Development and Testing of a Tree Height Measurement Device

Abstract

Tree height is a key indicator in forest resource inventories, playing a vital role in evaluating forest resources, carbon stocks, and biomass. However, conventional tree height measurement methods often suffer from limitations such as inadequate accuracy and low efficiency. This paper proposes a portable tree height measurement device based on the integration of ultra-wideband (UWB) technology and an accelerometer, enabling high-precision, low-cost, and rapid tree height measurements. The device adopts a modular design, integrating a UWB ranging sensor, a triaxial accelerometer, a main control unit, and wireless communication modules. It acquires precise distance information via the double-sided two-way ranging (DS-TWR) algorithm and computes tree height by incorporating the pitch angle measured by the accelerometer. Through measurements on 80 trees of various species, compared to results from Total Station, the root mean square error (RMSE) was 0.621 m, with an overall bias of 0.104 m (0.79%) and an overall device accuracy of 95.75%. Additionally, the device features real-time data transmission and cloud storage capabilities, offering an efficient and convenient technical solution for the digital management of forest resources. It holds promising application prospects in areas such as forest resource inventories, ecological monitoring, and forestry production management.

1. Introduction

Forests, as the world’s most important terrestrial ecosystems, provide key ecological services such as carbon storage, climate regulation, and biodiversity conservation [1,2]. Accurate assessment of forest resource conditions, particularly tree height measurement, constitutes the foundation for forest resource inventories and management [3]. Tree height is directly linked to biomass estimation, carbon stock assessment, and the construction of forest growth models; therefore, precise tree height measurement is central to achieving sustainable forest resource management [4].

Conventional tree height measurement methods, such as the trigonometric method, projection method, and optical hypsometers, while capable of meeting requirements to a certain extent, often encounter issues of insufficient accuracy and low efficiency in complex forest environments [5,6]. Particularly in dense forests, steep slopes, and intricate terrains, traditional methods exhibit substantial measurement errors, with the measurement process being cumbersome and time-consuming. Although Terrestrial Laser Scanning (TLS) offers high measurement accuracy, its application in routine forestry surveys still faces certain challenges. These systems typically require complex post-processing workflows and demand a high level of technical expertise from operators. As a result, their use is somewhat limited in routine forestry investigations that require rapid, large-scale, and low-cost data collection [7,8]. Therefore, improving the operational simplicity and applicability of devices while ensuring accuracy remains an urgent technical challenge to be addressed.

In recent years, scholars both domestically and internationally have conducted extensive research on tree height measurement. Andersen et al. proposed a tree height extraction method based on airborne LiDAR, which offers efficiency advantages for large-area forest surveys. However, in narrow conical tree crowns and dense forest stands, issues such as treetop detection errors and systematic underestimation due to beam divergence effects persist [9]. Yuan et al. developed a tree height meter based on an infrared sensor, which achieves high accuracy but fails to address errors arising from occlusion [10]. Tian et al. derived point clouds from terrestrial laser scanning and UAV (Unmanned Aerial Vehicle) imagery, and employed a canopy height model to extract tree heights in high-density coniferous forests, achieving a root mean square error of 6 cm [11]. Shen et al. proposed a 3D reconstruction method for tree height measurement based on smartphones and deep learning, with an average relative error of 3.2%; however, the proposed method and its results remain at the experimental stage and are not yet suitable for actual application in forestry operations [12]. Mahmud et al. developed a geometric-principle-based mobile application, M-Tree, for tree height measurement. This app computes tree heights by capturing images of trees and utilizing pixel marking, while also establishing a global tree height database, demonstrating high precision and broad application potential [13].

With the development of wireless communication and sensor technologies, new solutions are provided for forest resource inventories [14,15]. Ultra-wideband (UWB) technology, due to its advantages such as high precision, strong anti-interference capability, and low power consumption, is gradually gaining widespread application across various industries [16]. UWB technology is a distance measurement method based on time-domain signal acquisition, utilizing the signal’s time of flight (TOF) to determine the distance between two UWB sensors [17]. Furthermore, UWB technology can effectively improve ranging accuracy and maintain good signal transmission quality in complex environments [18]. Currently, UWB technology has been widely applied in agriculture and forestry. Liu et al. [19] analyzed the performance of UWB positioning systems within forest canopies, highlighting their potential for forestry automation, particularly in robot-assisted measurements. Pham et al. [20] integrated UWB with inertial measurement unit (IMU) technology to develop a navigation system for automated spraying operations in precision agriculture, demonstrating its potential to reduce pesticide usage and improve operational accuracy.

