediction is based on the total contribution of the individual trees, which is known as score. The accuracy of the TreeNet score will improve steadily by increasing the number of trees until to reach an optimal number of trees [55].
We used a dataset including 2000 sample objects. Twenty percent of the sample objects were randomly assigned as the testing set and the remaining 80% as the learning set. The TreeNet loss function was set on Huber-M. The mean square error (MSE) was chosen as the criterion for determining the number of optimal trees. We set the initial tree size at 10,000 and generated 12 TreeNet models based on the different learning rates and tree complexity levels. The optimal model was selected based on the one that recorded the minimum MSE, and its parameters were tuned for the final TreeNet model. The performance of the model was tested using the area under the receiver operating characteristic (ROC) curve. A value greater than 0.9 represents high performance, while values less than 0.7 indicate low performance [56] of the TreeNet model.
The influence of features on the positioning accuracy of the u-blox ZED-F9P was determined via relative importance [55]. The importance values of the features are ranged between 0 and 100. The most influential feature gains a value of 100 and the remaining features are rescaled to reflect their importance relative to this feature. We produced partial dependence (PD) plots for individual and pairs of features that contributed to the predicted positioning accuracy in the model. The PD plots represent the response of the target variable to individual or pairs of features, as all remaining features are taken into account [57]. Table 1. Object features affecting on the accuracy of positioning by u-blox ZED-F9P, derived from different metrics of high-density LiDAR data.

Category Features Description
Ground-surface/canopy-surface conditions

Elevation
The mean of ground/canopy elevation (m) [58] in an object.

Slope ( • )
The average of maximum changes in elevation value [59] within each object.

Aspect
The direction of compass of downhill slope [59] in each object. Mean curvature The combination of the plan and profile curvatures within an object [48,49].
Tree characteristics

Canopy height
The difference between the elevation of canopy surface and ground surface in an object [50].

Canopy density
The density of nonground returns of LiDAR points in an object [51].
Canopy cover The percentage of canopy cover within an object, delineated from the CHM [52].

Species type
The type of species trees extracted from the intensity image, derived from the high-density LiDAR data and orthophoto images.

The Accuracy of Positions
The mean of absolute errors of positions between those measured by u-blox ZED-F9P and control points was obtained as about 43 cm. The result of the one-sample t-test showed that the positioning accuracy of u-blox has no significant deviation from the area of logging trails (test value = 0.5 m, p-value > 0.05). However, the absolute errors are distributed between 1.5 cm to 1.8 m (Figure 4).

Tree characteristics
Canopy cover The percentage of canopy cover within an object, delineated from the CHM [52].

Species type
The type of species trees extracted from the intensity image, derived from the high-density LiDAR data and orthophoto images.

The Accuracy of Positions
The mean of absolute errors of positions between those measured by u-blox ZED-F9P and control points was obtained as about 43 cm. The result of the one-sample t-test showed that the positioning accuracy of u-blox has no significant deviation from the area of logging trails (test value = 0.5 m, p-value > 0.05). However, the absolute errors are distributed between 1.5 cm to 1.5 m (Figure 4).

TreeNet Performance
The optimal TreeNet model was obtained after building 490 trees with a learning rate of 0.011 and tree complexity of 7 ( Figure 5). The ROC values were 0.977 for the training dataset and 0.745 for the testing dataset. It indicates that TreeNet demonstrated high performance for expressing the features that are determining the positioning accuracy of the GNSS receivers in forest.

TreeNet Performance
The optimal TreeNet model was obtained after building 490 trees with a learning rate of 0.011 and tree complexity of 7 ( Figure 5). The ROC values were 0.977 for the training dataset and 0.745 for the testing dataset. It indicates that TreeNet demonstrated high performance for expressing the features that are determining the positioning accuracy of the GNSS receivers in forest.

Features' Importance
The results of evaluation the importance values of features indicated that all of the features have affected the positioning accuracy of u-blox ZED-F9P. The top influential feature was tree height. Then, the influential features were ranked by their importance to the tree height feature. The ground elevation and aspect have gained 79% and 62% importance of the tree height, respectively. The importance of the other features has steadily decreased from the canopy surface elevation to the surface aspect. Two out of five top influential features were classified in the category of tree characteristics ( Figure 6).

