*3.4. 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).

**Figure 6.** Importance scores of the features affecting the positioning accuracy of u-blox ZED-F9P. The top influential feature is tree height. Other features are ranked based on their importance to the tree height.

**Figure 7.** Univariate partial dependence plots for features affecting the positioning accuracy of the u-blox ZED-F9P. (**a**–**d**) tree characteristics, (**e**–**k**) topography conditions, and (**l**–**r**) canopy-surface conditions.

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).

#### *3.5. Marginal Effects of Pairs of Features*

Figure 8 shows the interactions of five top pairs of features on the positioning accuracy of u-blox ZED-F9P. The increasing height of trees (Figure 8a), tree density (Figure 8c), surface elevation (Figure 8f), and ground elevation (Figure 8j) in the western and southern

portions increased the probability of errors in the receiver. The interaction of large trees and high tree-density (Figure 8b), surface elevation (Figure 8d), and ground elevation (Figure 8g) increased the errors. The interaction of increasing the tree density and surface elevation (Figure 8e) and ground elevation (Figure 8i) led to errors in positions. Whenever both ground elevation and surface elevation increased, the errors increased (Figure 8h).

**Figure 8.** Bivariate partial dependence plots for five top features affecting the positioning accuracy of the u-blox ZED-F9P. (**a**) tree height and aspect, (**b**) tree height and tree density, (**c**) tree density and aspect, (**d**) tree height and surface elevation, (**e**) tree density and surface elevation, (**f**) surface elevation and aspect, (**g**) tree height and ground elevation, (**h**) surface elevation and ground elevation, (**i**) tree density and ground elevation, and (**j**) aspect and ground elevation.

#### **4. Discussion**

#### *4.1. 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 [66–68] devices.