Although existing tree height measurement techniques each have their advantages, a practical solution that simultaneously achieves high accuracy, low cost, portability, and strong adaptability to complex terrain is still lacking. This study aims to address this critical gap. Accordingly, the main objectives are as follows:

(1)

To design and develop a portable tree height measurement device that integrates ultra-wideband (UWB) ranging technology with an accelerometer sensor.

(2)

To develop compensation algorithms for sloped terrain and operational errors, thereby enhancing the measurement accuracy and stability of the device under real forestry conditions.

(3)

To conduct systematic field comparison experiments with a high-precision total station in order to comprehensively evaluate the device’s accuracy, reliability, and performance under different observational geometries.

2. Development of the Tree Height Measurement Device

2.1. Mechanical Structure Design

The structure of the tree height measurement device is illustrated in Figure 1, primarily comprising components such as the device enclosure, UWB ranging sensor, and circuit board. The device housing is equipped with an OLED display screen, power switch, charging interface, and data exchange interface; internal components include a PCB, 4G communication module, UWB ranging sensor, three-axis accelerometer, and lithium-ion battery. A single-channel UWB tag and antenna are positioned at the center of the device, with the antenna externally mounted to enhance signal strength for long-distance outdoor applications. The lower section of the device features two button panels, facilitating rapid operations by the operator during the measurement process and enabling interaction with the device interface. To enhance operational convenience, the device is assembled using three limiting frames, minimizing the use of screws while ensuring structural stability. The frame clasps are configured with sighting apertures, allowing the operator to perform precise aiming, thereby enhancing measurement convenience and supporting further augmentation of the aiming function through extension accessories, such as telescopes or sighting scopes.

2.2. Circuit and Component Integration Design

The tree height measurement device comprises a mobile measuring unit and an anchor base station, with the overall circuit framework illustrated in Figure 2. The device integrates various functional modules, including the main control module, sampling module, power module, interaction module, and communication module, with the main control module coordinating the operations of all modules. The main control module employs an STC15 series microcontroller, featuring low power consumption and robust anti-interference capabilities. The power management module includes a buck converter, power level detection, control switches, and power inputs, etc. The buck converter provides multiple voltage levels to various modules, while the built-in 4000 mAh lithium battery allows for real-time monitoring of power status via the power management module, ensuring stable system operation. Field tests indicate that the device’s battery life can last up to 30 h, providing reliable power support for tree height measurements. The sampling module consists of an accelerometer and a UWB ranging module, responsible for distance measurement and extraction of the pitch angle relative to the horizontal plane. The angle data undergoes processing and conversion through the analog-to-digital conversion module. The UWB ranging tag measures the distance between the device and the anchor base station. The 4G communication module uploads collected data to the server, while the Bluetooth communication module Android application facilitates real-time data transmission to Android devices. The storage module is equipped with an SD card for real-time data storage, preventing data loss. The real-time interaction module displays measurement data to the user via an OLED screen, allowing users to select desired functions through a touchscreen. The UWB anchor base station primarily comprises a power supply and a UWB tag module, facilitating placement at the tree base.

The tree height measurement device designed in this study utilizes a double-layer printed circuit board (PCB). Based on the design principles of the aforementioned modules, the components are rationally arranged, as illustrated in the device’s PCB diagram shown in Figure 3.

2.3. Design Principles

2.3.1. Principles of UWB Distance Measurement

The ranging modes of UWB technology include Single-Sided Two-Way Ranging (SS-TWR) and Double-Sided Two-Way Ranging (DS-TWR) [21]. Due to potential measurement errors arising from the accumulation of response delay and signal time-of-flight, the SS-TWR mode is typically employed in scenarios requiring short-duration and relatively coarse measurements. In contrast, the DS-TWR mode, by recording signal round-trip times, can more effectively mitigate errors and enhance measurement precision. The strengths of UWB technology lie in its capability to maintain stable signal transmission in complex environments, rendering it widely applicable in domains such as indoor positioning, industrial manufacturing, and energy transportation [22,23,24]. Compared to laser ranging technology, UWB not only offers lower costs and greater portability but also effectively circumvents the limitations of laser techniques in certain environments, such as interference from intense light or obstruction by transparent objects. The UWB module used in this study is the D-DWM-PG3.6, with a center frequency of 4492.8 MHz, and it incorporates a built-in Kalman filtering algorithm.