Marginal Effect of Individual Features
The interpretation of univariate PD plots regarding the tree characteristics shows that when tree height increases to 14 m, the error in positioning by u-blox ZED-F9P increases (Figure 7a). By increasing tree density, the positioning error drastically increases, at a density over 0.25 (Figure 7b). Canopy cover of more than 30% shows a positive response to error in positions of the GNSS receiver (Figure 7c). The mixed species and pine show a positive response to the high number of errors among tree species (Figure 7d).

Features' Importance
The results of evaluation the importance values of features indicated that all of the features have affected the positioning accuracy of u-blox ZED-F9P. The top influential feature was tree height. Then, the influential features were ranked by their importance to the tree height feature. The ground elevation and aspect have gained 79% and 62% importance of the tree height, respectively. The importance of the other features has steadily decreased from the canopy surface elevation to the surface aspect. Two out of five top influential features were classified in the category of tree characteristics ( Figure 6).

Marginal Effect of Individual Features
The interpretation of univariate PD plots regarding the tree characteristics shows that when tree height increases to 14 m, the error in positioning by u-blox ZED-F9P increases (Figure 7a). By increasing tree density, the positioning error drastically increases, at a density over 0.25 (Figure 7b). Canopy cover of more than 30% shows a positive response  The univariate PD plots of the topographic features show that, when the ground elevation exceeds 134 m in the study area, the error of positioning by u-blox increases (Figure 7e). The areas with a slope of less than 10% show a positive response to the errors (Figure 7f). Increasing complexity in the topographic position increases the errors ( Figure  7g). The western direction shows the greatest errors among the topographic aspects. The southern, south-western, and south-eastern directions show a positive response to the errors (Figure 7h). The concave curvatures show a positive response to errors in plan, profile, and mean curvatures (Figure 7i-k).
The PD plots show that the surface elevation positively responds to the high error in recorded positions by u-blox ZED-F9P after 137 m (Figure 7l). The areas with a surface slope of less than 60% show an increase in the errors (Figure 7m). High complexity in the canopy-surface position coincides with high errors in positioning (Figure 7n). Canopies with the domination of the north-eastern direction show higher errors (Figure 7o). The canopies with concave curvatures demonstrate mostly high errors totally, vertically, and horizontally (Figure 7p-r).  The univariate PD plots of the topographic features show that, when the ground elevation exceeds 134 m in the study area, the error of positioning by u-blox increases (Figure 7e). The areas with a slope of less than 10% show a positive response to the errors (Figure 7f). Increasing complexity in the topographic position increases the errors (Figure 7g). The western direction shows the greatest errors among the topographic aspects. The southern, south-western, and south-eastern directions show a positive response to the errors (Figure 7h). The concave curvatures show a positive response to errors in plan, profile, and mean curvatures (Figure 7i-k).

Marginal Effects of Pairs of Features
The PD plots show that the surface elevation positively responds to the high error in recorded positions by u-blox ZED-F9P after 137 m (Figure 7l). The areas with a surface slope of less than 60% show an increase in the errors (Figure 7m). High complexity in the canopy-surface position coincides with high errors in positioning (Figure 7n). Canopies with the domination of the north-eastern direction show higher errors (Figure 7o). The canopies with concave curvatures demonstrate mostly high errors totally, vertically, and horizontally (Figure 7p-r).

The Positioning Accuracy of the Low-Cost GNSS Receiver
We reach an absolute error of 0.43 m for positioning accuracy by the low-cost u-blox ZED-F9P GNSS receiver with its equipped standard patch antenna in movable RTK mode in forest environment. This level of positioning accuracy is promising for forest

The Positioning Accuracy of the Low-Cost GNSS Receiver
We reach an absolute error of 0.43 m for positioning accuracy by the low-cost u-blox ZED-F9P GNSS receiver with its equipped standard patch antenna in movable RTK mode in forest environment. This level of positioning accuracy is promising for forest operations, particularly relative to the positioning accuracy of current GNSS receivers used by vehicles in forest. Alternatively, the development of LiDAR systems has provided the possibility of producing high precision maps of the forest environment and tree characteristics at centimetre-level accuracy, with a significant reduction in costs and improvement in time of processing. Our findings verify the trust in positioning by the low-cost receiver in RTK mode for integration with the forest features derived from high-density LiDAR data, such as logging trails. This may have wide implications for the improvement of the safety of crews, autonomous navigation, ergonomics, and reduction of environmental impacts and costs [61] during forest operations down the pathways of precision forestry. Although the positioning accuracy of the low-cost GNSS receivers in static mode was reported higher than the RTK mode in complex non-forest environments [2,37], their positioning accuracy was considerable in this mode [28,30] as well. We should stress that our results are only based on using the standard patch antenna. Further work is required to test the performance of the low-cost GNSS receivers when equipped with additional antennas in the forest environment. Previous experiments acknowledged significant improvement in the positioning accuracy of the low-cost receivers, for example, when using with a geodetic-grade antenna [29,34,35].
The u-blox ZED-F9P obtains signals in multiband from four global GNSS. Multi-GNSS contributes to increasing the continuity and integrity of positioning by the receivers, particularly in environments with obstacles [62,63]. The effect of receiver types on the accuracy of positioning was reported in earlier studies. The survey-grade devices recorded higher accuracy than consumer-grade [16,64], mapping-grade [13,65], or smartphonegrade [66][67][68] devices.

