LIDR SYSTEM CLIRTION USIN OVERLPPIN STRIPS Calibação do sistema LiDR utilizando faias sobepostas KI IN N 1 YMN F. HI 1 MURICIO MÜLLER 2 1 Dept. of eomatics Engineeing, Univesity of Calgay, 25 Univesity Dive NW, Calgay,, T2N 1N4, Canada email: {kibang, ahbib}@ucalgay.ca 2 LCTEC Institute of Technology fo the Development, Cento Politécnico da UFPR, Caia Postal - 1967 - CEP: 81531-98, Jadim das méicas - Cuitiba - Paaná asil email: mulle@lactec.og.b STRCT LiDR system calibation pocedue estimates a set of paametes that epesent biases in the system paametes and measuements. These paametes can be used to impove the quality of any subsequently-collected LiDR data. Cuent LiDR calibation techniques equie full access to the system paametes and aw measuements (e.g., platfom position and oientation, lase anges, and scan-mio angles). Unfotunately, the aw measuements ae not usually available to end-uses. The absence of such infomation is limiting the widespead adoption of LiDR calibation activities by the end uses. This eseach poposes altenative methods fo LiDR system calibation, without the need fo the system aw measuements. The simplified method that is poposed in this pape uses the available coodinates of the LiDR points in ovelapping paallel stips to estimate biases in the system paametes and measuements (moe specifically, biases in the planimetic leve-am offset components, boesight angles, anges, and mio-angles). In this appoach, the conventional LiDR equation is simplified based on a few easonable assumptions; the simplified LiDR equation is then used to model the mathematical elationship between conjugate suface elements in ovelapping ol. Ciênc. eod., v. 15, n. 5 Special Issue on Mobile Mapping Technology, p. 725-742, 29.
726 Lida system calibation using ovelapping stips paallel stips in the pesence of the systematic biases. In addition, a quasiigoous calibation method is also poposed to deal with non-paallel ovelapping stips. The quasi-igoous method can handle heading angle and elevation vaiations of platfom tajectoies since it also makes use of timetagged point cloud and tajectoy position data. To illustate the feasibility and the pefomance of the poposed calibation methods, epeimental esults fom simulated and eal datasets ae intoduced. Keywods: LiDR; Lase Scanning; Calibation; eo-feencing; ccuacy. 1. INTRODUCTION typical LiDR system consists of a lase anging and scanning unit togethe with a Position and Oientation System (POS), which encompasses an integated Diffeential lobal Positioning System (DPS) and an Inetial Navigation System (INS). lase scanne mounted on the platfom scans object sufaces and poduces a wide swath ove which the distance to an object is measued. The angle at which the lase is scanned is measued. To coect fo the platfom s movement, the motion of the platfom is ecoded by the PS/INS navigation system and the infomation is used in a post-pocessing mode. The fundamentals and detailed pinciples of the lase anging opeation was well documented by altsavias (1999); Weh and Loh (1999), and the common method to detemine the coodinates of LiDR footpints was fully eplained by Vaughn et al. (1996). The accuacy of LiDR poducts is elatively high (vetical: 5-3 cm, hoizontal: about 8cm), and the quality of the LiDR data is affected by many factos: a) position and attitude measuement quality, b) system calibation quality, and c) flying height and speed (Mclone, 24). The coodinates of the LiDR footpints ae the esult of combining the deived measuements fom each of its system components, as well as the mounting paametes elating such components. The elationship between the system measuements and paametes is embodied in the LiDR equation (Vaughn et al., 1996 and Schenk, 21), Equation 1. The position of the LiDR footpint,, can be deived though the summation of thee vectos (, P and ρ ) afte applying the appopiate otations: R yaw,pitch,oll, R ωφκ, and R α. In Equation 1, is the vecto between the oigins of the gound and the Inetial Measuement Unit (IMU) body fame, P is the offset between the lase unit fame and the IMU body fame (leve-am offset), and ρ is the lase ange vecto whose magnitude is equivalent to the distance fom the lase fiing point to its footpint. The tem R yaw,pitch,oll stands fo the otation mati elating the gound and IMU body fame, R ωφκ epesents the otation mati elating the IMU and lase unit fame (boesight mati), and R α efes to the otation mati elating the lase unit fame and lase beam fame with α and ol. Ciênc. eod., v. 15, n. 5 Special Issue on Mobile Mapping Technology, p. 725-742, 29.