In the actual distance measurement process, the base station initially transmits a request frame signal to the tag, with the signal’s time-of-flight from the base station to the tag denoted as TOF1. Upon receiving the signal, the tag enters a preparatory delay phase (TreplyA), after which it returns a response signal to the base station, with the time-of-flight from the tag to the base station being TOF2. In this process, TreplyB represents the second delay interval for the tag to complete signal processing and prepare the return transmission. Finally, the base station sends a concluding frame signal, with the signal’s time-of-flight denoted as TOF3. The structure of this ranging model is illustrated in Figure 4.

The total round-trip time for UWB Double-Sided Two-Way Ranging (DS-TWR) is calculated using the following formula:

$$TOF=\left({\displaystyle \frac{T_{roundA}\times T_{roundB}-T_{raplyA}\times T_{raplyB}}{T_{roundA}+T_{roundB}+T_{raplyA}+T_{raplyB}}}\right)$$

(1)

The propagation speed of wireless signals in air is equivalent to the speed of light c (2.998 × 10⁸ m/s). By measuring the signal’s time-of-flight (TOF), the distance (L) between the tag and the base station can be calculated using the following formula:

$$L=c\times TOF$$

(2)

2.3.2. Principles of Angle Measurement

Angle sensors compute angular changes by measuring the rotational amplitude of an object, with common types including accelerometers, gyroscopes, magnetometers, and optical angle sensors [25]. Accelerometers utilize gravitational acceleration to directly calculate the tilt angle of a device without requiring external references, and they possess advantages such as low power consumption, compact size, and low cost, which make them highly suitable for portable battery-powered devices [26].

The GY-291 accelerometer used in this device adopts a MEMS capacitive detection principle, wherein the displacement of a micro-mass block induces capacitance changes, thereby calculating tilt angles [27]. The sensor is based on the gravity vector projection principle to detect three-axis accelerations (X, Y, Z) for determining angular changes. Following internal signal processing, the acceleration signals are converted into voltage signals, which are then digitized via an ADC to ultimately output precise three-axis acceleration data. This sensor supports measurement ranges from ±2 g to ±16 g, with a resolution of up to 13 bits, enabling high-precision angle measurement capabilities. To obtain more stable and accurate pitch angle measurements, the accelerometer used in this device employs a short-term mean filtering strategy. At the moment the user initiates a measurement, the system rapidly collects multiple sets of angle data within an approximately 100-millisecond time window and computes their average. This approach is equivalent to a low-pass filter, effectively reducing the influence of random noise and thereby improving measurement stability.

2.4. Software Design

The software functionalities of the device are primarily dedicated to tree height measurement, encompassing button control, angle computation, UWB ranging, height calculation, and data management. The system’s workflow is illustrated in Figure 5, comprising the object layer, physical layer, hardware layer, data layer, and software layer. The software layer incorporates multiple subroutines, primarily including the human–machine interaction program for key input and display control, the sampling program for extracting tree height information, and the data management program for data storage and communication. Upon completion of the tree height measurement, the system automatically consolidates the measurement data into a series of comprehensive datasets, thereby achieving data integration and management. The upper computer interface, as depicted in Figure 6, primarily implements functions such as reading device information, data statistics, and exporting data, enabling measurement personnel to process and analyze data more efficiently.

3. Tree Height Measurement Design

To enhance the precision of tree height measurements, this study proposes a tree height measurement approach that integrates UWB wireless ranging technology with high-precision angle measurement techniques. This approach enables effective tree height measurements under diverse terrain conditions and is applicable to various environments, including flat ground and slopes.

3.1. Tree Height Measurement on Flat Ground

The tree height measurement process is illustrated in Figure 7, where the position of the measurement device be denoted as point A, the base of the tree as point B, and the treetop as point C. The entire measurement process can be divided into two key steps: determining the relative positional relationship between the measurement device and the base of the tree, and acquiring angular information at the tree’s apex, thereby deriving the actual height of the tree. The specific measurement steps are as follows:

1.

Base Station Positioning and Horizontal Distance Determination:

(1)

Place a UWB anchor base station at the base of the tree and ensure that the measurement device is aligned with the base station. The UWB transmitting unit of the device sends ultra-short pulsed radio waves to the base station.

(2)

Upon arrival of the UWB signal at the base station, the signal is received by the base station, which then returns a response signal to the receiving unit of the measurement device. By calculating the signal’s time-of-flight (TOF), the system can precisely determine the absolute line-of-sight distance AB between the measurement device and the base station.

2.

Tree Height Calculation:

(1)

Acquire the tilt angle α using the accelerometer within the measurement device and, according to Equation (3), compute the horizontal distance AD between the device and the base of the tree.