The Performance of TreeNet
This study applied high-density LiDAR data and a novel object-based TreeNet approach to determine influential features that degrade the positioning accuracy of the novel developed low-cost GNSS receivers in a forest context. Earlier studies mostly modelled the influential variables of positioning accuracy using traditional regression models [12,14,17,66], which are limited with few variables and data. Conversely, we adopted TreeNet, as one of the most powerful machine learning algorithms, with remarkable abilities in handling big data and numerous variables without any preselection, pre-processing, or reduction in dataset. It reveals that a combination of forest characteristics and terrain features express the positioning errors of GNSS receivers. However, the importance of features are different.

Influential Forest Features
Based on our analyses, LiDAR-derived tree height is the top feature that influence on the positioning accuracy of the low-cost GNSS receiver in movable RTK mode. Tree density is among top five influential features ( Figure 6). The complexity of the forest structure causes multipath effects [69], which is one of the main sources of increasing positioning errors in forest. Tree's characteristics, such as height, volume, tree density and canopy may block or weaken the signals [70]. A closed canopy can cause cycle slips [63], which clogs the signals to reach the receivers. Our analyses demonstrated that the low-cost GNSS receiver continuously recorded the signals throughout the logging trails, and it was resistant against cycle slips effects. Conversely, the great majority of work has focused on the canopy cover [11,13,14,16,[71][72][73] as the main factors that affect the positioning accuracy of the GNSS receivers. Nevertheless, no priority between the forest cover factors on the positioning accuracy of GNSS was reported in the research of Ordóñez Galán et al. [15], while our study shows that there is a distinct difference between the impacts of tree characteristic factors on the positioning accuracy of the GNSS receiver. Moreover, some earlier studies reported the higher impact of the broadleaved tree species on increasing the errors of positioning by the GNSS receiver [13,14]. Our research showed that the importance of the tree species is less than other tree characteristics. The influence of pine and mixture species is positive against the spruce and birch.
Using high-density LiDAR data enabled us to take into account precisely some features of tree characteristics that were less a focus of earlier studies, such as tree height or tree density, not in plot scale but over the entire surveyed logging trails. For example, due to limitations involved in using traditional methods to measure tree height, the preponderance of the studies focused instead on forest cover or forest type [13][14][15][16]64] as potential effective factors of tree characteristics to determine the positioning accuracy of GNSS receivers. We considered trees' characteristics inside an object, which is much more similar to the natural condition of a forest stand. Furthermore, we carried out the experiments in a season which the leaf of some tree species such as birch is almost off. Hence, canopy cover or tree species did show lower importance than tree height or tree density in the current research. Likewise, topographic conditions affect the signals and cause the multipath effects. Our study revealed that topography directions and elevation are among top five important features that determine the positioning accuracy of the low-cost GNSS receiver ( Figure 6). Aspect and slope derived from the DTM showed higher importance than was shown by the corresponding features derived from the DSM. The high ability of DTM to visualise the morphology of the bare earth under the forest canopy [74], such as variations in slope directions and values, might be one reason for this difference. On the other hand, the high variation in the curvature of the forest canopy may lead to a higher influence of DSM-derived plan curvature and mean curvature when compared to the corresponding derivatives from the DTM. Although there is no holistic research about the impact of topographic conditions in forest environment, some studies verified significant impacts of terrain in non-forest environments on the positioning accuracy of the GNSS receivers [1,18]. Based on the PD plots, the positioning errors of the low-cost GNSS receiver increase in forest areas with tree height above 14 m, tree density above 30%, western topographic directions or high elevation ( Figure 6). These thresholds are based on our results in southern Finland, and similar studies should be repeated to achieve fixed values over the Nordic region. The performance of the antenna, as a sky view, is presented for a specific measured position during our experiment in Figure 9. The number of satellites that are used in navigation with a valid fixed position in the eastern direction is higher than in the western direction. We can infer that the geometric location of the satellites and their signal qualities may cause that aspect to be one of the top features determining the accuracy of the positioning by the low-cost GNSS receiver. Lower fixing rates and position errors of GNSS on west aspects were reported by D'eon and Delparte [75]. However, they reported that the differences in these values between different directions were not significant. The effect of aspect and convex slopes on the odds of missing signals was reported in the forest as well. Zimmerman and Keefe [76] verified that the alert delay of GNSS in the west directions is higher than in the east directions, which increases the error of positioning under forest canopies.
In addition, our analyses indicated that the interaction of the conditioning features intensifies the positioning errors by the receiver (Figure 8). It seems that using extra antenna or geodetic antenna [29][30][31]35] may mitigate the impact of the forest structure or topographic conditions on the positioning errors of this type of low-cost GNSS receivers in forest environments.

