The authors have declared that no competing interests exist.

Real-time positioning on mobile devices using global navigation satellite system (GNSS) technology paired with radio frequency (RF) transmission (GNSS-RF) may help to improve safety on logging operations by increasing situational awareness. However, GNSS positional accuracy for ground workers in motion may be reduced by multipath error, satellite signal obstruction, or other factors. Radio propagation of GNSS locations may also be impacted due to line-of-sight (LOS) obstruction in remote, forested areas. The objective of this study was to characterize the effects of forest stand characteristics, topography, and other LOS obstructions on the GNSS accuracy and radio signal propagation quality of multiple Raveon Atlas PT GNSS-RF transponders functioning as a network in a range of forest conditions. Because most previous research with GNSS in forestry has focused on stationary units, we chose to analyze units in motion by evaluating the time-to-signal accuracy of geofence crossings in 21 randomly-selected stands on the University of Idaho Experimental Forest. Specifically, we studied the effects of forest stand characteristics, topography, and LOS obstructions on (1) the odds of missed GNSS-RF signals, (2) the root mean squared error (RMSE) of Atlas PTs, and (3) the time-to-signal accuracy of safety geofence crossings in forested environments. Mixed-effects models used to analyze the data showed that stand characteristics, topography, and obstructions in the LOS affected the odds of missed radio signals while stand variables alone affected RMSE. Both stand characteristics and topography affected the accuracy of geofence alerts.

Since the Department of Defense launched its first Navigation System with Timing and Ranging (NAVSTAR) satellite in 1978, global positioning system (GPS) technology has become an integral component of national defense, homeland security, civilian life, and scientific research [

The accuracy of GNSS coordinate readings is dependent upon the number and geometry of satellites visible to a GNSS unit at any point in time. Positional dilution of precision (PDOP) is an index of the influence of satellite geometry on GNSS measurements [

GNSS use in forestry is often affected by error associated with satellite signal obstruction by the canopy or other solid objects and the reflection or diffraction of satellite signals from nearby objects or surfaces, an error known as multipathing [

Advances in positioning technology for remote environments have emerged simultaneously for several uses, ranging from recreation to public safety and defense. These devices link GNSS positional information with radio frequency (RF) transmission of location coordinates (GNSS-RF) to form ad-hoc networks in which the locations of all units can be monitored on mobile phones or tablets. Like traditional GNSS devices, each GNSS-RF transponder determines its coordinates using one or more satellite-based positioning systems. However, the RF transmission is a second component that allows those coordinates to be sent to other, nearby GNSS-RF units at user-defined intervals. GNSS-RF transponders include consumer-grade units for recreational use like the Garmin Rino and Garmin Alpha 100, devices such as the Raveon Atlas PT marketed for public safety, a variety of military-grade GNSS radios designed for defense applications, and consumer-grade mobile-based solutions from goTenna and Beartooth that turn smartphones into two-way radios for voice or text communication in areas without cellular service. While traditional GNSS devices allow users to see their own positions, GNSS-RF devices enable real-time positioning through location sharing among individuals and equipment in remote locations [

Many GNSS-RF transponders support geofencing, in which a virtual boundary is defined around a user-defined geographic zone. Geofences are either circular or polygonal in shape, can vary widely in size depending on intended application, and can be stationary or mobile. Alert notifications are triggered as tracked mobile objects cross into or out of the geofence, and this functionality may be useful for a range of operational forestry applications such as detecting the amount of time workers spend near cable logging hazards [

GNSS-RF and related technologies pose new challenges for quantifying positional accuracy because positional error is associated with both the accuracy of GNSS locations and successful propagation of radio signals between devices. In other words, the accuracy of GNSS-RF position sharing depends not only on factors that influence GNSS accuracy as described above, but also on factors that affect radio signal propagation and attenuation. Radio signals experience diffraction, scattering and reflection as they travel through vegetation [

The purpose of this study was to characterize the factors affecting real-time positioning on irregular, forested terrain through analysis of the effects of forest stand characteristics, topography and other line-of-sight (LOS) obstructions on the GNSS accuracy and radio signal propagation quality of multiple Raveon Atlas PT GNSS-RF transponders (Raveon Technologies, Vista, California, USA) functioning as a network. Until recently, most previous research evaluating GNSS for forestry applications has focused on stationary units. Recent studies characterizing GNSS units in motion include work by Kaartinen et al. [