(2)

Next, the operator adjusts the line of sight to the tree top C and performs another measurement to obtain the pitch angle β at the tree top. Based on these data, in conjunction with the trigonometric calculation formula in Equation (4), the actual tree height (H) is ultimately derived:

$$\mathrm{AD}=\mathrm{AB}\times \cos (\alpha )$$

(3)

$$\mathrm{H}=\mathrm{AD}\times \tan (\beta )+\mathrm{AB}\times \sin (\alpha )$$

(4)

Figure 7. Illustration of Tree Height Measurement on Flat Ground.

Figure 7. Illustration of Tree Height Measurement on Flat Ground.

3.2. Slope Terrain Tree Height Measurement Method

On sloped terrain, tree height measurement is influenced by topographic gradient. To accurately measure tree height, this device employs a slope optimization algorithm that comprehensively considers the measurement angle, the elevation difference between the observer and the base of the tree, and the tilt angle of the device, thereby correcting the tree height based on geometric relationships. During the measurement process, the system automatically determines the measurer’s position, ascertaining whether it is uphill or downhill relative to the base of the tree, and applies the corresponding formulas for tree height correction according to the different scenarios.

1.

Tree Height Measurement in Downslope Scenarios

As illustrated in Figure 8a, in practical downslope measurements, when the measurement angle is below the horizontal plane, it indicates that the observer is positioned above the base of the tree, with the tree base at a lower elevation than the measurement device. As depicted in the schematic diagram in Figure 8b, the device first determines the horizontal distance AB between the tree and the measurement device, while obtaining the pitch angles α and β relative to the horizontal plane via the accelerometer. Concurrently, the system computes the elevation difference BD between the observer and the tree base. Based on these parameters, the actual tree height H is calculated using Equation (5):

$$H=AB\times sin\alpha +AB\times cos\alpha \times tan\beta$$

(5)

2.

Tree Height Measurement in Upslope Scenarios

As shown in Figure 9, when the tree is situated upslope, the horizontal distance AB and elevation difference BD between the observer and the tree base, along with the pitch angles α and β, must still be determined. However, since the observer is positioned below the tree base, the tree height calculation differs. The actual tree height H is derived using Equation (6):

$$H=AB\times cos\alpha \times tan\beta -AB\times sin\alpha$$

(6)

3.3. Operational Error Compensation Method

During the measurement process, separate aiming at the tree base and treetop is required; however, positional shifts in the device may occur between these two measurements, as illustrated in Figure 10, particularly due to arm-raising motions that can induce height deviations.

Therefore, relying solely on angle measurements to estimate tree height may introduce additional errors. To address this issue, it is necessary to establish a motion trajectory model of the device, analyze its positional changes, and apply error compensation. Assuming that the device movement during the arm-raising process can be approximated as linear with relatively small displacement, the inclination state of the device can be monitored in real time using an accelerometer. Combined with UWB range measurements that provide the distances AD and AC between the device and the anchor point before and after arm-raising, the height variation H of the device during this process can be calculated using Equation (7), thereby improving measurement accuracy.

$$\mathrm{H}=CD=BD-BC=\left|\sqrt{{\mathrm{AD}}^2-{\left(\mathrm{AC}\times \mathrm{s}in\alpha \right)}^2}\right|-\mathrm{AC}\times \cos \alpha$$

(7)

In the equation, CD denotes the device error before and after arm-raising, BC and BD represent the height differences between the device (before and after arm-raising) and the tree base, and AD and AC correspond to the slant distances from the device (before and after arm-raising) to the anchor point. The derivation process is provided in Appendix B.

4. Experiments and Analysis

4.1. Experimental Site and Subjects

This study was conducted at the Donghu Campus of Zhejiang A&F University (geographical coordinates: 30°15′ N, 119°43′ E, located in Lin’an District, Hangzhou, China). The campus features typical mountainous terrain with mixed coniferous and broadleaf forests, providing an ideal environment for testing the functionality of the device.

To comprehensively evaluate the measurement performance of the developed device, the experimental design encompassed three representative application scenarios, namely different tree species, terrain conditions, and observation distances. The specific experiments were as follows:

(1)

Overall accuracy assessment: Eighty trees of varying heights and species were randomly selected from the campus forest as measurement subjects, including Pine, Goldenrain Tree, Ginkgo, Soapberry, and London Plane Tree. The true heights of all samples were obtained by averaging multiple measurements with a total station (model: NTS-332R15M) and used as the reference standard. Independent measurements of all samples were then conducted using both the proposed device and a laser rangefinder (manufactured by SNDWAY Technology Co., Ltd., Humen Town, China). A schematic illustration of the measurements using the proposed device and the total station is shown in Figure 11.