ang, K.I et al. being the mio scan angles. Fo a linea scanne, which is the focus of this pape, the mio is otated in one diection only (i.e., α is equal to zeo). 727 = Ryaw, pitch, oll P R, φ, ρ ω κ Rα, (1) The involved quantities in the LiDR equation ae all measued duing the acquisition pocess ecept fo the leve-am offset and boesight angles, which ae usually detemined though a calibation pocedue. To make sue that the LiDR data meets the equied and pedicted quality, LiDR system calibation has been investigated in many ways, and conventional calibation methods have been caied out based on system aw measuements and LiDR equation. Schenk (21) intoduced the souces of systematic eos that can occu in a LiDR system, and a calibation pocedue was then poposed based on such an analysis. This wok compehensively eplained possible eos in a LiDR system, but it seems too comple in tems of an effective calibation pocedue. Futhemoe, all intoduced calibation paametes wee not solved fo simultaneously due to thei coelations; fo eample, biases in the scanne mio angles and lase scanne mounting eos. The calibation pocedue intoduced by Moin (22) solves fo the boesight angles and the scanne tosion. These paametes ae eithe estimated using gound contol points o by manually obseving discepancies between tie points in ovelapping stips. The dawback of this appoach is that the identification of distinct contol and tie points in LiDR data is a difficult task due to the iegula and spase natue of the collected point cloud. Skaloud and Lichti (26) pesented a calibation technique using tie plana patches in ovelapping stips. The undelying assumption of this pocedue is that systematic eos in the LiDR system will lead to non-coplanaity of conjugate plana patches as well as bending effects in these patches. The calibation method uses the LiDR equation to simultaneously solve fo the plane paametes as well as the boesight angles and a bias in lase anges. Howeve, this appoach equies elatively lage plana patches, which might not always be available, especially in ual aeas. ccoding to Habib et al. (27), when the leve-am offset and boesight angles ae consideed at the same time, one of the difficulties is the coelations between these paametes. Theefoe, the use of plana patches should be caefully handled though the use of an optimal flight plan, as well as optimal plana patch distibution due to the coelations between these calibation paametes (Habib et al., 27). ol. Ciênc. eod., v. 15, n. 5 Special Issue on Mobile Mapping Technology, p. 725-742, 29.
728 Lida system calibation using ovelapping stips Since ckemann (1999) intoduced the potential integation of imaging and lase sensos, eseach has been pefomed to investigate the potential and limitations of the integation of LiDR and photogammetic data. Fo eample, Postolov et al. (1999) and hanma (26) intoduced the co-egistation between LiDR and photogammetic data, and eta (24) geneated a DSM fom photogammetic data which was then compaed with LiDR data fo the stip adjustment. Habib et al. (27) used plana patches deived fom photogammetic data fo LiDR system calibation, whee the photogammetic bundle adjustment was augmented by adding the LiDR equation to the collineaity equations using the LiDR system aw measuements. This pape intoduces two appoimate methods fo the LiDR system calibation: a simplified method using ovelapping stips without system aw measuements, and a quasi-igoous method using time-tagged lase footpint coodinates of ovelapping stips and tajectoy positions. In these methods, the discepancies between ovelapping stips ae utilized to detemine the coection tems to the initial calibation paametes. In the net section, we will discuss how to modify the LiDR equation fo the simplified method and the utilization of the time-tagged point cloud and tajectoy positions fo the quasi-igoous method. Then, epeiment esults fom simulated and eal datasets ae pesented. Finally, the manuscipt summaizes its conclusions and ecommendations fo futue woks. 2. PROPOSED METHODS The LiDR system calibation consides the alignment of integated sensos and the systematic eos in a lase scanne. igoous calibation method is commonly caied out using system aw measuements (fom PS/INS and lase scanne) and the conventional LiDR equation (efe to Equation 1). This pape intoduces new methods, whee system aw measuements ae not equied and the biases in the system paametes ae detemined using ovelapping stips. The simplified method using only point cloud coodinates consists of two steps: 1) detemination of discepancies between paallel ovelapping stips though a conventional 3D tansfomation pocedue, and 2) estimation of biases in system paametes fom the obtained tansfomation paametes. nothe poposed method, the quasi-igoous method, can handle non-paallel ovelapping stips using timetagged point cloud coodinates and tajectoy position data. In this method, time infomation is utilized to igoously detemine the locations of the fiing points fo lase footpints. 2.1 Simplified method Discepancies among ovelapping stips occu if LiDR footpints ae geneated by incoect system paametes. The new poposed method detects and ol. Ciênc. eod., v. 15, n. 5 Special Issue on Mobile Mapping Technology, p. 725-742, 29.
