# Use of Real‐Time GNSS‐RF Data to Characterize the Swing Movements of Forestry Equipment

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results

#### 3.1. Summary

#### 3.2. Binomial Logistic Regression-Element Characterization

#### 3.3. Swing Angle Analysis

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**Bar chart representing the proportion of correct classifications of the Swing Unload cycle element at the grapple and heel locations at 18 angle intervals.

**Figure 4.**Bar chart representing the proportion of correct classifications of the Return cycle elements at the grapple and heel locations at 18 angle intervals.

**Figure 5.**These figures represent the relationship between GNSS-RF derived angle measurements and observed angle intervals at the Grapple and Heel locations for the (

**a**) Swing Unload and (

**b**) Return elements.

**Figure 6.**The GNSS-RF transponders create a movement progression track between data points through the duration of the trials which are shown for the two (2) transponder locations and three (3) transmission intervals used in the experiment in addition to the cab location.

Variable | Df ^{1} | Deviance | Resid. Df ^{2} | Resid. Dev. ^{3} | Pr (>Chi) ^{4} |
---|---|---|---|---|---|

NULL | 2680 | 2054 | |||

Interval | 2 | 74.18 | 2678 | 1980 | <0.001 |

Swing Angle | 1 | 42.38 | 2677 | 1937 | <0.001 |

Location | 1 | 37.62 | 2676 | 1900 | <0.001 |

Cycle Element | 1 | 0.04 | 2675 | 1900 | 0.8421 |

Interval: Swing Angle | 2 | 1.00 | 2673 | 1899 | 0.6043 |

^{1}Degrees of freedom;

^{2}Degrees of freedom of the residuals;

^{3}Deviance of the residuals;

^{4}p-value for the level of significance on correct classification.

Location | Interval | Element | Data Points | Total Angle (Degrees) Observed (GPS) | Proportion Correct |
---|---|---|---|---|---|

Grapple | 1339 | 0.84 ^{1} | |||

2.5 | 769 | 27,360 (23,882) | 0.94 | ||

Swing Unload | 451 | 13,680 (12,950) | 0.99 | ||

Return | 318 | 13,680 (10,932) | 0.88 | ||

5.0 | 382 | 27,360 (21,442) | 0.90 | ||

Swing Unload | 219 | 13,680 (11,698) | 0.89 | ||

Return | 163 | 13,680 (9744) | 0.91 | ||

10.0 | 188 | 27,360 (14,918) | 0.68 | ||

Swing Unload | 113 | 13,680 (8751) | 0.71 | ||

Return | 75 | 13,680 (6167) | 0.66 | ||

Heel | 1342 | 0.79 ^{1} | |||

2.5 | 773 | 27,360 (24,455) | 0.82 | ||

Swing Unload | 443 | 13,680 (12,495) | 0.84 | ||

Return | 330 | 13,680 (11,960) | 0.80 | ||

5.0 | 376 | 27,360 (22,740) | 0.86 | ||

Swing Unload | 227 | 13,680 (12,609) | 0.84 | ||

Return | 149 | 13,680 (10,131) | 0.87 | ||

10.0 | 193 | 27,360 (15,558) | 0.69 | ||

Swing Unload | 110 | 13,680 (9195) | 0.71 | ||

Return | 83 | 13,680 (6363) | 0.68 |

^{1}Mean proportion of correctly classified elements across all treatments for Heel or Grapple location.

**Table 3.**Logistic regression coefficients associated with model describing variable impact on whether GPS returned correct element classification as represented by field observations.

Variable | Estimate | SE ^{1} | p-Value | Odds Ratio | 95% Confidence |
---|---|---|---|---|---|

