An Integrated Method for Coding Trees, Measuring Tree Diameter, and Estimating Tree Positions

Stephen F. Austin State University SFA ScholarWorks

Faculty Publications Forestry

2020

An Integrated Method for Coding Trees, Measuring Tree Diameter, and Estimating Tree Positions

Linhao Sun Zhejiang A & F University

Luming Fang Zhejiang A & F University

Yuhi Weng Arthur Temple College of Forestry and Agriculture, Stephen F. Austin State University, [email protected]

Siqing Zheng Zhejiang A & F University

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Repository Citation Sun, Linhao; Fang, Luming; Weng, Yuhi; and Zheng, Siqing, "An Integrated Method for Coding Trees, Measuring Tree Diameter, and Estimating Tree Positions" (2020). Faculty Publications. 527. https://scholarworks.sfasu.edu/forestry/527

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Article An Integrated Method for Coding Trees, Measuring Tree Diameter, and Estimating Tree Positions

Linhao Sun 1,2, Luming Fang 1,2,*, Yuhui Weng 3 and Siqing Zheng 1,2

1 Key Laboratory of Forestry Intelligent Monitoring and Information Technology Research of Zhejiang Province, Zhejiang A & F University, Lin’an 311300, Zhejiang, China; [email protected] (L.S.); [email protected] (S.Z.) 2 School of Information Engineering, Zhejiang A & F University, Lin’an 311300, Zhejiang, China 3 Arthur Temple College of Forestry and Agriculture, Stephen F. Austin State University, Nacogdoches, TX 75962, USA; [email protected] * Correspondence: ﬂ[email protected]; Tel.: +86-189-6815-6768

Received: 11 November 2019; Accepted: 20 December 2019; Published: 24 December 2019

Abstract: Accurately measuring tree diameter at breast height (DBH) and estimating tree positions in a sample plot are important in tree mensuration. The main aims of this paper include (1) developing a new, integrated device that can identify trees using the quick response (QR) code technique to record tree identifications, measure DBH, and estimate tree positions concurrently; (2) designing an innovative algorithm to measure DBH using only two angle sensors, which is simple and can reduce the impact of eccentric stems on DBH measures; and (3) designing an algorithm to estimate the position of the tree by combining ultra-wide band (UWB) technology and altitude sensors, which is based on the received signal strength indication (RSSI) algorithm and quadrilateral localization algorithm. This novel device was applied to measure ten 10 10 m square plots of diversified × environments and various tree species to test its accuracy. Before measuring a plot, a coded sticker was fixed at a height of 1.3 m on each individual tree stem, and four UWB module anchors were set up at the four corners of the plot. All individual trees’ DBHs and positions within the plot were then measured. Tree DBH, measured using a tree caliper, and the values of tree positions, measured using tape, angle ruler, and inclinometer, were used as the respective reference values for comparison. Across the plots, the decode rate of QR codes was 100%, with an average response time less than two seconds. The DBH values had a bias of 1.89 mm (1.88% in relative terms) and a root mean square error (RMSE) of 5.38 mm (4.53% in relative terms). The tree positions were accurately estimated; the biases on the x-axis and the y-axis of the tree position were 8.55–14.88 cm and 12.07–24.49 cm, − − respectively, and the corresponding RMSEs were 12.94–33.96 cm and 17.78–28.43 cm. The average error between the estimated and reference distances was 30.06 cm, with a standard deviation of 13.53 cm. The device is cheap and friendly to use in addition to its high accuracy. Although further studies are needed, our method provides a great alternative to conventional tools for improving the efficiency and accuracy of tree mensuration.

Keywords: forest inventory; quick response code technique; ultra-wide band technology; angle sensor

1. Introduction Diameter at breast height (DBH), measured at a height of 1.3 m on the bole of a tree, is the most commonly measured tree attribute [1–3], whether for inventory, management, or research purposes, since many tree and forest attributes [4,5], such as basal area, volume [6], and stand density [7], are derived from DBH measurements [8]. Therefore, developing tools that can measure tree DBH accurately, eﬃciently, and conveniently is always desirable.

Sensors 2020, 20, 144; doi:10.3390/s20010144 www.mdpi.com/journal/sensors Sensors 2020, 20, 144 2 of 19

Foresters rely on a variety of conventional dendrometers, such as diameter tapes (D-tapes) and tree calipers, to measure tree DBH. These tools are often based on the geometry of circles; trees are presumed to have circular cross-sections [9], although this is rarely true in reality [10,11]. Most tree stems violate this assumption to some level, either in the form of an oval, an ellipse, or a closed convex [12–15], resulting in biases (mostly overestimates) in DBH when measured by diameter tapers or tree calipers (which often take one measurement) [16,17]. D-tapes are more commonly used for measuring permanent sample plots because they are perceived as being more consistent for repeated DBH measurements [18], while calipers are often preferred for DBH measurements in temporary plots [19]. In tree mensuration, to reduce the impact of eccentric cross-section of a tree, it is often recommended to measure the major and minor diameters of the tree and obtain the average diameter of the two measurements as the tree DBH, which, in literature, is often used as the reference data for comparison purpose [20]. There are other limits to using a D-tape or caliper to measure tree DBH, such as the manual recording of measurements [16,17], thereby reducing efficiency and increasing mistakes in measurement and data entry [18,19]. Both tools, while relatively reliable, are labor-intensive. Some advanced, electronic measurement devices for DBH measurement [20–24], such as electronic tree-measuring forks and electronic tapes, have been developed. The electronic tapes do not solve the problem of eccentric cross-section, while electronic tree-measuring forks are based on an ultrasonic system [25,26], which can be easily affected by environments [27–29]. More recently, some methods for measuring DBH using non-contact methods, including terrestrial laser scanning (TLS) [30–34], mobile phones with time-of-flight (TOF) cameras [4,35,36], and close-range photogrammetry (CRP) [1,22,37], have been proposed. These methods use point clouds to extract data, which are expensive [28] and require high computational capacity of microprocessors, limiting their application in forestry inventory. Other than the method of CRP, estimating tree DBH based on the TLS and TOF methods is still based on the assumption that trees are circular in cross section. Other than tree size measurements, identifying trees and estimating the positions of the trees in a sample plot are important elements for measuring sampling plots [27,28], and this is particularly true for permanent inventory plots where successive measurements are always needed. Conventionally, foresters either use markers or tags to identify trees. This method, while still widely used, is labor-intensive. The spatial information, i.e., the tree positions, represents important information regarding the stand density, as well as in studies of distance-dependent growth and the dynamics of trees and stands. While tree position information is difficult to obtain, studies have shown that the individual tree positions can be determined using a total station or ultrasonic trilateration technology [25,26]. New developments in integrating DBH measurement and tree position estimation, using non-contact methods such as TLS [30–34], TOF cameras [4,35,36], and CRP [1,22,37], have been reported. However, results of these methods can easily be affected by the stand environments such as stand density, abundance of shrubs and vegetation, and light conditions. They are also time-consuming, labor-intensive, and require complicated procedures in data processing [38]. Therefore, many practical and technical restrictions still exist in applying these methods in forestry inventories. There is a pressing need to develop an integrated system that can identify trees, measure tree DBH, and estimate tree positions concurrently, accurately, and efficiently in terms of both labor and cost. The recent developments in computer science and electronics make this possible. Quick response (QR) code technology [39] is now widely used due to its characteristics of a high capacity in encoding data, strong damage resistance, and fast decoding [39–42]. The ultra-wide band (UWB) technology is based on sending and receiving carrier-less radio impulses using extremely accurate timing, and it is particularly suitable for estimating distance and positions [43,44]. This technology has constantly gained interest thanks to its high accuracy (i.e., a typical error of 30 cm or less), making it more attractive than other wireless technologies, such as WiFi, ZigBee, and Bluetooth, which can normally estimate the location with an accuracy of several meters [45–48]. In this paper, we integrated these technologies into a device to identify trees, measure tree DBH, and estimate tree positions concurrently. The device Sensors 2019, 19, x 3 of 19 Sensors 2020, 20, 144 3 of 19 tree positions concurrently. The device was applied to measure trees in forest plots of different wasenvironments applied to and measure tree species trees in to forest evaluate plots its of accuracy different and environments efficiency. and tree species to evaluate its accuracy and efficiency. 2. Technology and Theory 2. Technology and Theory 2.1. Design of the Main Device 2.1. Design of the Main Device The main device and its components can be found in Figure 1, and their attribute descriptions are listedThe main in Table device 1. The and itsdevice components consists canof a be microprocessor, found in Figure an1, andanalog-to-digital their attribute sampling descriptions (ADS) are module,listed in Tablea QR1 .scanner, The device a secure consists digital of a microprocessor, memory card an(SD analog-to-digital card), an interface, sampling Bluetooth, (ADS) a module, power managementa QR scanner, circuit, a secure a digital keyboard memory interface, card (SD an card),altitude an interface,sensor, a Bluetooth,display interface, a power managementand a UWB module.circuit, a keyboardNote that interface,the angle an between altitude the sensor, left arm a display and the interface, middle and beam a UWB is defined module. as Note α1 and that that the α betweenangle between the middle the left beam arm and theright middle arm as beam α2 (Figure is defined 1). The as 1geometricand that betweencenters of the the middle vertex beam and middleand right component arm as α2 are(Figure on the1). same The geometric line. centers of the vertex and middle component are on the same line.