ang, K.I et al. evaluates the discepancies between ovelapping stips using the conventional 3D tansfomation pocedue. The esult of this pocedue is epesented by tansfomation paametes: otation angles and shifts. Then, the poposed method estimates coection tems of the LiDR system paametes using the tansfomation paametes. The key issue of this methodology is defining the elationship between the tansfomation paametes and LiDR system paametes. In ode to establish the elationship, we simplify the conventional LiDR equation. Fo the mathematical deivation of the simplified LiDR equation, a few easonable assumptions ae consideed egading the platfom tajectoy and the object suface: i) linea scanning systems ae consideed, ii) the object suface is nealy flat in compaison to the flying height, iii) the flight lines ae paallel, iv) the platfom tajectoy is staight, v) the oll and pitch angles of the platfom ae zeo, and vi) the boesight angles ae consideed as vey small angles. The simplified method woks with an additional coodinate system which is defined within the ovelapping aea. Its Y-ais is paallel and halfway between the flight lines, Figue 1. The positive diection of the Y-ais indicates the fowad flight diection, and the ais is along the scan line (acoss the flight diection). In the figue, and denote lateal coodinates of a gound object point, P, w..t. the lase unit fames fo the fowad and backwad flights, espectively; the lateal distance between two flight lines is epesented by D. Using the above assumptions and the use defined coodinate system, the oiginal LiDR equation can be appoimated by Equation 2. In this equation,, Y, Z, ω, φ, and κ denote the leve-am offset and boesight angles, S is the scale facto of the scan angles, and ρ is the lase ange. The lase unit fame coodinate and flying height H ae the same as the tems ρsin(s) and ρcos(s) in Equation 2. The multiple signs ( ± & m ) indicate two paallel stips with the uppe sign efeing to the fowad stip, while the lowe sign efeing to the backwad stip. The impact of the systematic eos is epesented in tems of the system paametes in Equation 3; is the eo-fee coodinates, while Tue denotes the iased deived lase footpint coodinate which may be distoted by biases ( ) in the system paametes. The impacts of biases in leve-am offset, boesight angles, lase ange, and scan angle scale ae intoduced in the second line of Equation 3, in detail. These eo tems ae deived though the patial deivatives of Equation 2 w..t. the consideed calibation paametes, afte ignoing second and highe ode bias tems. 729 ol. Ciênc. eod., v. 15, n. 5 Special Issue on Mobile Mapping Technology, p. 725-742, 29.
Lida system calibation using ovelapping stips ol. Ciênc. eod., v. 15, n. 5 Special Issue on Mobile Mapping Technology, p. 725-742, 29. 73 Figue 1 - Flight lines and definitions of the used coodinate systems in paallel ovelapping stips ± ± ± ± ± ± ) cos( ) sin( 1 1 1 ρ ρ ω φ ω κ φ κ S S Z Y m m (2) 14243 m 4 43 4 14 2 m 44 4 3 44 14 2 m 4243 1 facto scale bias ange angles boesighting am offset leve Tue Tue iased S S H S S H H Z Y f ± ± ± ± = ρ ρ φ ω κ φ ) cos( ) sin( (3) Fo ovelapping stips, the discepancies between two stips can be consideed as the accumulated impact of the systematic eos on these stips; it is mathematically epesented in Equation 4. To detemine all the biases in the system paametes, ecept fo Z, two kinds of ovelapping stip pais ae consideed: case 1 consist of ovelapping stips captued with 1% ovelap atio and opposite flight diections (fowad and backwad), and case 2 consists of ovelapping stips captued with less than 1% ovelap atio and the same flight diection (Figue 2). f f iased iased (4)
ang, K.I et al. 731 Figue 2 - Two ovelapping cases ae specified to de-couple involved calibation paametes Equations 5.a and 5.b show the final foms fo cases 1 and 2, espectively. s shown in Equation 5.a, case 1 (opposite diections and 1% ovelap atio) can be used to solve fo the system biases,, Y, ω, and φ, while case 2 (same diection and less than 1% ovelap atio) contibute to the estimation of ρ, S, φ, and κ. fte e-paameteization, we can notice that the foms of Equations 5.a and 5.b ae simila to the conventional 3D tansfomation function with 4 paametes: thee shifts and one otation aound Y ais (oll angle). n additional obsevation that has sufaced fom this pocedue is that the 4-paamete tansfomation is appopiate fo the stip adjustment while consideing the system biases (, Y, ω, φ, κ, ρ, and S) intoduced in this pape. To use this simplified method, one should note two facts. The fist, Z, the bias in the leve-am offset along the Z diection, cannot be estimated in this pocedue because ovelapping stips do not have any discepancy caused by this bias egadless of the flight diection, flying height, o scan mio angle. The second, two diffeent flying heights (see cases 1.a and 1.b in Figue 2) ae equied to de-couple Y and ω; as we can see in Equation 5.a, Y and ω ae coupled togethe. Using two flying heights, one can solve this poblem since the impact of Y is independent of the flying height; howeve, ω poduces diffeent eos as the flying height changes. ' 2 2Hφ = 2Y 2Hω R2 φ { oll 144 2444 3 shifts ' (5.a) ol. Ciênc. eod., v. 15, n. 5 Special Issue on Mobile Mapping Technology, p. 725-742, 29.