Five Raveon Atlas PT GNSS-RF transponders collected positional data during the field experiment. As GNSS-RF units, the PTs receive their coordinates and then transmit that information to other PTs using radio frequency. The units can be attached to tablets or computers, which allows ground workers and equipment operators on logging operations to see all other positioning devices in real-time. PTs receive their coordinates from NAVSTAR GPS satellites only and have a specified 24-hour static accuracy of < 2.5 m for 50% of measurements and of < 5 m for 90% of measurements [

In this study, real-time geofence alert signals were evaluated in a random sample of 21 stands on the University of Idaho Experimental Forest (UIEF) (

(A) The 21 stands are delineated according to total basal area (m^{2}/ha) and the UIEF unit boundaries are shown in blue. Background map is 1-m NAIP imagery. (B) Illustration of global navigation satellite system (GNSS) technology paired with radio frequency (RF) transmission (GNSS-RF). GNSS-RF transponders (Atlas PTs) receive positional information from GNSS satellites and relay this information to one another using radio frequency transmission. Atlas PT X is located at the geofence intersection point, while Atlas PTs A, B, and C are located at the triangle points A, B, and C, respectively. The manual faller carried a PT attached at the hip (Atlas PT F).

The orientation of geofence crossing in each stand was also randomly selected from the sample of whole numbers between 1 and 360, with replacement. A rectangular geofence was established in each stand using a Suunto sight-through azimuth compass, fiberglass tape, and an Eos Arrow 100 GNSS unit (Eos Positioning Systems, Terrebonne, Quebec, Canada) with a specified accuracy of < 0.6 m [

In each stand, a manual faller carrying a PT attached at the belt crossed the geofence once by walking a 90-m route oriented perpendicular to the geofence (i.e., in the chosen geofence crossing direction), starting and ending 45 m from the intersection point. For consistency, the manual faller walked at a pace of 45 bpm, as dictated by a digital metronome. The route was established using a compass and 50-m fiberglass tape and was marked with pin flags. The observed time at which the faller crossed the geofence was recorded in the field using a custom script in R [

Within each stand, topographic, physical, and vegetative obstructions present along each LOS path between the geofence intersection point and the PTs located at triangle points A, B, and C were quantified during setup using a modification of the FIREMON line intercept method [_{i} is the measured distance of all vegetative obstructions recorded for the three 5-m sections along the _{i}, _{i}, _{i}, _{i}, _{i}, _{i}, and _{i} represent the distance of vegetative obstructions defined in _{i} represents the total distance of vegetation along the entire _{i} is the measured distance of all vegetative obstructions recorded in the three 5-m sections along the

Each LOS path was divided into 20 5-m sections and three sections were randomly selected for each LOS path. This figure shows the 20 sections and their locations along the LOS path. Sections highlighted in green represent the three randomly selected sections for which all vegetative obstructions were measured using the key in

Obstacle ID | Vegetative Obstruction |
---|---|

S | Deciduous shrub |

C | Coniferous vegetation |

T | Tree (stem) |

W | Coarse woody debris (CWD) |

SC | Deciduous shrub/coniferous vegetation |

SW | Deciduous shrub/CWD |

CW | Coniferous vegetation/CWD |

Once all obstructions were quantified and recorded, each LOS path was walked carrying a Garmin Alpha 100 GNSS-RF unit (Garmin, Olathe, Kansas, USA) to record the vertical elevation profile. Using the Garmin data, each LOS path was classified in terms of the presence or absence of concavity and convexity. A LOS path was concave if the minimum elevation along the path was at least 3 m below the lower of the two path endpoints. A LOS path was convex if the maximum elevation along the path was at least 3 m above the higher of the two path endpoints. The classification criteria for concavity and convexity is illustrated in

Blue dots represent the higher of the two LOS endpoints while red dots represent the lower of the two LOS endpoints. Green lines represent the ground surface along the LOS path.