10 3 7 8 1 5 α1 α2 5cm 2 4 6 9 11 35cm Figure 1. The main device and its components: 1, 1, the the left left arm; arm; 2, 2, the the middle middle beam beam;; 3, 3, the the right right arm; arm; 4, 4, the vertex; 5, the keys; 6, the display panel; 7, the fl ﬂange;ange; 8, the first ﬁrst angle sens sensor;or; 9, the battery; 10, the printed circuit board (PCB); andand 11,11, thethe secondsecond angleangle sensor.sensor.

Table 1. Descriptive statistics of the device’s components 1. Table 1. Descriptive statistics of the device's components 1.

ChipChip Model Model Component InterfaceInterface TypeType Pa Parameterrameter FunctionFunction /Type/Type SPI,SPI, I2C,I2C, Digital,Digital, SRAM:SRAM: 4 4 KB; KB; Microprocessor STC15W4K56STC15W4K56 Data processing SerialSerial port,port, etc.etc. Flash:Flash: 56 56 KB; KB; QR scanner M800 M800 Serial Serial portport Resolution: 20 20 mil; mil; QR scanning Analog-to-digital ADS1115ADS1115 I2C, I2C, AnalogAnalog 16 16 bits; bits; 4 4 channels channels AD sampling sampling module module Resolution:Resolution: 1 1cm; cm; Distance UWB module module D-DWM-PG1.7 D-DWM-PG1.7 Serial Serial portport Range:Range: 0–50 0–50 m m Measurement Altitude Altitude sensor sensor JY901B JY901B Serial Serial portport Resolution: 1 1 cm cm Measurement COMM with COMM with Bluetooth HC-06 HC-06 Serial Serial portport Range: Range: 0–15 0–15 m m upperupper computer SDSD card card microSD microSD SPI SPI 2 2 GB GB Data Data storagestorage Angle sensor P3014-V1 Analog Resolution: 0.088° Angle MeasurementAngle Angle sensor P3014-V1 Analog Resolution: 0.088 ◦ Measurement Display OLED SPI 128 × 64 pixels Data display Display OLED SPI 128 64 pixels Data display × Keyboard PVC PVC Digital Digital 7 7 keys keys Command input Power managementPower TP4056, DW01, Input: 3.7–4.2 V, 5 V; TP4056, DW01, Digital, Power Input: 3.7–4.2 V, 5 V; Power Powermanagement managementcircuit AMS1117, etc. Digital, Power Output: 3.3 V, 5 V AMS1117, etc. Output: 3.3 V, 5 V management circuit Battery Lithium battery Power 4000 mAh Power supply Battery Lithium battery Power 4000 mAh Power supply 1. SPI, serial peripheral interface; I2C, inter-integrated circuit; KB, kilobyte; GB, gigabyte; SRAM, static 1. SPI, serial peripheral interface; I2C, inter-integrated circuit; KB, kilobyte; GB, gigabyte; SRAM, static random-access random-accessmemory; COMM, memory; communication; COMM, communication; V, voltage; mAh, V, milliampere-hour. voltage; mAh, milliampere-hour.

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2.2. Technology of Coding Trees A QR scanner (Figure 22a)a) isis usedused toto decodedecode thethe QRQR codecode (encoded(encoded byby NiceLabelNiceLabel 20172017 BarcodeBarcode software [19[19]),]), which which is printedis printed on a stickeron a sticker (Figure 2(Figureb). Other 2b). information, Other information, such as the identiﬁcationsuch as the (ID)identification numbers (ID) of the numbers plot and of the the plot tree and and the the tree reference and the point,reference can point, also becan found also be on found the sticker.on the Forsticker. example, For example, for the QR for code the ofQR “TN0002 code of| YN0001”“TN0002 (Figure| YN0001”2b); “TN0002”(Figure 2b); is the“TN0002” tree ID, andis the “YN0001” tree ID, isand the “YN0001” sample plot is ID.the Note sample that, plot if stickers ID. Note are notthat, used, if stickers the tree-codes are not will used, be generated the tree-codes automatically will be ingenerated the process automatically of measuring in the trees’ process DBH of and measuring positions. trees’ DBH and positions.

Plot number

Tree number QR Scanner:

QR code Reference Point

(a) (b)

Figure 2. The QR scanner and an example of a tree code: ( a) QR scanner ( b) coded sticker

2.3. Angle Calculation α As shown in Figure1 1,, treetree DBH DBH is is measured measured by by measuring measuring αii (i(i == 1, 2) values. When the central axis of thethe angleangle sensorsensor rotates, rotates, the the change change in in the the angle angle has has a lineara linear relationship relationship with with the the change change in the in α outputthe output voltage voltage signal. signal. Therefore, Therefore, the voltagethe voltag signalse signals from from ADS modulesADS modules can be can converted be converted to i (i to= α1,i 2)(i = using 1, 2) using the following the following equation: equation:

