Calibration of a Terrestrial Laser Scanner - Institute of Geodesy and ...

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122 6. Applications of Terrestrial Laser Scanning6.3.2 Kinematic Model: Regression LineThe velocity of the test trolley is estimated with a mathematical model of the regression line, cf. Section5.3.3. Since the test tunnel can be sufficiently approximated by a straight line and since the tracking totalstation is set up in extension from this line, cf. Section 3.1.1 and Section 5.1, the reference frame is orientedso that the trolley moves along the x- axis whereas the y- and z- componentsare set to zero. The azimuthalorientation is defined by surveying a control point with an azimuth that is given with respect to the globalreference frame of the test tunnel.Before calculating the regression line, the data acquired by the total station have to be pre-processed. First,the spherical coordinates in terms of the angulardirections hz and v and the distance s arefiltered byapplying a median filter with a window size of five. The distance data mayeliminated beforehand. Second, the sphericalshow blunders that have to becoordinates are transformed to Cartesian coordinates withxayaza= s cos(v) cos(hz)= s cos(v) sin(hz) (6-1)= s sin(v)According to Equation (5.1), the moving trolley is defined by the vector xa with respectto the absolutecoordinate system. The rotation matrix R for a possible rotation of the local coordinate system defined bythe moving trolley can be replaced by the identity matrix due to the experimental setup,local coordinates acquired by the laser scanner are described bycf. Section 5.1. Thexi= 0yi=ys (6.2)Zl=zswhereas ys and zs are the coordinates supported bythe laser scanner. Due to the orientation of the verticalprofiles normal to the moving direction, the coordinates in the x- direction are set to zero and are onlydefined by the tracking total station. Based on the internal time tag given by the rotation time T, cf. Section5.2, each point measured by the laser scanner has a relative time reference. Knowing the absolute timetag for the first point of the first vertical profile, the absolute time tags for all other points of the followingvertical profiles can be derived, cf. Section 5.4. Thus, all laser points are time-referenced and the absoluteposition and orientation are determined by a mathematical model for the motion of the trolley.model introduced is defined by the following parameters:The motion• v y= v z= const = 0• vx = constThe velocity along the x- axis is assumed to be constant and is computed by applying the regressionline onthe data of the x- components. Since the motion of the trolley is not changed during the data set, additionalblunders can be identified within the adjustment algorithm usingnormalized residuals or a distance offset.The missing coordinates in the x- direction of the points acquired by the laser scanner can be obtained byusing the regression line. Since the time tag of each laser point as well as the motion of the trolley areknown, the position vectors p of the interpolated points are obtained by
6.3 Kinematic Application: Test Tunnel 123Px=xa + xi + AtvxPy=Va+Vl+At-Vy (6.3)Pz=Za+Zi+At-VzAt = 3-—5—(6.4)^^profilewhereas the time interval At isdefined by the rotation time T, the number of points within each verticalprofile nrprofile (depending on the scanning mode) and the current point number j of the whole point cloud.Table 6.1:Characteristics of one total station data set.tracking time [s] : 410number of measurements : 3278measured velocity [m/s] : 0.100216standard deviation of velocity [m/s] : 0.000001Several data series varying in length, rotation time and scan resolution were acquired and processed. Forexample, the calculation of one regression line is presented. The characteristics of the data set are givenin Table 6.1. The residuals to the regression line are shown in Figure 6.14. It can be seen that the velocityisestimated within high accuracy and the residuals do not to exceed ±5 mm. Therefore, blunders wereeliminated within the adjustment algorithm.'1°4oO 4450 4500 4550 4600 4650 4700 4750time tag [s]Figure 6.14: Residuals of total station data to regression line.The quality of the mathematical model is verified by comparingthe coordinates of the calculated centerpoints of the control points, i.e. spheres, with their nominal values. Therefore, the center pointscan bederived using the 'free' adjustment and the 'fix' adjustment, cf. Section 3.1.5. The results of a completedata set for the velocity v = 0.1 are given in Table 6.2. The 3D accuracyis about 3 mm for the centerpoints derived by the 'free' adjustment. In addition, the use of the well-known diameter of the spheresincreases the 3D accuracy to 2 mm. The data sets differ in the rotation time, length,scan resolution andnumber of control points.The table shows that neither the rotation time nor the scan resolution influencedthe accuracy significantly. Only treatment of the diameter of the spheres increased the accuracy. Changingthe velocity 0.3m,=to v 0.2 and = v the results are similar to the results shown in Table 6.2.6.3.3 Kinematic Model: Kaiman FilterThe system state of the moving test trolley along the track line is estimated bya Kaiman filter. The to¬tal station data defining the absolute reference frame are pre-processed in two steps.First, blunders are
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DISS. ETH NO. 17036Calibration of a
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ZusammenfassungSeit einigen Jahren
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ContentsAbstractiiiZusammenfassungv
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Contentsix6.1.3 Results Ill6.2 Stat
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1Introduction1.1 Terrestrial Laser
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1.2 Motivation 3Precision [m10~1 "1
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6 1. Introduction
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8 2. Components of Terrestrial Lase
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10 2. Components of Terrestrial Las
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24 3. Calibration of Terrestrial La
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'28 3. Calibration of Terrestrial L
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"[m] of system 90%) 3540 distance b
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!36 3. Calibration of Terrestrial L
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138 3. Calibration of Terrestrial L
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Inormal axis,intersectionpoint axis
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j/-*'.-,•66 3. Calibration of Ter
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Page 84 and 85: 74 4. Static Laser Scanning4.1.2 Mi
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Page 122 and 123: 112 6. Applications of Terrestrial
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Page 142 and 143: 132 7. Summaryrange, achievable by
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Page 146 and 147: 136 A. Imaging System of Imager 500
Page 148 and 149: 138 B. Technical Data of Imager 500
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Page 152 and 153: 142 C. Adjustment of Sphere
Page 154 and 155: 144 D. Electronic Circuit for Deter
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Page 158 and 159: Accuracy-AeinTPS1200 AG, -Version 1
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Page 162 and 163: 152 BibliographyWunderlich, T. A. [
Page 164 and 165: List of Figures3.22 Residuals of th
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