**1. 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

**Citation:** Abdi, O.; Uusitalo, J.; Pietarinen, J.; Lajunen, A. Evaluation of Forest Features Determining GNSS Positioning Accuracy of a Novel Low-Cost, Mobile RTK System Using LiDAR and TreeNet. *Remote Sens.* **2022**, *14*, 2856. https://doi.org/ 10.3390/rs14122856

Academic Editors: Yuwei Chen, Changhui Jiang, Qian Meng, Bing Xu, Wang Gao, Panlong Wu, Lianwu Guan and Zeyu Li

Received: 28 April 2022 Accepted: 10 June 2022 Published: 15 June 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

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 [11–14] 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 [28–30,34–36] 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, Kadeˇrábek 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.