732 Lida system calibation using ovelapping stips ' D ρ DS H = Dκ R 2D S H D 14243 φ oll 14 42444 3 shifts ' (5.b) 2.2 Quasi-igoous method The quasi-igoous method can deal with non-paallel stips. In addition, this method can handle heading vaiation and vaying elevations since it makes use of time-tagged point cloud and tajectoy position data. In othe wods, this method is developed unde the following assumptions: a) we ae dealing with a linea scanne, b) the LiDR system is almost vetical (i.e., pitch and oll angles ae close zeo), and c) the LiDR system has elatively small boesight angles. Such assumptions simplify the LiDR geometic model as epesented by Equation 1 to the fom in Equation 6. cosκ sinκ o sinκ cosκ Y 1 Z cosκ sinκ 1 κ sinκ cosκ κ 1 1 ϕ ω ϕ ω 1 z (6) The diffeence between Equations 6 and 2 (which is deived fo the simplified method) is the additional otation mati defined by the heading angle, κ. The quasiigoous method is developed fo handling geneal flight lines, which means that the tajectoy is not limited to a staight line. The platfom positions ae available fom the tajectoy position data, which is linked to the time-tagged point cloud coodinates. Theefoe, the location of the fiing point coesponding to each LiDR point can be estimated. In Equation 6, and z ae the coodinates of the LiDR point with espect to the lase unit fame (efe to Figue 1); those ae appoimately estimated by the fiing point and LiDR point coodinates. The coodinate z is the elevation diffeence between the fiing point and LiDR point. s shown in Figue 3, the coodinate epesents the lateal distance between the LiDR point in question and the pojection of the flight tajectoy onto the gound. The tajectoy line fo a given LiDR point is detemined by a line-fitting ol. Ciênc. eod., v. 15, n. 5 Special Issue on Mobile Mapping Technology, p. 725-742, 29.
ang, K.I et al. ol. Ciênc. eod., v. 15, n. 5 Special Issue on Mobile Mapping Technology, p. 725-742, 29. 733 pocedue using seveal tajectoy positions at the vicinity of the time associated with the point in question. Figue 3 - Lateal distance between the LiDR point in question and the pojection of the flight tajectoy onto the gound Tajectoy position Lida point Fitted line In the pesence of biases in the system paametes, Equation 7 shows the biased LiDR point coodinates, iased, which is a function of the system paametes,, the biases in the system paametes,, and the measuements, l. Equation 7 can be lineaized with espect to the system paametes using Taylo seies epansion to get the fom in Equation 8, afte ignoing second and highe ode tems. ), ( l f iased = (7) S Z Y Tue Tue Tue iased Z Y Z Y Z Y Z Y Z Y f f l f ρ κ ϕ ω = = =,,,, ), ( (8) Due to the pesence of vaious systematic eos, the bias-contaminated coodinates of conjugate points in ovelapping stips will show systematic discepancies. The mathematical elationship between these points can be deived by ewiting Equation 8 fo two ovelapping stips ( and ) and subtacting the esulting equations fom each othe. Such a elationship is shown in Equation 9.