The Application
The new generation of harvesters is equipped with sensors, computers, and GNSS receivers that store big data obtained from the processed trees and machine parameters as a standard format of StanForD (Standard for Forest Data and communication) [3]. Despite the high capacity of these data for modelling forest productivity, the errors in positions significantly degrade the efficiency of these data [6][7][8]. This type of low-cost GNSS receiver can improve the accuracy, integrity, and continuity of positions for the harvesters, with a significant impact on increasing the efficiency of forest productivity maps to Improve the sustainability of future rotations and precision forestry. Moreover, understanding the influential features that affect the positioning accuracy of the low-cost GNSS devices contributes to developing algorithms for the correction of positioning errors or for the selection of appropriate low-cost receivers or antennas to minimize the influence of environmental features on positioning accuracy during forest operations.

The Application
The new generation of harvesters is equipped with sensors, computers, and GNSS receivers that store big data obtained from the processed trees and machine parameters as a standard format of StanForD (Standard for Forest Data and communication) [3]. Despite the high capacity of these data for modelling forest productivity, the errors in positions significantly degrade the efficiency of these data [6][7][8]. This type of low-cost GNSS receiver can improve the accuracy, integrity, and continuity of positions for the harvesters, with a significant impact on increasing the efficiency of forest productivity maps to Improve the sustainability of future rotations and precision forestry. Moreover, understanding the influential features that affect the positioning accuracy of the low-cost GNSS devices contributes to developing algorithms for the correction of positioning errors or for the selection of appropriate low-cost receivers or antennas to minimize the influence of environmental features on positioning accuracy during forest operations.

Conclusions
In this study, we presented a geographic object-based TreeNet approach to determine influential environmental features that affect the positioning accuracy of a newly developed, low-cost, high-precision GNSS receiver, u-blox ZED-F9P, in forests. The experiment concentrated on some logging trails in commercial forests in Southern Finland. The low-cost receiver showed reliable positioning accuracy when integrated with high-density LiDAR data in the forest. The TreeNet model showed a high performance for expressing features that determine the positioning accuracy of the low-cost receiver in the forest. A combination of features increased the positioning errors of the low-cost receiver, in which the most important feature was tree height and then the topographic features, such as elevation and slope direction over the study stands. In the current research, we merely used the standard patched antenna packed with the low-cost receiver. However, we suggest testing the efficiency of other types of antennas, e.g., geodetic-grade ones, or a combination of antennas with the low-cost receiver to improve the positioning accuracy in the forest environment.

Conclusions
In this study, we presented a geographic object-based TreeNet approach to determine influential environmental features that affect the positioning accuracy of a newly developed, low-cost, high-precision GNSS receiver, u-blox ZED-F9P, in forests. The experiment concentrated on some logging trails in commercial forests in Southern Finland. The low-cost receiver showed reliable positioning accuracy when integrated with high-density LiDAR data in the forest. The TreeNet model showed a high performance for expressing features that determine the positioning accuracy of the low-cost receiver in the forest. A combination of features increased the positioning errors of the low-cost receiver, in which the most important feature was tree height and then the topographic features, such as elevation and slope direction over the study stands. In the current research, we merely used the standard patched antenna packed with the low-cost receiver. However, we suggest testing the efficiency of other types of antennas, e.g., geodetic-grade ones, or a combination of antennas with the low-cost receiver to improve the positioning accuracy in the forest environment.