To quantify forest stand characteristics, a 0.03-hectare fixed-area plot was established in each stand, centered at the intersection point. The DBH, total height, and height to the base of the live crown were quantified for all trees ≥ 12.5-cm DBH within the plot. Using these measurements, total basal area (TBA), trees per hectare (TPH), mean height (Ht), and quadratic mean diameter (QMD) were calculated for each stand and used as variables representing forest stand characteristics during analysis. Quadratic mean diameter is a commonly used metric in forestry that refers to the diameter of the tree of mean basal area (stem cross-sectional surface area), as measured at breast height (1.37 m). QMD is calculated as the square root of the squared stem diameters divided by the number of stems sampled, as defined in Eq (_{i} is the DBH of the

To quantify missed radio signals in each stand, the number of missed position updates transmitted from the faller’s PT (PT F) to the three PTs at the triangle points (PTs A, B, and C) was calculated for the 90-s interval centered on the observed geofence intersection time. Because all units were set to transmit their coordinates at 1-s intervals, 90 position updates would have been received in this time period in the absence of missed signals.

Stationary GNSS accuracy was summarized using RMSE, which is a common measure of GNSS positional error and represents the difference between the predicted and observed coordinates of a GNSS unit. In each stand, the predicted coordinates were obtained using the stationary PT located at the geofence crossing point (denoted as Atlas PT X in _{i} is the RMSE value in the _{i} is the observed easting value in the _{i} is the observed northing value in the _{ij} is the

The overall geofence intersection alert delay for each stand was derived by averaging the time-to-signal delay calculated at each of the three triangle points (A, B, and C) (Eq (_{i} is the overall delay for the geofence intersection in the _{i} is the observed time at which the faller crossed the geofence in the _{ij} is the predicted intersection time in the _{ik} is the predicted intersection time in the _{il} is the predicted intersection time in the

To test the null hypothesis that the probability of successful GNSS-RF signal propagation was not related to forest stand characteristics, topography, or obstructions in the line-of-sight, a binomial generalized linear mixed-effects model was used to evaluate relationships between the odds of missed signals as a function of vegetative LOS obstructions, topography, and forest stand characteristics. The model was fitted using the glmer function in the R lme4 package [_{i}), TBA, TPH, Ht, QMD, slope, aspect, and the presence or absence of forest roads, streams, convex slopes, and concave slopes (

Variable | Category |
---|---|

_{i}^{a} |
LOS obstruction |

_{mean}^{b} |
LOS obstruction |

TBA | Forest stand characteristic |

TPH | Forest stand characteristic |

Ht | Forest stand characteristic |

QMD | Forest stand characteristic |

Slope | Topography |

Aspect | Topography |

Presence/absence of forest roads | Topography |

Presence/absence of streams | Topography |

Presence/absence of convex slopes | Topography |

Presence/absence of concave slopes | Topography |

^{a} _{i} was used only in the analysis of missed radio signals.

^{b} _{mean} was used only in the analysis of RMSE and geofence intersection alert delay.

A linear mixed-effects model was also used to test the null hypothesis that neither forest stand characteristics, topography, nor physical obstructions affected GNSS accuracy. The model was fitted using the lmer function in the R lme4 package [_{mean}), TBA, TPH, Ht, QMD, slope, aspect, and the presence or absence of forest roads, streams, convex slopes, and concave slopes (_{mean} for each stand was calculated by averaging the total distance of vegetation (_{i}) from the three LOS paths within each stand. Also, because variables recorded as either present or absent (forest roads, streams, convex slopes, and concave slopes) were quantified along each LOS path, these variables were also considered to be present in this stand-level analysis if they were present along any of the LOS paths. The response variable was the PT RMSE in each stand (_{i}) calculated using Eq (

To test the null hypothesis that neither forest stand characteristics, topography, nor physical obstructions affected the time-to-signal accuracy of geofence crossings, a linear mixed-effects model was used to quantify relationships between the magnitude of geofence intersection alert delay as a function of forest stand characteristics, topographic structure, and vegetative LOS obstructions. The model was fitted using the lmer function in the R lme4 package [_{mean}), TBA, TPH, Ht, QMD, slope, aspect, and the presence or absence of forest roads, streams, convex slopes, and concave slopes (_{mean} for each stand was calculated by averaging the total distance of vegetation (_{i}) from the three LOS paths within each stand. Also, because variables recorded as either present or absent (forest roads, streams, convex slopes, and concave slopes) were quantified along each LOS path, these variables were also considered to be present in this stand-level analysis if they were present along any of the LOS paths. The response variable was the overall intersection alert delay in each stand (_{i}) calculated using Eq (