Lida system calibation using ovelapping stips 734 ( cosκ cosκ ) ( sinκ sinκ ) Y Y Y = ( sinκ sinκ ) ( cosκ cosκ ) Y Z Z iased iased ( sinκ z sin κ z ) ω ( cosκ z cosκ z ) φ ( sinκ sinκ ) κ ( cosκ z cosκ z ) ω ( sinκ z sin κ z ) φ( cosκ cosκ ) κ (9) ( ) φ [ cosκ sin( S ) cosκ sin( S )] ρ ( cosκ z cosκ z ) S [ ( ) ( )] ( ) [ ( ) ( )] sin κ sin S sin κ sin S ρ sin κ z sin κ z S cos S cos S ρ ( ) S Equation 9 is the final linea obsevation equations when dealing with ovelapping stips in the quasi-igoous method. These equations allow us to ecove the biases in the system paametes. It should be noted that, when using only ovelapping stips, the bias in the leve-am offset along the Z diection (Z) cannot be estimated. Such inability is caused by the fact that a vetical bias in the leve-am offset paametes poduces the same effect egadless of the flight diection, flying height, o scan mio angle. When vetical contol data ove flat hoizontal suface is also employed, we cannot ecove Z and ρ simultaneously due to the high coelation between these paametes. This type of contol data will only contibute fo the estimation of the oll (φ), the ange bias (ρ) and the mio angle scale biases (S). The use of full contol data ove sloped sufaces will contibute fo the estimation of all paametes and might help decoupling Z and ρ. Equation 1 shows the fom deived fo contol data use. This equation can be also used to coect the biased LiDR point cloud afte estimating the eo tems in the system paametes. In this case, the left-hand side epesents the coected coodinates calculated using the given coodinates and estimated paametes. One should note that the mathematical models fo the simplified and the quasi-igoous calibation methods ae deived based on a point pimitive (i.e., conjugate points in ovelapping stips). Howeve, it is known that point coespondence is not available in point cloud data. Fo this eason, linea featues and plana patches have been altenatively used as conjugate suface elements in ovelapping stips (Lee et al., 27; Habib and et al., 27). In this eseach, howeve, the Iteative Closest Patch (ICPatch) pocedue is applied to establish coespondence between two ovelapping stips using conjugate point and TIN patch pais. Fo moe infomation egading the ICPatch method and how it can be used to estimate descipancies between ovelapping stips, inteested eades can efe to Habib et al., 26 and ang et al., 28. ol. Ciênc. eod., v. 15, n. 5 Special Issue on Mobile Mapping Technology, p. 725-742, 29.
ang, K.I et al. C Y C = Y Z Z C Contol LiDR cosκ sin κ Y sin κ z ω cosκ z φ sin κ cosκ Y cosκ z ω sin κ z φ φ sin κ κ cosκ sin( S ) ρ cosκ z S ( ) ( ) cosκ κ sin κ sin S ρ sinκ z S cos S ρ S 735 (1) 3. EPERIMENTS In this section, feasibility tests fo the poposed calibation methods using simulated and eal datasets ae epesented. The main pupose of utilizing simulated data fo the epeiments is to veify the pefomance of the poposed models in a contolled envionment. In addition, we can veify the impact of deviations fom the listed assumptions peviously mentioned. 3.1 Simulated datasets The simulated data was poduced using a LiDR system with a pulse epetition ate of 167 khz, a scan ate of 1 Hz, and a scan angle vaiation fom - 22 o to 22 o. Si stips in thee ovelapping pais ae simulated (see Table 1 and Figue 4). Stips 1 and 2 ae captued fom a flying height of 1,m in opposite diections with 1% ovelap atio. Stips 3 and 4 captued fom a 2,5m flying height with 5% ovelap atio and in the same flight diections. Stips 5 and 6 ae flown at 2,m flying height with 1% ovelap atio and opposite flight diections. This testing configuation allows the maimization of the impact of systematic biases and has the ability to de-couple the diffeent biases fom each othe. Fo testing the impact of deviations fom the undelying assumptions, thee cases ae designed in tems of the paallelism of the flight lines. In Table 1, one can see that thee ovelapping cases ae simulated. In the fist case, ovelapping stips ae paallel to each othe; in the second case, ovelapping stips ae non-paallel to each othe with 1 deviation; in the thid case, the degee of the non-paallelism is 3 (see the flying diections in Table 1). s it can be seen in Figue 4, the simulated suface has vaious plana patches with well distibuted aspects. The heights in the simulated suface ae in the ange [. 112.5m]. Using the simulated suface and flight-line tajectoies, the LiDR measuements wee deived. Then, biases wee intoduced to the system paametes (the magnitudes of these biases ae listed in Table 2). ol. Ciênc. eod., v. 15, n. 5 Special Issue on Mobile Mapping Technology, p. 725-742, 29.
