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

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