Error Analysis of Measuring the Diameter, Tree Height, and Volume of Standing Tree Using Electronic Theodolite

The ability to measure diameter, tree height, and tree volume is of great value in forestry investigations. These three factors are not considered together when error analyses of measurement results are conducted. The aim of this study was to quantify the system error analysis of the three factors mentioned above. Based on the principle of electronic theodolite non-destructive measurement of stem and error propagation theory, a mathematical model for calculating diameter, tree height, and volume error was derived to calculate the error in theoretical measurements. Moreover, a method utilizing F tests was proposed for analyzing the relative error based on the diameter, tree height, and volume factors. A total of 87 trees in Beijing were chosen as the experimental sample; the trees were divided into three sample groups according to size. The accuracy was assessed using the traditional method. The results showed that the error varied slightly with the size of the tree. The system error of the measured diameter was 0.44–0.59%; for tree height, this was 0.29–0.89%, and for the volume, it was 0.31–0.99%. There were no significant differences between the measured values and the true values of the resolved wood. The relative mean errors of volume, tree height, and diameter in practice were 4.47%, 1.18%, and 2.02%, respectively. The results suggest that the precision in electronic theodolite measurements in China is much higher than the accuracy requirement of relative error not exceeding 3–5%.