(2)

Tree height measurement at different distances: Sixteen structurally intact trees without occlusion were selected from the above sample set, which allowed repeated measurements at four observation distances (5 m, 10 m, 15 m, and 20 m) under good line-of-sight conditions. These tests were used to analyze the stability and error variation in the proposed device across different observation distances.

(3)

Slope correction and arm-raising compensation experiment: To examine the impact of complex terrain on measurement accuracy, four trees located on sites with different slope gradients were selected. Measurements were conducted under three conditions—Uncorrected, Slope Correction, and Full Correction—to compare performance and evaluate the system’s capability for error suppression and algorithmic adaptability under terrain-induced disturbances.

4.2. Measurement Procedure Design

(1)

Step 1: Place the UWB anchor base station at the base of the tree, activate the measurement device, and select the “Tree Height Measurement” function. The device enters measurement mode, with the screen displaying in real-time the horizontal distance between the device and the UWB anchor base station, as well as the current tilt angle.

(2)

Step 2: The operator moves to a position where the base and apex of the measured tree can be viewed simultaneously, aligns the measurement device with the UWB anchor at the tree base, and the system automatically computes and displays the horizontal distance from the measurement point to the tree base, along with the pitch angle.

(3)

Step 3: The operator presses the confirmation key, whereupon the system records the base data and prompts adjustment of the device to align with the tree apex. Upon pressing the confirmation key again, the system acquires the apex tilt angle and, based on the measurement model, automatically calculates and displays the tree height.

(4)

Step 4: Upon completion of the tree height measurement, connect the device to a computer to upload the data to the PC-based upper computer for statistical analysis.

4.3. Data Accuracy Assessment

In this study, a multi-group data comparison method was employed to verify the accuracy of the tree height measurement device, with the tree height measured by the total station taken as the reference value. The height values obtained by the proposed device and by a laser altimeter were used as comparative values and analyzed against those measured by the total station. Accuracy evaluation of the measurement data was conducted using indicators from Equation (8), including error (Error), bias (BIAS), relative bias (relBIAS), root mean square error (RMSE), relative root mean square error (relRMSE), and relative accuracy.

$$\left\{\begin{array}{}Error=t{h}_i-T{H}_i\\ BIAS={\displaystyle \frac{{{\displaystyle \sum }}_{i-1}^n\left(t{h}_i-T{H}_i\right)}{n}}\\ relBIAS=\frac{{{\displaystyle \sum }}_{i-1}^n\left(\frac{{th}_i}{{TH}_i}-1\right)}{n}\times 100\%\\ RMSE=\sqrt{{\displaystyle \frac{{{\displaystyle \sum }}_{i-1}^n{({th}_i-{TH}_i)}^2}{n}}}\\ relRMSE=\sqrt{{\displaystyle \frac{{{\displaystyle \sum }}_{i-\mathrm{l}}^n{(\frac{{th}_i}{{TH}_i}-1)}^2}{n}}}\times 100\%\\ relativeAccuracy=1-relativeRMSE\end{array}\right.$$

(8)

where THi is the total station measurement value, thi is the comparison device measurement value, and n is the number of data points.

4.4. Experimental Analysis

4.4.1. Overall Measurement Accuracy Evaluation

To objectively and comprehensively evaluate the overall performance of the tree height measurement device developed in this study, height data from 80 trees (ranging from 4.8 m to 26.56 m) were collected. The measurement results obtained from the proposed device and the laser altimeter were systematically compared with those of the total station (considered as the ground truth). The tree heights were categorized into three groups—less than 10 m, 10–20 m, and greater than 20 m—and for each category, the following metrics were calculated: bias (BIAS), relative bias (relBIAS), root mean square error (RMSE), relative root mean square error (relRMSE), and relative accuracy. The results are summarized in

Table 1. Comparison of tree height measurements obtained from different devices.

Tree Height Category	Number of Trees	Proposed Device				Laser Altimeter
		BIAS (m)	relBIAS (%)	RMSE (m)	relRMSE (%)	BIAS (m)	relBIAS (%)	RMSE (m)	relRMSE (%)
Less than 10 m	36	0.042	0.57	0.254	3.28	−0.163	−1.72	0.596	7.56
10–20 m	36	0.246	1.48	0.713	4.95	0.374	1.77	1.48	10
Greater than 20 m	8	−0.256	−1.33	1.132	4.72	0.461	2.33	2.27	9.47
Total	80	0.104	0.79	0.621	4.25	0.141	0.26	1.289	8.93

.