736 Lida system calibation using ovelapping stips Table 1-6 stips ae simulated with one paallel and two non-paallel ovelapping cases Flying diection [ ] Stip Flying Case 1 Case 2 Case 3 s height [m] Paallel 1 non-paallel 3 non-paallel 1 5 15 1, 2 18 175 165 1, 3 5 15 2,5 4-5 -15 2,5 5 5 15 2, 6 18 175 165 2, Figue 4 - Illustation of the simulated suface and flight lines Table 2 -. Systematic biases intentionally added to the system paametes Y Z ω φ κ ρ S (m) (m) (m) (deg) (deg) (deg) (m).5.5.5.1.1.1.5.1 ol. Ciênc. eod., v. 15, n. 5 Special Issue on Mobile Mapping Technology, p. 725-742, 29.
ang, K.I et al. s it is mentioned ealie, the simplified method consists of a two-step pocedue. Fist, the discepancies between ovelapping stips ae evaluated using a 3D tansfomation; second, the system biases ae estimated fom the estimated paametes. The tansfomation paametes (w..t. the local coodinate system) fo the simulated ovelapping stips ae shown in Table 3. It should be noted that only the 3D shifts and the oll angle (φ) acoss the flight diection ae used fo the estimation of biases in the system paametes accoding to the simplified calibation pocedue. The deviations of the estimated pitch and heading angles (ω and κ) fom zeos can be used to indicate the pesence of additional biases beyond what is consideed in this manuscipt. Moeove, the pitch and heading angles would also indicate any deviation fom the undelying assumptions (e.g., non-paallel stips). s it can be seen in Table 3 case 1, the estimated pitch and heading angles of the 3D tansfomation paametes ae quite small. On the othe hand, the estimated heading angles fo cases 2 and 3 show the impact of dealing with non-paallel stips. Table 3 - Estimated 3D Tansfomation paametes w..t. the local coodinate system between the simulated stips, whose specifications ae shown in Table 1 Case Stips T (m) Y T (m) Z T (m) ω(deg) φ(deg) κ(deg) (1) paallel (2) 1 (3) 3 1&2 -.23.42..4.2.1 4&3-1.42 -.2.23 -.4.58 -.1 5&6 -.58.78..2.2.1 1&2 -.24.42..1.21.38 4&3-1.47 -.3.26.1.57.14 5&6 -.58.76. -.3.21.41 1&2 -.23 -.41 -..2.19.45 4&3-1.54 -.39.22 -.3.54.34 5&6 -.54.75 -..3.18.37 Table 4 pesents the biases in the system paametes which ae estimated fom the detemined tansfomation paametes in Table 3 based on Equations 5.a and 5.b Compaing Tables 2 and 4, one can see that the estimated biases ae quite close to the intoduced biases. We can also obseve in Table 4 that the non-paallelism of the flight lines mainly affected the heading bias. lthough we see some deviation, we can say that the estimated biases ae quite close to the eal ones, which indicate the validity of the poposed simplified method fo scenaios with easonable deviations fom the listed assumptions. In the LiDR simulation pocedue, the platfom tajectoy positions ae ecoded fo the quasi-igoous method tests. Table 5 epesents the biases in the system paametes estimated by the quasi-igoous method. Those estimated paametes ae vey close to the paametes intoduced in the simulated datasets and 737 ol. Ciênc. eod., v. 15, n. 5 Special Issue on Mobile Mapping Technology, p. 725-742, 29.