360  Un α = 360◦ (Uc Vz Un), (1) αii = Un ××(Uci −i − Vzi Vri ) (1) Un Vr , where Un is the ADS value of the current input voltage of the two angle sensors, Uci is the ADS value th th ofwhere the outputUn is the voltage ADS ofvalue thei ofangle the current sensor, inpu Vzi ist thevoltage reference of the value two ofangle the outputsensors, voltage Uci is the of the ADS i th anglevalue sensorof the output at initialization voltage whenof the αi i equalsangle sensor, 0◦, and V Vzir isis thethe referencereference value value of of the the input output voltage voltage of the of twothe i angleth angle sensors sensor at at initialization. initialization when αi equals 0°, and Vr is the reference value of the input voltage of the two angle sensors at initialization. 2.4. Double-Sided Two-Way Ranging 2.4. Double-Sided Two-Way Ranging The basic ranging principle of the UWB modules used in this method is double-sided two-way rangingThe (DS-TWR)basic ranging [46– principle50]. Clock of drift the UWB correction modules and used signal in power this method error may is double-sided affect the accuracy two-way of theranging position. (DS-TWR) The DS-TWR [46–50]. isClock an additional drift correction round an ofd communication signal power error based may on single-sidedaffect the accuracy two-way of rangingthe position. (SS-TWR) The DS-TWR [46–51]. Theis an time additional of the two round types of ofcommunication communication based can compensate on single-sided each two-way other for theranging errors (SS-TWR) caused by [46–51]. the clock The off timeset [ 46of– the52] two and signaltypes of power communication error [51,52 ]can to improvecompensate the accuracyeach other of thefor DS-TWR.the errors Figure caused3 presents by the anclock example offset of [46–52 calculating] and thesignal distance power (Dis) error between [51,52] two to nodesimprove (A and the B).accuracy The distance of the DS-TWR. between nodeFigure A 3 and presents node Ban can exam beple calculated of calculating as follows: the distance (Dis) between two nodes (A and B). The distance between node A and node B can be calculated as follows: tround1 tround2 treply1 treply2 Dis = c tp = c × − × , (2) × × ttround1×+tround2t - treply1+ t× treply2+ t Dis = c× tp = c× round1 round2 reply1 reply 2 + + + (2) tround1 tround2 treply1 treply2 , where node A and node B are two communication UWB nodes; Dis is the distance between node A and node B; tp is the time of the wireless signal propagation in the air; c is the speed of light in the air; time is the time axis; T1 is the time when node A sends the first pulse; T2 is the time when node B receives the first pulse; T3 is the time when node B sends the first pulse; T4 is the time when node A receives the first pulse; T5 is the time when node A sends the second pulse; T6 is the time when node

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B receives the second pulse; tround1 is the total time of node A sending and receiving pulses in the ﬁrst round of communication; treply1 is the reply time for node B in the ﬁrst round of communication; tround2 is the total time of node B sending and receiving pulses in the second round of communication; Sensorstreply2 2019is the, 19, replyx time for node A in the second round of communication. 5 of 19

Node A Node B

T1 tp T2 tround1 treply1 T3 tp T4 treply2 tround2 T5 tp T6

time time FigureFigure 3. 3. SchemeScheme of of double-sided, double-sided, two-way two-way ranging ranging (DS-TWR). (DS-TWR). 3. Materials and Methods where node A and node B are two communication UWB nodes; Dis is the distance between node A and3.1. node Study B; Area tp is the time of the wireless signal propagation in the air; c is the speed of light in the air; time is the time axis; T1 is the time when node A sends the first pulse; T2 is the time when node B This study was carried out in Lin’an (N30◦150, E119◦430), China. We selected 10 square plots with receives the first pulse; T3 is the time when node B sends the first pulse; T4 is the time when node A a size of 10 10 m. These plots varied greatly in average tree DBH, environment, and tree species receives the first× pulse; T5 is the time when node A sends the second pulse; T6 is the time when node composition (Table2). Plots 1–5 were located at the Botanical Garden of Zhejiang A&F University, B receives the second pulse; tround1 is the total time of node A sending and receiving pulses in the first dominated by artiﬁcial forest and turf. Plots 6–10 were located in the suburb of Lin’an, dominated by round of communication; treply1 is the reply time for node B in the first round of communication; tround2 natural forest, dense weeds, and shrubs. is the total time of node B sending and receiving pulses in the second round of communication; treply2 is the reply time for node A inTable the 2.secondDescriptive round statistics of communication. of the sample plots 1.

3. Materials and Methods Dominant DBH (mm) Number Slope ( ) Plot Species ◦ of Trees Mean Max Min Std 3.1. Study Area 1 16 S1, S2, S3 3.1 140.31 280.32 59.29 61.29 This2 study was 19 carried out S1, S4in Lin’an (N30°15 5.5′, E119°43’), 136.33 China. 183.91 We selected 83.34 10 square 28.74 plots with a 3size of 10 × 15 10 m. These S1, S5plots varied 6.8 greatly 144.82in average tree 210.24 DBH, environment, 86.07 and 32.57 tree 4 18 S2, S3, S6 15.3 153.72 334.63 70.54 75.13 species5 composition 28 (Table S1,2). S3,Plots S6 1–5 were 28.7 located 125.90 at the Botanical 215.37 Garden 67.14 of Zhejiang 49.19 A&F University,6 dominated 37 by artificial S7 forest and 4.8 turf. Plots 102.43 6–10 were 153.97 located in the 52.75 suburb of 30.38Lin’an, dominated7 by natural 30 forest, dense S7 weeds, and 5.9 shrubs. 112.91 219.90 51.19 40.16 8 24 S2, S3, S7 18.3 179.74 340.21 52.60 88.00 9 20Table S3, S7, 2. S8 Descriptive 26.0 statistics of 118.09 the sample plots 187.99 1. 53.94 39.40 10 18 S7, S9 33.2 127.31 209.57 67.67 45.60 1. Number of DBH (mm) Plot Std, standard deviation; S1,Dominant Sapindus Species mukurossi Gaertn; Slope S2, (°) Cinnamomum camphora; S3, Magnolia denudata; S4, Michelia maudiaeTrees Dunn; S5, Ginkgo biloba; S6, Liriodendron chinensis;Mean S7, Cunninghamia Max lanceolata; Min S8, MagnoliaStd 1 Grandiflora; 16 S9, Camellia japonica. S1, S2, S3 3.1 140.31 280.32 59.29 61.29 2 19 S1, S4 5.5 136.33 183.91 83.34 28.74 3.2.3 Methods 15 S1, S5 6.8 144.82 210.24 86.07 32.57 4 18 S2, S3, S6 15.3 153.72 334.63 70.54 75.13 3.2.1.5 The System 28 Workflow S1, S3, S6 28.7 125.90 215.37 67.14 49.19 6 37 S7 4.8 102.43 153.97 52.75 30.38 7 As shown30 in Figure4, the system S7 flow, from top to5.9 bottom,112.91 consisted of219.90 the software51.19 layer, data40.16 layer, hardware8 layer, 24 physical layer, S2, and S3, S7 object layer. A 18.3 few subprograms, 179.74 including 340.21 a 52.60human–computer 88.00 9 20 S3, S7, S8 26.0 118.09 187.99 53.94 39.40 interaction10 program,18 which is used S7, S9 for keyboard input33.2 and display127.31 control,209.57 a sampling 67.67 program, 45.60 which is used1. Std, for standard reading deviation; tree codes S1, Sapi andndus DBH mukurossi values andGaertn; tree S2, position Cinnamomum data extraction,camphora; S3, and Magnolia a data denudata; management program,S4, Michelia which maudiae is used Dunn; for encodingS5, Ginkgo databiloba; storage S6, Liriod andendron data chinensis; communication, S7, Cunninghamia were incorporatedlanceolata; S8, into Magnolia Grandiflora; S9, Camellia japonica.

3.2. Methods

3.2.1. The System Workflow

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As shown in Figure 4, the system flow, from top to bottom, consisted of the software layer, data layer, hardware layer, physical layer, and object layer. A few subprograms, including a human–computer interaction program, which is used for keyboard input and display control, a Sensorssampling2020 , program,20, 144 which is used for reading tree codes and DBH values and tree position6 data of 19 extraction, and a data management program, which is used for encoding data storage and data communication, were incorporated into the software layer. After completing an individual tree’s themeasurement software layer. (see Section After completing 3.2.2), the antree individual ID, its DBH tree’s value, measurement and position (see were Section automatically 3.2.2), the tree saved ID, itsto the DBH system. value, and position were automatically saved to the system.

Figure 4. The system workflow workﬂow of the device for coding trees and estimating diameter.