Intercept | 1.748 | 0.212 | <0.001 | 5.741 | 3.813–8.772 |

Rate 5 | 0.144 | 0.320 | 0.6525 | 1.155 | 0.621–2.182 |

Rate 10 | −1.339 | 0.328 | <0.001 | 0.262 | 0.138–0.499 |

Swing Angle | 0.004 | 0.001 | <0.001 | 1.004 | 1.003–1.006 |

Location Heel | −0.744 | 0.124 | <0.001 | 0.476 | 0.372–0.605 |

Cycle Element | 0.025 | 0.122 | 0.8374 | 1.025 | 0.807–1.300 |

Rate 5: Swing Angle | −0.001 | 0.002 | 0.3789 | 0.999 | 0.996–1.002 |

Rate 10: Swing Angle | 0.000 | 0.002 | 0.8781 | 1.000 | 0.999–1.003 |

^{1}Standard error of the variable estimate

**Table 4.**Summary of equivalence-based regression results. The model represents the various combinations of transmission interval (2.5,5,10); transponder location, grapple (G) or heel (H); and cycle element, swing unload (SU), and return (R). Sample size is denoted by n, and the approximate joint two one-sided 95% confidence intervals for the slope and intercept are: (${{C}^{-}}_{{\beta}_{1}}$, ${{C}^{+}}_{{\beta}_{1}}$) and (${{C}^{-}}_{{\beta}_{0}}$, ${{C}^{+}}_{{\beta}_{0}}$), respectively. The former should be contained by the intercept interval of equivalence, (${{I}^{-}}_{{\beta}_{0}}$, ${{I}^{+}}_{{\beta}_{0}}$) = $\overline{y}$ ± 25%, and the latter by the slope interval of equivalence (${{I}^{-}}_{{\beta}_{1}}$, ${{I}^{+}}_{{\beta}_{1}}$) = 1 ± 0.25.

Model | n | ${{\mathit{C}}^{-}}_{{\mathit{\beta}}_{0}}$ | ${{\mathit{C}}^{+}}_{{\mathit{\beta}}_{0}}$ | ${{\mathit{I}}^{-}}_{{\mathit{\beta}}_{0}}$ | ${{\mathit{I}}^{+}}_{{\mathit{\beta}}_{0}}$ | ${\mathit{\beta}}_{0}$ Result | ${{\mathit{C}}^{-}}_{{\mathit{\beta}}_{1}}$ | ${{\mathit{C}}^{+}}_{{\mathit{\beta}}_{1}}$ | ${{\mathit{I}}^{-}}_{{\mathit{\beta}}_{1}}$ | ${{\mathit{I}}^{+}}_{{\mathit{\beta}}_{1}}$ | ${\mathit{\beta}}_{1}$ Result |
---|---|---|---|---|---|---|---|---|---|---|---|

G.SU.2.5 | 72 | 186.29 | 194.13 | 161.88 | 197.85 | Reject | 0.988 | 1.057 | 0.9 | 1.1 | Reject |

G.SU.5 | 72 | 184.46 | 195.91 | 146.23 | 178.72 | Fail | 0.934 | 1.042 | 0.9 | 1.1 | Reject |

G.SU.10 | 65 | 188.92 | 221.63 | 141.74 | 173.23 | Fail | 0.539 | 0.876 | 0.9 | 1.1 | Fail |

H.SU.2.5 | 72 | 175.16 | 205.88 | 156.19 | 190.90 | Fail | 0.533 | 0.779 | 0.9 | 1.1 | Fail |

H.SU.5 | 72 | 177.62 | 203.34 | 157.62 | 192.64 | Fail | 0.717 | 0.972 | 0.9 | 1.1 | Fail |

H.SU.10 | 64 | 192.70 | 220.46 | 129.30 | 158.04 | Fail | 0.625 | 0.893 | 0.9 | 1.1 | Fail |

G.R.2.5 | 68 | 195.02 | 205.03 | 144.68 | 176.83 | Fail | 0.946 | 1.035 | 0.9 | 1.1 | Reject |

G.R.5 | 66 | 196.55 | 212.46 | 132.87 | 162.40 | Fail | 0.886 | 1.044 | 0.9 | 1.1 | Fail |

G.R.10 | 44 | 229.89 | 263.50 | 95.75 | 117.03 | Fail | 0.468 | 0.902 | 0.9 | 1.1 | Fail |

H.R.2.5 | 67 | 187.15 | 218.16 | 160.66 | 196.36 | Fail | 0.603 | 0.920 | 0.9 | 1.1 | Fail |

H.R.5 | 63 | 199.18 | 221.60 | 144.72 | 176.88 | Fail | 0.864 | 1.097 | 0.9 | 1.1 | Fail |

H.R.10 | 48 | 216.13 | 245.22 | 119.30 | 145.81 | Fail | 0.699 | 1.022 | 0.9 | 1.1 | Fail |

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**MDPI and ACS Style**

Becker, R.M.; Keefe, R.F.; Anderson, N.M. Use of Real‐Time GNSS‐RF Data to Characterize the Swing Movements of Forestry Equipment. *Forests* **2017**, *8*, 44.
https://doi.org/10.3390/f8020044

**AMA Style**

Becker RM, Keefe RF, Anderson NM. Use of Real‐Time GNSS‐RF Data to Characterize the Swing Movements of Forestry Equipment. *Forests*. 2017; 8(2):44.
https://doi.org/10.3390/f8020044

**Chicago/Turabian Style**

Becker, Ryer M., Robert F. Keefe, and Nathaniel M. Anderson. 2017. "Use of Real‐Time GNSS‐RF Data to Characterize the Swing Movements of Forestry Equipment" *Forests* 8, no. 2: 44.
https://doi.org/10.3390/f8020044