738 Lida system calibation using ovelapping stips ae quite bette compaed to the esults fom the simplified method, especially fo the non-paallel stips. s shown in Table 5, the estimated paametes ae elatively consistent in all thee cases. Fom these esults, we can veify that the quasiigoous method accuately estimates the systematic biases egadless of the flight diection deviations. This pefomance is not a supise since the quasi-igoous method can handle non-paallel stips with vaying heading. Such stength enables the quasi-igoous method to be widely applied to geneal ovelapping stips. Table 4 - iases in the system paametes estimated by the simplified method fom the tansfomation paametes (thee shifts and oll angle) pesented in Table 3 Y ω φ κ ρ Case S (m) (m) (deg) (deg) (deg) (m) 1.5.4.13.1.95.37.11 2.6.5.97.15.143.52.11 3.5.5.96.94.189.83.9 Table 5 - iases in the system paametes estimated by the quasi-igoous method Case Y ω φ κ ρ (m) (m) (deg) (deg) (deg) (m) S 1.5.5.99.1.89.48.1 2.5.5.11.1.96.5.9 3.5.5.1.1.96.53.1 3.2 Real datasets To evaluate the pefomance of the poposed methodology, a LiDR dataset, which was captued by an Optech LTM 25 using the optimum flight configuation, was utilized. In addition to stips in the optimum configuation, some eta stips wee acquied as well. In Figue 5, stips 1, 2, and 6 ae captued fom 2,m flying height; the othe stips have 1,m flying height. When it comes to the flight diections, stips 1, 3, 5, and 8 ae flown fom SW to NE; the othe stip ae fom NE to SW. Table 6 pesents the seven ovelapping stip pais configued fo the poposed methods. Table 7 shows the tansfomation paametes (w..t. the local coodinate system) pepaed fo the simplified method, and the estimated system biases detemined fom the tansfomation paametes ae epoted in Table 8. In Table 7, we can see that the estimated heading angles show some deviation fom the epected zeo value. Such deviation can be attibuted to possible navigation eos and the non-paallelism of the flight lines. ol. Ciênc. eod., v. 15, n. 5 Special Issue on Mobile Mapping Technology, p. 725-742, 29.
ang, K.I et al. Fo the quasi-igoous method, two conditions ae tested: 1) using only ovelapping stip pais and 2) using ovelapping stip pais togethe with a contol suface, which consists of 9 points obseved by PS suveying ove the aipot unway. Table 9 shows the biases estimated by the quasi-igoous method using only ovelapping stip pais; Table 1 epots the esult using the ovelapping stip pais and the contol suface. The significant diffeence between the two tests is obseved in the estimates of ρ and S. Such a diffeence is due to the coelation between these two paametes, which can be de-coupled using contol data. Figue 5 - Illustation of the 8 stip configuation of the eal dataset 739 Flightline 8 Flightline 7 Flightline 5 Flightline 6 Flight lines 1,2,3 and 4 Table 6-7 ovelapping stip pais consideed fo the eal dataset calibation Ovelapping pais Ovelap atio Diection (i) Stips 1&2 1% Opposite diections (ii) Stips 3&4 1% Opposite diections (iii) Stips 3&5 5% Same diection (vi) Stips 1&6 7% Opposite diections (v) Stips 5&7 5% Opposite diections (vi) Stips 7&8 4% Opposite diections (vii) Stips 2&6 7% Same diection ol. Ciênc. eod., v. 15, n. 5 Special Issue on Mobile Mapping Technology, p. 725-742, 29.
74 Lida system calibation using ovelapping stips Table 7 - Estimated 3D tansfomation paametes fo 7 ovelapping stip pais w..t. the local gound coodinate system Stips T (m) YT (m) ZT (m) ω (sec) φ (sec) κ (sec) 1&2 -.25 1.27 -.1 1.54 1.34 67.68 3&4 -.1.52.2-2.59-9.72 2.52 3&5 -.32 -.19 -.6 7.2 96.48 6.48 2&6 -.42.15.1-4.65 74.61-136.1 1&6 -.67 1.51 -.6 4.68 91.8 71.64 5&7 -.13.55.4.68 12.96-5.4 7&8.48.82.6 1.62-166.32-2.84 Table 8 - iases in the system paametes estimated by the simplified method using the tansfomation paametes epoted in Table 7 (m) Y (m) ω (sec) φ (sec) κ (sec) ρ (m) S -.11 -.1 86. -16. 41..28.67 Table 9 - iases in the system paametes estimated by the quasi-igoous method using only ovelapping stip pais (m) Y (m) ω (sec) φ (sec) κ (sec) ρ (m) S -.5 -.9 84.3-1.2 32.5 -.9.13 Table 1 - iases in the system paametes estimated by the quasi-igoous method using ovelapping stip pais and the contol suface (m) Y (m) ω (sec) φ (sec) κ (sec) ρ (m) S -.4 -.3 67.7 -.87 33.67 -.6.99 4. CONCLUSIONS ND RECOMMENDTIONS FOR FUTURE WORK In this pape, new appoaches fo the estimation of biases in LiDR system paametes wee intoduced: the simplified method using ovelapping stips and the quasi-igoous method using time-tagged point coodinates of ovelapping stips and tajectoy position data. The simplified method equies paallel ovelapping LiDR stips acquied by fied wing platfom ove an aea with modeate elevation change compaed to the flying height. It utilizes only the LiDR point cloud and the system biases ae estimated using the detected discepancies between ovelapping LiDR stips. The quasi-igoous method can deal with non-paallel stips and can handle tajectoy heading vaiations and hilly teain since it makes use of time-tagged point cloud and tajectoy position data. ol. Ciênc. eod., v. 15, n. 5 Special Issue on Mobile Mapping Technology, p. 725-742, 29.