The results show that, compared with the total station measurements, the proposed device achieved an overall bias (BIAS) of 0.104 m (0.79%), a root mean square error (RMSE) of 0.621 m (4.25%), and an overall accuracy of 95.75%. In contrast, the laser altimeter exhibited an overall bias (BIAS) of 0.141 m (0.26%), an RMSE of 1.289 m (8.93%), and an overall accuracy of 91.07%.

A comparative analysis was conducted between the tree heights measured by the total station (THts), the proposed device (thi), and the laser altimeter (thlaser). The corresponding linear fitting results are presented in Figure 12. The coefficient of determination (R²) for the proposed device was 0.98774, whereas that for the laser altimeter was 0.94534, indicating that the proposed device exhibited a better fit than the laser altimeter.

To objectively evaluate the measurement performance of the proposed device, this study employed the Bland–Altman analysis method to assess the agreement between the measurements obtained from the proposed device (thi) and the laser altimeter (thlaser) with the total station reference values (THts). The statistical indicators are presented in

Table 2. Bland–Altman statistical analysis comparing the measurements of the proposed device and the laser altimeter with those of the total station.

Statistic	Proposed Device	Laser Altimeter
Bias (m)	0.104	0.141
95% CI for Bias (m)	[−0.033, +0.241]	[−0.428, +0.146]
p-value for Bias	0.135	0.330
95% Limits of Agreement (m)	[−1.105, +1.313]	[−2.385, +2.667]
Width of LoA (m)	2.418	5.052
Coefficient of Repeatability (m)	1.218	2.526

, and the corresponding visualization results are shown in Figure 13.

As shown in Figure 13a and Table 2, the proposed device exhibited a systematic bias of +0.104 m relative to the total station, indicating a slight overestimation of approximately 0.1 m. Its 95% limits of agreement (LoA) were [−1.105, +1.313] m, with a width of 2.418 m, implying that single-measurement errors fall within this range with 95% probability. This level of accuracy is fully acceptable for routine forest resource surveys and plot monitoring. Moreover, the scatter distribution did not reveal any systematic variation in error with increasing tree height, indicating stable performance of the proposed device across different height measurements. In contrast, Figure 13b and Table 2 show that the laser altimeter had a similar systematic bias of +0.141 m, but its 95% limits of agreement were [−2.385, +2.667] m, with a width of 5.052 m, which is considerably larger than that of the proposed device.

In summary, although both methods exhibited relatively small systematic biases, comparison of the LoA widths reveals that the proposed device had a markedly lower error dispersion than the laser altimeter. This indicates that the proposed device not only achieved a smaller systematic error but also demonstrated superior control of random error, resulting in higher consistency with the total station measurements. Consequently, it demonstrates superior reliability and accuracy compared to the laser altimeter.

4.4.2. Evaluation of Tree Height Measurements at Different Distances

To further evaluate the measurement performance of the proposed device under different observation distances, this study used the tree heights measured by the total station as the ground truth and designed a comparative experiment at varying distances. Sixteen sample trees of different heights (ranging from 5.4 m to 23.21 m) were selected, and measurements with the proposed device were conducted at four fixed distances from the tree base: 5 m, 10 m, 15 m, and 20 m.

Preliminary analysis revealed that fixed measurement distances had varying effects on trees of different heights. To identify a more generalizable pattern, this study introduced two standardized indicators: the “distance-to-height ratio” (i.e., measurement distance/true tree height) and the “absolute error” (i.e., |measured value − true value|). By examining the relationship between these two indicators, the influence of tree height magnitude can be eliminated, thereby revealing the fundamental effect of measurement distance on accuracy.

As shown in Figure 14a, the error distribution at 5 m was the most dispersed, with noticeable outliers on the positive side. Both the mean and median were positively biased, indicating that close-range measurements with steep viewing angles tend to overestimate tree height. In contrast, the error distribution at 10 m was the most concentrated, with a median close to zero and the smallest dispersion, suggesting that this distance yielded the most stable measurements. The error levels at 15 m and 20 m were comparable to those at 10 m, though with slightly greater variability. As illustrated in Figure 14b, the absolute error of tree height measurements exhibited a typical U-shaped trend with respect to the distance-to-height ratio (D/H). Each scatter point represents a single observation (n = 64), and the red dashed line denotes the quadratic polynomial fitting curve. It can be observed that measurement errors were minimized when D/H was close to 1, with the optimal range approximately between 0.9 and 1.2, indicating that the device achieved the highest accuracy when the observation distance was roughly equal to the tree height. Conversely, when D/H was too small (close distance, steep angle) or too large (far distance, shallow angle), the measurement errors increased significantly.