For each of the three analyses, a full model was first fitted to the data using all fixed effect terms. These fixed effects were removed one at a time in order of highest

The proportion of missed radio signals ranged from 0/90 to 20/90, with a mean of 3.30/90. The mixed-effects logistic regression model with the lowest AICc had total distance of vegetation along the LOS path (_{i}), TPH*0.01, convex, stream, road, and aspect as fixed effects (_{i} (^{−7}), while the odds of a missed signal increased by a factor of 1.10 per unit increase in TPH*0.01 (^{−3}). The odds of a missed signal were 1.61 times higher when a slope was convex vs. not convex (^{−2}) and 2.00 times higher in the presence of roads (^{−5}). In the presence of streams, the odds of a missed signal decreased by a factor of 0.66 (^{−2}). The odds of a missed signal were 1.05 times higher on east, 2.17 times higher on north, and 2.92 times higher on west aspects (as compared to south aspects), although this effect was only significant on north (^{−3}) and west (^{−4}) aspects.

Model term | Estimate | SE | Lower CI | Upper CI | DF | ||
---|---|---|---|---|---|---|---|

(Intercept) | 0.0187 | 0.2759 | 0.0109 | 0.0321 | −14.4247 | Inf | 3.6198 × 10^{−47} |

_{i} |
0.9331 | 0.0138 | 0.9082 | 0.9588 | −5.0028 | Inf | 5.6502 × 10^{−07} |

TPH*0.01 | 1.1048 | 0.0313 | 1.0391 | 1.1747 | 3.1837 | Inf | 1.4539 × 10^{−03} |

Convex^{a} |
1.6084 | 0.2264 | 1.0320 | 2.5067 | 2.0989 | Inf | 3.5823 × 10^{−02} |

Stream^{a} |
0.6552 | 0.1967 | 0.4455 | 0.9634 | −2.1495 | Inf | 3.1597 × 10^{−02} |

Forest road^{a} |
2.0042 | 0.1644 | 1.4522 | 2.7659 | 4.2298 | Inf | 2.3395 × 10^{−05} |

Aspect (E) | 1.0531 | 0.3147 | 0.5683 | 1.9515 | 0.1644 | Inf | 8.6941 × 10^{−01} |

Aspect (N) | 2.1718 | 0.3011 | 1.2038 | 3.9182 | 2.5761 | Inf | 9.9911 × 10^{−03} |

Aspect (W) | 2.9186 | 0.2843 | 1.6719 | 5.0950 | 3.7679 | Inf | 1.6464 × 10^{−04} |

Coefficient estimates, standard errors, and lower and upper bounds have been exponentiated to be on the odds scale.

^{a} Indicator variables represent the presence of each respective feature.

RMSE ranged from 1.81 m to 16.69 m, with a mean of 6.61 m. For the RMSE analysis, the mixed-effects model with the lowest AICc had Ht and QMD as fixed effects, both of which affected RMSE (^{−6}) but varied indirectly with QMD (^{−3}).

Predicted RMSE as a function of the two model variables (Ht and QMD). Predictions for each variable were made using the mean of the other predictor. 95% confidence intervals computed using the bootstrap are shown as colored bands. Points on each plot represent partial residuals.

Model term | Estimate | SE | Lower CI | Upper CI | DF | ||
---|---|---|---|---|---|---|---|

(Intercept) | 3.7528 | 1.2790 | 1.2461 | 6.2595 | 2.9343 | Inf | 3.3435 × 10^{−03} |

Ht | 0.6276 | 0.1415 | 0.3503 | 0.9048 | 4.4363 | Inf | 9.1526 × 10^{−06} |

QMD | −0.2737 | 0.0923 | −0.4547 | −0.0928 | −2.9653 | Inf | 3.0243 × 10^{−03} |

Geofence intersection alert delay ranged from −5.33 s to 66 s, with a mean of 18.62 s. The final mixed-effects model used to analyze the delay had TBA, concave, and aspect as fixed effects (^{−4}) and was also higher in the presence of concave slopes when compared to slopes that were not concave (^{−2}). Finally, the delay was smaller on east, north, and south aspects (as compared to west aspects), although this effect was only significant on east aspects (^{−2}).