ang, K.I et al. The pefomance of the developed calibation pocedues has been veified using simulated and eal datasets. It has been established that the simplified calibation method is not sensitive to easonable deviations fom the pesented assumptions. The quasi-igoous method, on the othe hand, shows a good pefomance egadless of deviations fom paallelism in the flight lines. The esults using eal data have illustated the feasibility of the poposed calibation pocedues in opeational envionments. s a futue wok, we will impove the quasi-igoous method by consideing possible pitch and oll vaiations in the flight tajectoy. In addition, the possibility of eliminating the need fo the time-tagged tajectoy data will be investigated. 741 CKNOWLEDEMENT This wok was suppoted by the Canadian EOIDE NCE Netwok (SII-72) and the National Science and Engineeing Council of Canada (Discovey ant). The authos would like to thanks LCTEC, UFPR, azil fo poviding the eal datasets. REFERENCES Mclone, J.C. Manual of Photogammety, 5th Edition, meican Society fo Photogammety and Remote Sensing, pp. 994-995, 24. ckemann, F. ibone Lase Scanning - Pesent Status and Futue Epectations, ISPRS Jounal of Photogammety & Remote Sensing, v. 54, n. 2-3, p. 64-67, 1999. altsavias, E.P. ibone Lase Scanning - asic Relations and Fomulas, ISPRS Jounal of Photogammety & Remote Sensing, v. 54, n. 2-3 p. 199-214, 1999. ang, K.I. et al. Integation of Teestial and ibone LiDR Data fo System Calibation. The Intenational chives of the Photogammety, Remote Sensing and Spatial Infomation Sciences, W I/2, 3-11 July, eijing, China, p. 391-398, 28. eta F. et al. Solving the Stip djustment Poblem of 3D ibone Lida Data, Poceedings of the IEEE IRSS 4, nchoage, US, 2-24 Sep., 24. [CDROM] hanma, M. Integation of Photogammety and LIDR, Ph.D. Dissetation, Depatment of eomatics Engineeing, the Univetisy of Calgay, Calgay, Canada, 26. Habib, F.. et al. utomatic Suface Matching fo the Registation of LiDR Data and MR Imagey, ETRI Jounal, v. 28, n. 2, p. 162-174, 26. Habib, F. et al. LiDR system Self-calibation Using Plana Patches fom Photogammetic Data, The 5th Inetnational Symposium on Mobile Mapping Technology, Padua, Italy, 28-31 May, 27. [CDROM] ol. Ciênc. eod., v. 15, n. 5 Special Issue on Mobile Mapping Technology, p. 725-742, 29.
742 Lida system calibation using ovelapping stips Lee, J. et al. djustment of Discepancies between LiDR Data Stips Using Linea Featues, IEEE eoscience and Remote Sensing Lette, v. 4, n. 3, p. 475-479, 27. Moin, K.W. Calibation of ibone Lase Scannes, M.S. Dissetation, Depatment of eomatics Engineeing, the Univetisy of Calgay, Calgay, Canada, 2. Postolov, Y. et al. Registation of ibone Lase Data to Suface eneated y Photogammetic Means, Intenational chieve of Photogammety and Remote Sensing, 32(3W13): p. 95-99, 1999. Schenk, T.Modeling and nalyzing Systematic Eos in ibone Lase Scannes, Technical Notes in Photogammety. The Ohio State Univesity, v. 19, 21. Skaloud, J.; Lichti, D. Rigoous ppoach to oesight Self-calibation in ibone Lase Scanning, ISPRS Jounal of Photogammety & Remote Sensing, v. 61, n. 6, p. 47-59, 26. Vaughn, C. R. et al. eoefeencing of ibone Lase ltimete Measuements, Intenational Jounal of Remote Sensing, v. 17, n. 11, p. 2185-22, 1996. Weh,.; Loh, U. ibone Lase Scanning - an Intoduction and Oveview, ISPRS Jounal of Photogammety & Remote Sensing, v. 54, n. 2-3, p. 68-82, 1999. ol. Ciênc. eod., v. 15, n. 5 Special Issue on Mobile Mapping Technology, p. 725-742, 29.