4.4.3. Evaluation of Slope Correction and Arm-Raising Compensation Experiments

Since forest surveys are often conducted in mountainous or hilly areas, observation points are frequently located on non-level terrain. Therefore, this experiment aimed to evaluate the measurement performance of the proposed device under different slope conditions and to verify the effectiveness of the designed slope correction and arm-raising compensation algorithms.

Four trees of similar height were selected, located on terrains with slopes of 18.34°, 26.5°, 34.21°and 46.57°, respectively (slope measured by the total station). The tree heights measured by the total station were taken as the ground truth (8.24 m, 9.02 m, 9.34 m, and 8.47 m, respectively). Measurements were then conducted using the proposed device under three modes:

(1)

Uncorrected: slope correction and arm-raising compensation disabled;

(2)

Slope Correction: slope correction enabled, arm-raising compensation disabled;

(3)

Full Correction: both slope correction and arm-raising compensation enabled.

The measurement results and corresponding errors are presented in

Table 3. Tree height measurement results and errors under different slope conditions.

Slope (°)	Total Station (True Value, m)	Uncorrected (m)	Error (m)	Slope Correction (m)	Error (m)	Full Correction (m)	Error (m)
18.34	8.24	8.74	0.50	8.67	0.43	8.42	0.18
26.5	9.02	9.54	0.57	9.48	0.46	9.35	0.29
34.21	9.34	10.13	0.79	9.87	0.53	9.55	0.21
46.57	8.47	9.71	1.24	8.04	−0.43	8.23	−0.24

, while the measurement errors under different modes are illustrated in Figure 15.

The results indicate that in the uncorrected mode, the measurements were generally overestimated, with errors increasing significantly as the slope became steeper. The slope correction mode reduced systematic bias to some extent but still exhibited noticeable errors under high-slope conditions. In contrast, the full correction mode produced measurements much closer to the true values, with the maximum deviation controlled within 0.3 m across all slope conditions. These findings demonstrate that the proposed slope correction and arm-raising compensation functions can effectively improve measurement accuracy under sloped terrain conditions.

5. Discussion

This study developed a portable tree height measurement device by integrating ultra-wideband (UWB) ranging technology with a three-axis accelerometer, enabling rapid, high-precision, and low-cost measurement of tree height. Field tests were conducted on 80 trees of different species at the Donghu Campus of Zhejiang A&F University. Compared with total station measurements, the device achieved a root mean square error (RMSE) of 0.621 m, an overall bias of 0.104 m (0.79%), and an overall accuracy of 95.75%, which was significantly superior to that of a consumer-grade laser altimeter tested concurrently. In addition, the device integrates real-time data acquisition, wireless transmission, and cloud storage functions, providing an integrated solution for the digital management of forest resources.

Tree height, as an important structural parameter of forest ecosystems, is directly related to the estimation of stand volume, biomass, and carbon storage. The UWB two-way ranging (DS-TWR) method used in this study can effectively reduce errors caused by clock offsets by recording the signal round-trip time, thereby improving ranging accuracy. In addition, UWB signals feature nanosecond-level pulse widths, which provide strong anti-interference capability in complex forest environments. The accelerometer continuously measures the tilt angle of the observation device, and when combined with the slope correction algorithm, allows accurate tree height calculation on non-level terrain. Experimental results indicate that when both slope correction and arm-raising error compensation are applied, measurement deviations under all slope conditions can be controlled within 0.3 m. Furthermore, the device achieves optimal measurement accuracy when the distance-to-tree-height ratio is close to 1.0, minimizing overall errors. These technical designs enable the system to achieve high measurement accuracy while maintaining operational simplicity.

Compared with recent studies conducted domestically and internationally, the results of this research are competitive. Zhao et al. [28] developed a multifunctional UWB-based forest surveying instrument, which achieved a relative root mean square error (rRMSE) of 3.47–5.21% for tree height measurements, comparable to the error level of the proposed device. Similarly, Shen et al. [12] reconstructed tree height using smartphone images, reporting an average relative error of 3.20%, demonstrating the feasibility of mobile terminal approaches but with strong dependence on suitable imaging conditions. In contrast, the device developed in this study does not require complex image processing; reliable results can be obtained from single-point measurements, offering clear advantages in convenience. With respect to point cloud and LiDAR-based methods, Tian et al. [11] achieved an RMSE of 0.06 m in coniferous forests by integrating terrestrial laser scanning with UAV imagery, offering higher accuracy but requiring relatively expensive equipment and complex post-processing. Airborne LiDAR (ALS) and terrestrial TLS methods can also provide centimeter-level accuracy; however, they are prone to treetop detection errors under dense canopies. On the other hand, mobile laser altimeters typically require unobstructed line-of-sight across forest stands. By contrast, the proposed device combines the advantages of low cost and rapid measurement, demonstrating considerable potential for application in large-scale field surveys.