3.2.2. The Operation Workflow Workflow To completecomplete thethe measurementmeasurement ofof aa plot,plot, thethe followingfollowing toolstools andand instrumentsinstruments areare needed:needed: the device, codedcoded stickers,stickers, aa nailnail gun,gun, short short nails, nails, and and four four UWB UWB modules modules (referred (referred to to as as anchors anchors A, A, B, C,B, andC, and D). D). The The coded coded stickers stickers were were fixed fixed at a height at a height of 1.3 mof on1.3 individualm on individual trees in trees the plot. in the The plot. anchors The (Figuresanchors5 (Figures and6) were 5 and set 6) up were at plot set corners up at plot as follows: corners first, as follows: anchor Afirst, was anchor set up A in was one cornerset up ofin theone plot,corner and of thenthe plot, the device and then was the used device to measure was used the altitudeto measure of corner the altitude A (HA). of Second, corner anchorA (HA). B Second, was set upanchor in a neighboringB was set up plotin a cornerneighboring of A, and plot the corner altitude of A, of and the cornerthe altitude was measured of the corner (HB )was as well measured as the distance(HB) as well between as the anchors distance A between and B (Dis anchorsAB). The A sameand B step (Dis wasAB). The repeated same to step set was up anchors repeated C andto set D up in theanchors remaining C and plotD in corners, the remaining and their plot altitudes corners, (H andC and their HD altitudes) were measured (HC and asHD well) were as themeasured distances as betweenwellSensors as 2019the corners ,distances 19, x (Dis ACbetween, DisBC corners, DisAD ,(Dis DisACBD,, Dis andBC Dis, DisCDAD)., DisBD, and DisCD). 7 of 19 A tree was measured as follows (Figure 7): first, the investigator scanned the tree QR code, Anchor D Anchor C followed by measurement of the tree DBH twice at two different directions (mainly followed the major and minor DBH directions).Over For each measure, values of α1 and α2 were automatically used to calculate the tree DBH (see Section 3.2.3). The average of the two measurements was used as the tree DBH. Finally, the deviceSquare was placed Plot at the bottom of the tree to obtain Hn, An, Bn, Cn, and Dn. Here, Hn is the altitude of the device, An, Bn, Cn, or Dn is the distance between anchors A, B, C, or D Corner Area and the device, respectively, and n refers to the nth tree in the plot. The above steps were repeated Anchor Location to finish measuring all the trees in the plot. Similar to the DBH value, each tree’s position was Walking Path estimated twice, and the average was used as the tree position value. The measurement data were then uploaded to a person computer (PC) for further analysis. Start Anchor A Anchor B FigureFigure 5. 5.Anchors Anchors set set up up in in a a square square plot. plot.

Figure 6. An example to show the anchor installation in a plot.

Figure 7. Measurement of a tree. On the display screen, line 1 represents the tree code; line 2, the diameter at breast height (DBH) value of the previously measured tree; line 3, the measured DBH

value; line 4, the values of α1 and α2; line 5, the value of Hn; and line 6, the values of An, Bn, Cn,

and Dn.

3.2.3. Measurement Algorithm of a Tree’s DBH Figure 8 provides an example of measuring tree DBH using the device, with A, B, and C being the contact points of the device’s arms and beam against the tree trunk, which results in two arcs, arc BA and arc BC. Since the cross-section surface may be eccentric, arcs BA and BC have different

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Anchor D Anchor C Over

Square Plot Corner Area Anchor Location Walking Path

Sensors 2019, 19, x 7 of 19 Start Anchor AD AnchorAnchor B C Sensors 2020, 20, 144 7 of 19 FigureOver 5. Anchors set up in a square plot.

Square Plot Corner Area Anchor Location Walking Path

Start Anchor A Anchor B Figure 5. Anchors set up in a square plot.

Figure 6. An example to show the anch anchoror installation in a plot.

A tree was measured as follows (Figure7): first, the investigator scanned the tree QR code, followed by measurement of the tree DBH twice at two different directions (mainly followed the major and minor DBH directions). For each measure, values of α1 and α2 were automatically used to calculate the tree DBH (see Section 3.2.3). The average of the two measurements was used as the tree DBH. Finally, the device was placed at the bottom of the tree to obtain Hn,An,Bn,Cn, and Dn. Here, Hn is the altitude of the device, An,Bn,Cn, or Dn is the distance between anchors A, B, C, or D and the device, respectively, and n refers to the nth tree in the plot. The above steps were repeated to finish measuring all the trees in the plot. Similar to the DBH value, each tree’s position was estimated twice, and the average was used as the tree position value. The measurement data were then uploaded to a person computer (PC)Figure for further 6. An analysis.example to show the anchor installation in a plot.

Figure 7. Measurement of a tree. On the display screen, line 1 represents the tree code; line 2, the diameter at breast height (DBH) value of the previously measured tree; line 3, the measured DBH

value; line 4, the values of α1 and α2; line 5, the value of Hn; and line 6, the values of An, Bn, Cn,

and Dn.

Figure 7. Measurement of of a tree. On On the the display display screen, screen, line line 1 1 re representspresents the tree code; line 2, the diameter atat breastbreast height height (DBH) (DBH) value value of theof the previously previously measured measured tree; tree; line 3,line the 3, measured the measured DBH value;DBH

linevalue; 4, theline values 4, the ofvaluesα1 and ofα α2;1 lineand 5,α the2; line value 5, the of H valuen; and of line Hn 6,; and the valuesline 6, ofthe A nvalues,Bn,C ofn, andAn, DBnn, .Cn, and Dn. 3.2.3. Measurement Algorithm of a Tree’s DBH 3.2.3.Figure Measurement8 provides Algorithm an example of a ofTree’s measuring DBH tree DBH using the device, with A, B, and C being the contactFigure points8 provides of the an device’s example arms of measuring and beam tree against DBH theusing tree the trunk, device, which with results A, B, and in two C being arcs, arcthe BAcontact and points arc BC. of Since the device’s the cross-section arms and surface beam against may be the eccentric, tree trunk, arcs which BA and results BC have in two diﬀ erentarcs, centers,arc BA and O1 andarc BC. O2. Since Note the that, cross-section for the device, surface the values may be of eccentric, w (2.5 cm), arcs h (3.5BA and cm), BC and have s (15 different cm) are ﬁxed mechanical structural values (Figure8).

Sensors 2019, 19, x 8 of 19

1 2 centers,Sensors 2020 O, 20 and, 144 O . Note that, for the device, the values of w (2.5 cm), h (3.5 cm), and s (15 cm)8 ofare 19 fixed mechanical structural values (Figure 8).

w w w w

O2 O2 C A C A O1

O r1 r2 r 1 r 1 α 2 α1 B 2 α B h 1 α2 w w h

s1 s2 s1 s2 s s s s (a) (b)

FigureFigure 8. 8. MeasurementMeasurement method method of of tree tree DBH: DBH: ( (aa)) for for a a small small tree tree and and ( (b)) a large tree.