Predicted delay as a function of the three model variables (TBA, concave, and aspect). Predictions for each variable were made using the mean of the other predictors. 95% confidence intervals computed using the bootstrap are shown as colored bands. Points on each plot represent partial residuals.

Model term | Estimate | SE | Lower CI | Upper CI | DF | ||
---|---|---|---|---|---|---|---|

(Intercept) | 11.9425 | 8.5931 | −4.8998 | 28.7847 | 1.3898 | Inf | 1.6460 × 10^{−01} |

TBA | 0.4988 | 0.1463 | 0.2121 | 0.7855 | 3.4104 | Inf | 6.4876 × 10^{−04} |

Concave^{a} |
13.5946 | 6.0494 | 1.7381 | 25.4512 | 2.2473 | Inf | 2.4622 × 10^{−02} |

Aspect (E) | −19.0832 | 8.0855 | −34.9306 | −3.2359 | −2.3602 | Inf | 1.8267 × 10^{−02} |

Aspect (N) | −15.7249 | 9.4249 | −34.1974 | 2.7475 | −1.6684 | Inf | 9.5227 × 10^{−02} |

Aspect (S) | −12.5487 | 9.5119 | −31.1916 | 6.0942 | −1.3193 | Inf | 1.8708 × 10^{−01} |

^{a} Variable indicating the presence of concave slopes.

Analysis of missed radio signals indicated that forest stand characteristics, topography, and LOS obstructions affected the odds of missed signals. The odds of missed radio signals varied directly with stand density (TPH) and varied indirectly with LOS obstructions (_{i}). Because previous work has shown that radio signal attenuation increases with greater vegetation depth and density, this result is somewhat counterintuitive [

Analysis of the PT RMSE indicated that only stand variables affected stationary GNSS accuracy. RMSE varied directly with Ht, but decreased with increasing QMD. Because characteristics associated with increasing forest stand density, such as canopy cover, are known to reduce GNSS accuracy, we expected that both predictors would have positive relationships with RMSE. Thus, this result is counterintuitive and may be an artefact of the data. A few sampled stands had relatively open canopies with large, mature trees at low density that may have affected the relationship between RMSE and QMD.

Both stand and topographic variables affected geofence intersection alert delay. Because of the way time delays were calculated, positive delays represent late alerts while negative delays represent early alerts. The alert delay varied directly with TBA and was higher in the presence of concave slopes. Aspect also affected alert delay, with delay being smaller on east slopes compared to west slopes. Taken together these results show that the time-to-signal accuracy of GNSS-RF geofence crossings is affected by both GNSS accuracy and radio signal propagation.

The relationships among the response and predictor variables were not strong for any of the three models. In the case of the missed radio signals, this could be due to the fact that the proportion of missed signals was generally low and the distance between radios fairly small (100 m). In terms of alert delay and RMSE, it is important to note that PTs receive coordinates from NAVSTAR GPS satellites only. Newer GNSS devices receive coordinates from multiple satellite constellations (i.e., from GPS, GLONASS, and BeiDou), which may improve accuracy and reliability in forested environments [

Our results suggest that GNSS-RF radio signal propagation is related to stand density, topography, and obstructions in the line-of-sight and that geofence alert timing is related to stand characteristics and topography. This indicates that the accuracy and successful sharing of GNSS coordinates may change depending on stand conditions and topography, both of which vary on active timber sales. Thus, real-time positioning based on consumer-grade GNSS-RF units may improve general communication and situational awareness on logging operations by allowing ground workers and equipment operators to view the relative positions of nearby workers and machines in real-time on mobile devices. However, high-resolution, mission-critical safety applications of this technology (e.g., geofencing) are not yet advisable under mature forest conditions. Future work should focus on the development of correction methods that account for the effects of forest stand characteristics on GNSS accuracy and geofence alert delay. Previous work has shown that adjustments should also be made for the angle and speed at which a tracked object approaches a geofence [

(XLSX)

(XLSX)

(XLSX)

The authors would like to thank four field technicians, Molly Rard, Rebecca Ramsey, Kevin Cannon, and Andrew Naughton, for their valuable assistance with experiment setup, stand inventory, and data collection.