This study provides a practical technical solution for forest resource surveys that achieves a balance between accuracy and portability. The modular design of the device and its capability for real-time data transmission facilitate the digital transformation of forest resource monitoring and offer critical front-end sensing support for the development of smart forestry management systems. From a theoretical perspective, this study validates the feasibility of employing UWB technology for precision measurements in complex forest environments, thereby providing both technical references and practical experience for the future development of forestry measurement equipment based on UWB technology.

Limitations and Future Prospects

Although the proposed device demonstrated good performance in preliminary validation, several limitations remain that need to be addressed in future research:

(1)

Theoretical analysis of measurement uncertainty: This study primarily validated device performance through experimental tests but has not yet established a complete error budget model. Future work should employ approaches such as Monte Carlo simulations to systematically analyze the propagation of uncertainties arising from UWB ranging errors, angular measurement noise, and aiming deviations, thereby providing theoretical guidance for optimizing system design.

(2)

Signal propagation characteristics in complex environments: Multipath effects in forest environments are a major factor affecting the accuracy of UWB ranging. Although the DW1000 chip used in this device incorporates a leading-edge detection algorithm, tree trunk reflections and canopy scattering under dense stands and non-line-of-sight (NLOS) conditions may still lead to increased ranging errors. Future studies should investigate advanced multipath suppression algorithms based on channel impulse response analysis and evaluate performance degradation patterns under varying stand densities.

(3)

Influence mechanisms of environmental factors: Rapid fluctuations in temperature and humidity within forests can affect both the propagation speed of electromagnetic waves and sensor performance. While these influences may be negligible at the current accuracy level, for applications requiring higher precision, it will be necessary to establish atmospheric correction models and integrate environmental sensors for real-time compensation.

(4)

Improving accuracy under dynamic measurement conditions: The accelerometer performs reliably under static conditions; however, hand-held vibrations during operation reduce the accuracy of angle measurements. The arm-raising compensation model is based on a simplified linear motion assumption and has limited effectiveness under complex or non-standardized operations. Future work could consider incorporating an inertial measurement unit (IMU) for six-degree-of-freedom pose tracking and developing more precise motion compensation models.

(5)

Extended validation of applicability: At present, this study has only been validated in a campus-based mixed coniferous–broadleaf forest. Future work should apply the device to diverse conditions involving different tree species compositions, canopy densities, and complex terrains (e.g., dense forests, hilly areas, wetlands) to further assess its applicability and adapt the algorithms to accommodate varied environments.

(6)

Product engineering design: The current prototype has not undergone systematic protective engineering. For long-term field applications, structural robustness, sealing protection, and power management need to be further optimized to enhance water resistance, dust resistance, and impact resistance. In addition, both hardware-level interference mitigation (e.g., against leaf occlusion and multipath effects) and software-level filtering should be strengthened to improve the reliability and durability of the instrument.

In conclusion, this study demonstrates the technical potential of a tree height measurement device based on the integration of UWB and accelerometer technologies in terms of both accuracy and practicality, while also acknowledging the challenges encountered in multi-scenario applications. These findings provide clear directions for future optimization and broader deployment of the system.

6. Conclusions

This study aimed to address the technical challenge of balancing accuracy, cost, and portability in traditional tree height measurement methods by developing and validating a portable tree height measurement device that integrates ultra-wideband (UWB) technology with an accelerometer. Through systematic comparative experiments with a high-precision total station, the device achieved a root mean square error (RMSE) of 0.621 m and an overall measurement accuracy of 95.75%, effectively meeting the practical requirements of forestry surveys.

The contribution of this study lies in providing an innovative technical solution for tree height measurement, effectively bridging the gap between traditional manual methods and large-scale remote sensing equipment. This approach holds significant practical value for improving the efficiency of forest inventory and advancing digital forest management. Although further research is needed to enhance the adaptability of the device under extreme environmental conditions and to improve the generalizability of the algorithmic models, this study offers a feasible new pathway toward precise, efficient, and accessible forest resource monitoring, demonstrating broad application prospects in the field of smart forestry.