Here, w equals the half width of the arms or beam; h equals w plus the maximum width of the vertex; and s equals the half distance between the axes of two angle sensors. InIn order to obtain the value of the tree DBH,DBH, thethe ssii (i = 1,2) values are needed, which can be calculated using Taylor's Taylor’s expansion in the following equations:

 2 2 4 4 6 6  θi θiθi θiθi θi  × h (1 + + +)+w  h s (1-× − 2! -4! − )6! w (α 90 )  2! θ43! θ 65 ! θ 7 i , ◦ si = − θ i + i i ()i ≠  . (3) s - 3i 3! 5 5! 7 7! α 90 si =   θi − θi θ−i (3)  s θwi - + - (αi = 90◦)  − 3! 5! 7!  ()=  where θi = αi 3.141592/180 ands - w I = 1, 2. αi 90 × . The calculated si can then be used to calculate the radius, ri, using Taylor’s expansion, in the wherefollowing θi = equations:αi × 3.141592/180 and I = 1, 2.  θ θ 3 θ 5 θ 7 The calculated si can then be used toi calculatei + i thei radius, ri, using Taylor's expansion, in the  2 23 3! 25 5! 27 7!  − × × − × (α ) following equations:  si θ 2 θ 4 θ 6 i , 90◦ ri =  × 1 i + i i . (4)  − 22 2! 24 4! − 26 6!  3 × 5 × ×7  θi s θwi θi θi (α = 90 ) - − + - i ◦  2 23 ×3! 25 ×5! 27 × 7! i × ()i ≠  The tree DBH is then calculateds as2 the total4 of r1 and6 r2: α 90 ri =  θi θi θi (4) 1- + -  22 × 2! 24 × 4! 26 × 6!  DBH = r1 + r2. (5) s - w ()αi = 90  . Since r1 and r2 are calculated based on diﬀerent arcs, the impacts of eccentric tree cross-sections on measuringThe tree DBH DBH would is then be calculated accounted as for, the resultingtotal of r1 inand a morer2: accurate estimate than that obtained using conventional dendrometers. DBH = r1 + r2 . (5)

Since3.2.4. r Estimation1 and r2 are Algorithm calculated of based a Tree on Position different arcs, the impacts of eccentric tree cross-sections on measuring DBH would be accounted for, resulting in a more accurate estimate than that obtained In order to obtain a tree’s position in a plot, the spatial coordinate system of four anchors is ﬁrst using conventional dendrometers. transformed into a plane rectangular coordinate system OXY (Figure9). 3.2.4. Estimation Algorithm of a Tree Position In order to obtain a tree’s position in a plot, the spatial coordinate system of four anchors is first transformed into a plane rectangular coordinate system OXY (Figure 9).

Sensors 2020, 20, 144 9 of 19 Sensors 2019, 19, x 9 of 19

D C D C HD HC

A DisAB disAD disBC B HA H B O X A dis B AB Figure 9. ConversionConversion from from a three-dimens three-dimensionalional coordinate to a two-dimensionaltwo-dimensional coordinate in tree position estimation.

The plane OXY is perpendicular to the gravity direction, the origin O is the location of anchor A, The plane OXY is perpendicular to the gravity direction, the origin O is the location of anchor and the x-axis is the projection direction from anchor A to anchor B. The three-dimensional scalars A, and the x-axis is the projection direction from anchor A to anchor B. The three-dimensional HA,HB,HC,HD, DisAB, DisBC, DisAC, DisAD, and DisBD are then transformed into two-dimensional scalars HA, HB, HC, HD, DisAB, DisBC, DisAC, DisAD, and DisBD are then transformed into scalars in the OXY plane. two-dimensional scalars in the OXY plane. q dis = Dis 2 (H H )2 AB 2 AB A 2 B disAB = Disq AB - (H−A - HB)− dis = Dis 2 (H H )2 BC 2 BC B 2 C disBC = Disq BC - (H−B - HC)− 2 2 disAC = DisAC (HA HC) (6) 2 − −2 disAC = Disq AC - (HA - HC) 2 2 (6) disAD = DisAD (HA HD) = q 2 − −2 disAD DisAD - (H2 A - HD) 2 disBD = DisBD (HB HD) 2 − −2 disBD = DisBD - (HB - HD) The coordinates of anchors A, B, C, and D can then be obtained.. The coordinates of anchors A, B, C, and D can then be obtained. (XA,YA) = (0, 0) （XA(,XYA,Y）=)(0=,0 ()0, dis ) B B AB r 2 （ B B）= AB 2 2 2 2 2 2 X , Y (0,disdis)AB +disAC disBC 2 disAB +disAC disBC (7) (XC,YC) = ( 2dis − , disAC ( 2dis − ) ) 2 2 AB 2 − 2 2 AB 2 disAB + disAC − disBC r disAB + disAC − disBC = 2 2 2 2 − 2 2 2 2 2 （XC,YC） ( disAB +disAD disBD, disAC ( 2 disAB +disAD disBD) ) (7) (XD,YD) = ( 2disAB − , disAD ( 2disAB − ) ) 2disAB − 2disAB 2 + 2 − 2 2 + 2 − 2 disAB disAD disBD 2 disAB disAD disBD 2 Similarly,（X theD,Y projectionD）= ( distances an, bn, c,n, anddisAD dn−can( be calculated as follows:) ) 2disAB 2disAB . q 2 2 Similarly, the projection distancesa nan=, bn, cAn,n and(H dAn canH nbe) calculated as follows: q − − 2 2 b=n = 2Bn (HB 2Hn) an Aqn - (H−A - Hn−) (8) 2 2 cn== 2Cn (HC 2 Hn) bn Bqn - (H−B - Hn−) 2 2 (8) dn = 2Dn (HD 2 Hn) cn = Cn - (H−C - Hn)−

2 2 Here, an, bn, cn, and dn represent the projectiondn = Dn distances- (HD - Hn) between anchors A, B, C, and D, respectively, . and the device in the OXY plane. n refers to the nth tree in the plot. Here,Although an, bn, c UWBn, and wireless dn represent signals havethe veryprojection strong penetrationdistances between ability, in anchors reality, the A, random B, C, rangingand D, respectively,error may be causedand the by device humans in the and OXY/or the plane. tree n body refers [48 to–53 the], resultingnth tree in in the a prolonged plot. communication timeAlthough between the UWB UWB wireless nodes. signals Therefore, have the very values strong of a npenetration, bn, cn, and ability, dn may in be reality, slightly the higher random than rangingthe respective error actualmay be values, caused and by consequently, humans and/or the four the circlestree body may [48–53], not intersect resulting at one in common a prolonged point (Figurecommunication 10a). The time received between signal the strength UWB nodes. indication Therefore, (RSSI) algorithmthe values [50of –a56n, ],b suchn, cn, asand quadrilateral dn may be slightlylocalization higher (Figure than 10 thea), providesrespective an actual alternative values, to solve and thisconsequently, problem and the to four improve circles the may accuracy not intersectand precision. at one common point (Figure 10a). The received signal strength indication (RSSI) algorithm [50–56], such as quadrilateral localization (Figure 10a), provides an alternative to solve this problem and to improve the accuracy and precision.

Sensors 2020, 20, 144 10 of 19 Sensors 2019, 19, x 10 of 19

an bn B A A B

D C L3 L L 1 dn 2 C cn

(a) (b)

Figure 10.10. Position estimation using (a)) quadrilateralquadrilateral localizationlocalization andand ((bb)) trilaterationtrilateration localization.localization.

FromFrom FigureFigure 1010a,a, wewe cancan developdevelop fourfour trilaterationtrilateration localizationslocalizations withwith eacheach ofof threethree circlescircles (ABC,(ABC, ABD,ABD, ACD, and BCD). BCD). Taking Taking ABC ABC (Figure (Figure 10b) 10b) as as an an example, example, where where three three circles, circles, A, A,B, and B, and C are C areintersected, intersected, three three lines, lines, L1, LL12,,L and2, and L3,L are3, are formed formed by by linking linking the the intersections intersections of of any any two two circles. AccordingAccording toto the the trilateration trilateration localization localization algorithm algorithm [53–58 ],[53–58], the following the following equations equations can be developed: can be developed:  2 2 2 2 2 2  2(XA XB)X1 + 2(YA YB)Y1 = bn an + XA XB + YA YB  − + − = 2 −2 + 2 −2 + 2 2 −  2(2(XX A -XXB))XX 1 +22(Y(YA - YYB)Y)Y1 =bnc -2an b X2 +A X- X2B XY2A+-YYB2 Y 2 . (9)  B C 1 B C 1 n n B C B C   − + − = 2 2 −2 + 2 2 2 −2 + 2 2 2− 2 2(2(XXA B -XXCC))XX11+ 2((YYAB - YYCC)Y)Y1 1 =cn cn- bn anX+B X- AXC XYC B +-YAC YC − − − − − (9)  + = 2 2 + 2 2 + 2 2 2(XA - XC)X1 2(YA - YC)Y1 cn - an XA - XC YA - YC The coordinates of Q1 (X1,Y1) can be obtained from Equation (9). By. the same token, the coordinates of the three other connecting points of the three other trilateration localizations can The coordinates of Q1 (X1, Y1) can be obtained from Equation (9). By the same token, the be obtained—Q (X ,Y ), Q (X ,Y ), and Q (X ,Y ). Then, according to the RSSI algorithm and coordinates of the2 three2 2 other3 connecting3 3 points4 4of 4the three other trilateration localizations can be quadrilateral localization algorithm [59], the above equations can be used to calculate the coordinates obtained—Q2 (X2,Y2), Q3 (X3,Y3), and Q4 (X4,Y4). Then, according to the RSSI algorithm and of X and Y as follows: quadrilateraln n localization algorithm [59], the above equations can be used to calculate the  X X X X coordinates of Xn and Yn as follows: 1 + 2 + 3 + 4  X = an+bn+cn an+bn+dn an+cn+dn bn+cn+dn  n 1 + 1 + 1 + 1   X1 an+bn+cn X2an+bn+dn anX+c3n+dn bn+cn+Xd4n . (10)  +Y1 + Y2 + + Y3 ++ Y4   an+bn+cn an+bn+dn an+cn+dn bn+cn+dn an +Ybn=+ cn an + bn + dn an + cn + dn bn + cn + dn n =  n 1 1 1 1 X + + + + + + + + + + + 1 an+bn cn 1an bn +dn an 1cn dn +bn cn 1dn   an + bn + cn an + bn + dn an + cn + dn bn + cn + dn 3.2.5. Evaluation of the Accuracy of the DBH and Tree Position Y1 Y2 Y3 Y4 (10)  + + + an + bn + cn an + bn + dn an + cn + dn bn + cn + dn The major and minorYn = DBHs of each tree were measured using a caliper in the 10 plots, and their average was used as the reference1 DBH+ value1 for+ comparison.1 + The1 accuracy of using the device to  + + + + + + + + measure tree DBH was evaluatedan bn byc comparisonn an bn d withn an thecn referencedn bn DBHcn valuesdn . and by calculating the error, bias, relative bias, root mean square error (RMSE), relative RMSE, and mean absolute percent error3.2.5. (MAPE),Evaluation as of deﬁned the Accuracy in the following of the DBH equations: and Tree Position

The major and minor DBHs of eacherror tree =wered measuredd , using a caliper in the 10 plots, (11)and j − jr their average was used as the reference DBH value for comparison. The accuracy of using the Pn device to measure tree DBH was evaluated byj =comp1( djarisondjr with) the reference DBH values and by BIAS = − , (12) calculating the error, bias, relative bias, root mean squaren error (RMSE), relative RMSE, and mean absolute percent error (MAPE), as definedP in the following equations: n d /d 1 ) j=1 j jr − relBIAS =error = dj - djr 100%, (13) n , × (11)

n ( dj - djr )  j=1 BIAS = (12) n ,

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tv Pn 2 j=1 dj djr RMSE = − , (14) n tv Pn 2 j=1 dj /djr 1 ) relRMSE = − 100%, (15) n × Pn j=1 dj /djr 1 MAPE = − 100%, (16) n × where dj is the jth tree DBH measured using the device, djr is the jth tree reference DBH measured using the caliper, and n is the number of measured trees. The reference value of the tree position was also measured and converted into the OXY plane coordinate system. First, the plane coordinate of the tree bottom position nearest to the x-axis or y-axis was determined by the measured values of a tape scale, an angle ruler, and an inclinometer. Then, half of the tree DBH value was added to or subtracted from the reference position value of the plane coordinate in the y-axis or x-axis direction. The BIAS and RMSE were calculated to reﬂect the accuracy of the tree position in the x-axis and y-axis directions, respectively. The errors of the distance (Ed) between the estimated and the reference position values were calculated as follows: r 2 2 Ed = X X + Y Y ) . (17) j − jr j − jr

Here, xj and yj are the jth tree position estimators in the x- and y-axis directions, respectively; xjr and yjr are the jth position reference values in the x- and y-axis directions, respectively, of the OXY plane coordinate system.

4. Results

4.1. Tree Identiﬁcation The decoding rate of QR codes from the coded stickers on trees was 100%, and the decoding response time was short, less than two seconds.

4.2. Evaluation of DBH The DBHs measured by the device were similar to those measured by the caliper (Figure 11), resulting in an overall BIAS of 1.89 mm (1.88%) and an RMSE of 5.38 mm (4.53%) across all plots (Table3). The BIAS for an individual plot varied from 0.62 (Plot 10) to 5.13 mm (Plot 3), and on a − relative term from 0.25 to 3.54%. The RMSE values by plot were small, ranging from 3.48 to 6.84 mm, − and from 2.29 to 5.76% in a relative term. Variation in BIAS or RMSE was not strongly related to tree DBH size, tree species, and plot slope (Table3). Also, the BIAS or RMSE between the plots in the botanical garden (plots 1–5) and those in the natural stands (plots 6–10) were comparable. The error for each tree size distributed normally (Figure 12). There was a trend, however, that as the DBH increased, more variation in error was observed. The smaller DBH groups tended to have larger MAPEs. For the largest DBH group (from 250 to 350 mm), the average error was larger than zero, suggesting that the device overestimated the tree DBH compared to the caliper. Sensors 2020, 20, 144 12 of 19 SensorsSensors 2019 2019, ,19 19, ,x x 1212 of of 19 19

FigureFigureFigure 11. 11. 11.Scatter Scatter Scatter plot plot plot between between between the the measured measured DBH DBH values values values using using using the the thedevice device device and and andthe the reference thereference reference DBHs DBHsDBHs measuredmeasuredmeasured with with with a caliper.a a caliper. caliper.

FigureFigureFigure 12. 12. 12.Distribution Distribution Distribution of ofof the the error error in in in DB DB DBHHH for for for different different diﬀerent tree tree tree (DBH) (DBH) (DBH) sizes. sizes. sizes.

TableTable 3. 3. Accuracy Accuracy of of DBHs DBHs measured measured by by the the device device based based on on a a comparison comparison with with the the reference reference DBHs DBHs Table 3. Accuracy of DBHs measured by the device based on a comparison with the reference DBHs measuredmeasured by by a a caliper. caliper. measured by a caliper. PlotPlot BIAS BIAS (mm) (mm) relBIAS relBIAS (%) (%) RMSE RMSE (mm) (mm) relRMSE relRMSE (%) (%) Plot BIAS (mm) relBIAS (%) RMSE (mm) relRMSE (%) 11 −−2.042.04 −−2.042.04 6.656.65 5.76 5.76 1 2.04 2.04 6.65 5.76 22 −−1.221.22 −−0.640.64 3.523.52 2.29 2.29 233 5.135.131.22 3.503.500.64 6.446.44 3.52 4.434.43 2.29 − − 344 3.343.34 5.13 3.543.54 3.50 6.846.84 6.44 5.275.27 4.43 455 1.871.87 3.34 1.851.85 3.54 5.945.94 6.84 5.015.01 5.27 566 2.402.40 1.87 2.652.65 1.85 3.483.48 5.94 3.853.85 5.01 7 2.33 2.53 4.79 4.11 67 2.33 2.40 2.53 2.65 4.79 3.48 4.11 3.85 88 3.333.33 3.173.17 5.935.93 4.964.96 7 2.33 2.53 4.79 4.11 99 3.253.25 2.412.41 4.724.72 4.774.77 81010 −−0.62 3.330.62 −−0.25 3.170.25 6.426.42 5.93 4.76 4.76 4.96 9 3.25 2.41 4.72 4.77

10 0.62 0.25 6.42 4.76 − − Total 1.89 1.88 5.38 4.53 Sensors 2019, 19, x 13 of 19 Sensors 2020, 20, 144 13 of 19 Total 1.89 1.88 5.38 4.53

4.3. Evaluation of Tree Position Figure 13 presents the errors of thethe distancedistance (Ed)(Ed) betweenbetween the estimatedestimated and correspondingcorresponding reference positionposition values values by by individual individual tree, tree, ranging ranging from from 0 to 0 77 to cm 77 in cm the in plane the plane OXY. TheOXY. bias The ranged bias fromranged approximately from approximately8.55 to −8.55 14.88 to cm 14.88 on thecm x-axison the andx-axis from and 12.07from − cm12.07 to 24.69cm to cm24.69 on cm the on y-axis the − − (Tabley-axis 4(Table). The RMSEs4). The inRMSEs the x-axis in the (21.85 x-axis cm) (21.85 and cm) y-axis and (24.53 y-axis cm) (24.53 directions cm) directions were similar were (Table similar4). No(Table significant 4). No significant correlation correlation (approximately (approximately0.26 to 0.30) −0.26 was to found0.30) was between found the between errors the in the errors x-axis in − andthe x-axis y-axis and directions. y-axis directions. The mean The value mean of Edvalue was of 30.06 Ed was cm, 30.06 with acm, standard with a deviationstandard deviation of 13.53 cm of across13.53 cm plots across and plots ranged and from ranged 23.44 from to 38.08 23.44 cm to 38.08 by plot cm (Table by plot5). (Table The average 5). The Ed average of plots Ed 1 of to plots 5 was 1 relativelyto 5 was relatively lower than lower that ofthan plots that 6 to of 10. plots Additionally, 6 to 10. Additionally, if the plot had if athe larger plot slope had a or larger more trees,slope Edor wasmore relatively trees, Ed larger. was relatively Across all larger. plots, theAcross correlation all plots, coe theffi cientscorrelation of the coefficients mean Ed were of the 0.78 mean with theEd slopewere and0.78 0.24with with the theslope stand and density. 0.24 with Relatively, the stand slope density. had relatively Relatively, more slope influence had onrelatively mean Ed more than theinfluence stand density.on mean Ed than the stand density.

Figure 13. Errors in tree positions measured by the device. Table 4. Accuracy of tree positions in the x- and y-axis directions estimated by the device. Table 4. Accuracy of tree positions in the x- and y-axis directions estimated by the device. X (cm) Y (cm) Plot X (cm) Y (cm) ρxy Plot BIAS RMSE BIAS RMSE ρxy BIAS RMSE BIAS RMSE 1 6.51 20.21 6.40 19.72 0.22 − − 1 2 6.51 3.9720.21 18.45 −6.4012.07 21.7319.72 0.26−0.22 − − − 2 3−3.97 13.6518.45 16.82 −12.07 3.67 18.4421.73 0.13−0.26 4 0.26 23.54 3.86 23.06 0.21 3 13.65 16.82 3.67− 18.44 − 0.13 5 14.88 26.59 3.75 25.17 0.12 4 0.26 23.54 −3.86− 23.06 − −0.21 6 8.19 18.05 10.58 27.94 0.09 5 14.88 − 26.59 −3.75 25.17 − −0.12 7 8.55 19.37 3.19 25.12 0.11 − − 6 8−8.19 3.3618.05 23.93 10.589.57 24.0327.94 0.04−0.09 − 7 9 −8.55 1.8919.37 12.94 3.19 24.69 28.43 25.12 0.23−0.11 − 10 5.50 33.96 9.63 24.71 0.30 8 3.36 − 23.93 −9.57− 24.03 0.04 Total 0.80 21.91 1.21 24.62 0.07 9 −1.89 − 12.94 24.69 28.43 − 0.23 10 −5.50 33.96 −9.63 24.71 0.30

Total −0.80 21.91 1.21 24.62 −0.07

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Table 5. Summary statistics of the error of the distance (Ed) between the estimated point and the reference point.

Ed (cm) Plot Mean Max Min Std 1 26.21 47.10 11.20 10.84 2 26.19 66.18 12.56 11.25 3 23.44 47.84 11.58 8.88 4 30.84 58.23 10.85 11.61 5 33.98 69.34 12.18 13.26 6 29.42 68.47 6.18 15.53 7 29.37 60.12 4.78 11.96 8 31.99 58.87 10.05 10.77 9 28.00 64.92 3.84 13.36 10 38.08 76.40 11.27 16.99 Total 38.06 76.40 3.84 13.53

5. Discussion In this study, we reported a device that can identify trees using QR code technology, measure tree DBHs using angle sensors, and estimate tree positions using UWB modules and altitude sensors. Use of the QR code is very common in modern daily life, due to its low cost and advanced technology, but it is rarely used in forestry, especially in inventory plot surveys. To our knowledge, this is the first study to integrate QR code technology into a tree dendrometer to identify trees. In forestry inventories, tree identification data are of high value for retrospective data and database management development. Conventional dendrometers are only accurate for trees that are circular in cross-section. When a tree cross-section is eccentric, it is recommended to measure the major and minor diameters or two diameters perpendicular to each other, using a tree caliper, and to use their average as the tree DBH value [26]. Different from conventional tools, the device described here takes into account the fact that the cross-sections of trees are not always circular by calculating the radii of different arcs. We evaluated the accuracy of the device in measuring DBH by comparing it to the corresponding DBH values measured twice using a tree caliper. The resulting BIAS and RMSE were small (Table3), suggesting the device is accurate in measuring tree DBH. Modern tools to measure DBH have been developed to improve accuracy. Liang et al. [8] used a multi-single-scan TLS method to estimate tree DBH. Those authors mapped five dense forest plots, compared the results with manual field measurements, and reported an RMSE range from 0.90 to 1.90 cm. Reference [4] estimated the tree DBH of nine square plots using simultaneous localization and mapping (SLAM) algorithms paired with a time-of-flight (TOF) camera. The DBH estimations had a 0.33 mm (1.78%) BIAS and a 1.26 cm (6.39%) RMSE. Reference [1] used unmanned aerial system-based photogrammetry and terrestrial photogrammetry to estimate tree DBH. The error of the diameter estimation was observed to be less than 1 cm in terms of RMSE. Reference [27] used 3D point clouds of individual trees collected using the CRP method to estimate the tree DBH of four species. The relative RMSE varied from 0.90% to 1.85%, strongly depending on tree species. While the accuracies of the above methods are high and time-efficient, their practical applications in forest inventories, particular in large and dense forests, are still limited since these methods involve complicated procedures in data processing and require specific tools. Even though our method is based on a simple trigonometric theorem, the obtained BIAS (0.19 cm and 1.88%) and RMSE (0.54 cm and 4.53%) (Table3) were either comparable to or even lower than those reported above. The DBH measurement accuracy of the methods based on TLS, CRP, or TOF may be affected by environmental conditions such as light intensity and stand density. The effects of environmental conditions on our device’s accuracy may be small, which explains why the BIAS and RMSE (Table3) did not vary substantially with plot slope, tree species, or stand type. Our results also suggest that the device can estimate tree positions accurately, with the resulting BIAS ( 8.55 to 14.88 cm on the x-axis and 12.07 to 24.49 cm on the y-axis), RMSE (12.94–33.96 cm and − − Sensors 2019, 19, x 15 of 19

Our results also suggest that the device can estimate tree positions accurately, with the Sensorsresulting2020 , 20BIAS, 144 (−8.55 to 14.88 cm on the x-axis and −12.07 to 24.49 cm on the y-axis), 15RMSE of 19 (12.94–33.96 cm and 17.78–28.43 cm on the x-axis and the y-axis, respectively), and Ed (30.06 cm) being small. Reference [4] estimated the tree position using the SLAM algorithms paired with a TOF 17.78–28.43camera and cm reported on the x-axisan RMSE and theof 0.12 y-axis, m, respectively),regardless of andthe Edaxis (30.06 directions. cm) being Their small. results, Reference however, [4] estimatedwere based the on tree sample position plots using on a theflat SLAMsite with algorithms no weeds paired and small with shrubs; a TOF cameratherefore, and the reported actual use an RMSEof their of method 0.12 m, in regardless dense forests of the needs axis further directions. verification. Their results, While however,application were of SLAM based onalgorithms sample plotspaired on with a flat a siteTOF with seems no promising weeds and in small terms shrubs; of precision, therefore, it is the known actual to use be of affected their method by stand in denseenvironments, forests needs such further as stand verification. density, Whileabundance application of shrubs of SLAM and vegetation, algorithms pairedetc., and with involves a TOF seemscomplicated promising data inprocessing terms of procedures, precision, it limiting is known its to application be affected to by forest stand inventory. environments, Reference such [37] as standreported density, a position abundance error ofof shrubsless than and 0.5 vegetation, m, although etc., with and involvesa systematic complicated shift, and data they processing used five procedures,cameras to limitingrealize their its application method, towhich forest isinventory. impractical Reference for forest [37 surveys.] reported Reference a position [44] error used of less an thanextended 0.5 m, Kalman although filter with (EKF) a systematic method shift, that and integrated they used inertial five cameras navigation to realize system their (INS) method, and which UWB isdata. impractical They tested for foresttheir method surveys. in Reference an indoor [44 area] used of 10 an × extended 10 m and Kalman found that filter the (EKF) positioning method error that integratedof UWB was inertial between navigation 10 and system 30 cm (INS) and andINS-UWB UWB data. was Theyless testedthan 15 their cm. method Clearly, in our an indoordevice area can of 10 10 m and found that the positioning error of UWB was between 10 and 30 cm and INS-UWB obtain× similar or more accurate position estimates than the above cited methods, even our device wasonly less uses than the 15 trilateration cm. Clearly, localization our device canalgorith obtainm, similarRSSI algorithm, or more accurate and quadrilateral position estimates localization than thealgorithm, above citedwhich methods, have a much even lower our device complexity only uses in both the trilaterationtime and space. localization Note that algorithm, the accuracy RSSI in algorithm,estimating and tree quadrilateral positions using localization our device algorithm, may whichbe affected have a muchby stand lower environments. complexity in The both slope time andcorrelated space. more Note thatpositively the accuracy with Ed in than estimating the stand tree density positions did using (Table our 2 deviceand Figure may 14). be a ffTherefore,ected by standfurther environments. studies are needed The slope to correlatedimprove accuracy more positively in estimating with Ed positions than the standin various density environments did (Table2 andand Figurefind how 14). to Therefore, reduce influence further studiesfrom slope. are needed to improve accuracy in estimating positions in various environments and find how to reduce influence from slope.

40 Linear Fit 40 Linear Fit

y=0.29x+25.43 35 35 y=13.97x+26.61

30 30 Mean Ed (cm) Mean Ed (cm)

25 25

20 20 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0 5 10 15 20 25 30 35 Stand density (Number of trees/m2) Slope (°)

(a) (b)

FigureFigure 14.14. ScatterScatter plotplot ((aa)) betweenbetween meanmean EdEd andand standstand densitydensity ((bb)) andand slope.slope.

2 NoteNote thatthat thethe plotplot sizesize adoptedadopted inin thisthis studystudy isis 100100 mm2,, muchmuch smallersmaller thanthan thethe regularregular plotplot sizesize oftenoften usedused in in forestry forestry inventory. inventory. This This raises raises a concern a concern of using of using the devicethe device to estimate to estimate positions positions in more in realisticmore realistic scenarios scenarios since the since performance the performance of four UWBof four sensors UWB sensors would probably would probably degrade degrade when the when plot areathe plot is large. area However,is large. However, the range the accuracy range accuracy deteriorates deteriorates only when only the distancewhen the between distance two between UWB nodestwo UWB is over nodes 100 m is [ 59over], which 100 m is much[59], which longer is than much the sidelonger length than of the a typical side le plot.ngth In of a plota typical of regular plot. size,In a theplot line-of-sight of regular (LOS) size, paths the betweenline-of-sight nodes (LOS) may bepaths obstructed, between resulting nodes inmay None-Line-of-Sight be obstructed, (NLOS) situations, in particular when the plot is located within a natural, dense stand. Even the UWB resulting in None-Line-of-Sight (NLOS) situations, in particular when the plot is located within technology offers the great potential of achieving high ranging accuracy through its ability to resolve a natural, dense stand. Even the UWB technology offers the great potential of achieving high multipath and penetrate obstacles in harsh environments [60], its localization performance may be ranging accuracy through its ability to resolve multipath and penetrate obstacles in harsh reduced by NLOS propagation. Although UWB signal cannot penetrate metal media or thick wall, it environments [60], its localization performance may be reduced by NLOS propagation. does have capability of penetrating trees or weed, which was supported by measuring some of the Although UWB signal cannot penetrate metal media or thick wall, it does have capability of plots in this study where NLOS were true. Furthermore, several techniques have been proposed to reducepenetrating the impact trees ofor NLOS weed, range which estimates was supported on the estimated by measuring agent position some of [60 the]. Conventionally,plots in this study the RSSI is not popularly used for UWB because it does not exploit fine space resolution of impulsive signals [61]. In our method, at least three points are required in order to calculate the position on the Sensors 2020, 20, 144 16 of 19 plane, which fitted well for RSSI algorithm and four UWB Anchors. In every calculation, we need to deal with four positions (Q1 (X1,Y1), Q2 (X2,Y2), Q3 (X3,Y3), and Q4 (X4,Y4)) obtained from four tri-UWB Anchors combinations. If one position has a stronger signal, it will be given more weight (see Equation (10)). Overall, extension of the results to typical large plots, in particular when they are located in dense stands, should be taken with caution and further studies on this topic should be carried out to confirm our findings. Alternatively, measurements can be done based on four sensors for every 10 m 10 m area. This seems feasible, at least economically, since each UWB sensor costs less × than twenty dollars. The SLAM algorithm, convex hull algorithm, and point cloud algorithm used in other studies [4,25,27,37] usually need mobile phones or computers with 32- or 64-bit capacity. The device reported in this paper only needs the STC15, an 8-bit microprocessor, with the price being less than one dollar. In terms of computation, our method only needs four operations to obtain the estimates of DBH and tree position, making it much simpler than the other algorithm-based methods.

6. Conclusions The novelty of the dendrometer reported here is that the device can measure tree identiﬁcation, position, and DBH concurrently. Speciﬁcally, we integrated several advanced technologies (UWB, QR code, altitude sensor, and so on) into the device to improve the measurement accuracy. The experimental results show that this device can be used to accurately estimate DBH and tree positions. Additionally, the device is cheap and easy to use. Nonetheless, we will continue to improve the device, in particular, improving the measurement accuracy of DBH for large trees (i.e., with DBH > 50 cm) and tree positions in complex environments.

Author Contributions: Investigation, L.S. and S.Z.; Methodology, L.S. and L.F.; Resources, L.F.; Software, L.S.; Writing—original draft, L.S.; Writing—review and editing, Y.W. All authors have read and agreed to the published version of the manuscript. Funding: This work was financially supported by Zhejiang provincial key science and technology project (2018C02013). Conflicts of Interest: The authors declare no conflict of interest.

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