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A Direct Georeferencing Method for Terrestrial Laser Scanning Using GNSS Data and the Vertical Deflection from Global Earth Gravity Models

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A Direct Georeferencing Method for Terrestrial Laser Scanning Using GNSS Data and the Vertical Deflection from Global Earth Gravity Models sensors Article A Direct Georeferencing Method for Terrestrial Laser Scanning Using GNSS Data and the Vertical Deflection from Global Earth Gravity Models Edward Osada , Krzysztof So´snica , Andrzej Borkowski *, Magdalena Owczarek-Wesołowska and Anna Gromczak Institute of Geodesy and Geoinformatics, Wrocław University of Environmental and Life Sciences, ul, Grunwaldzka 53, 50-357 Wrocław, Poland; [email protected] (E.O.); [email protected] (K.S.); [email protected] (M.O.-W.); [email protected] (A.G.) * Correspondence: [email protected]; Tel.: +48-71-230-5609 Received: 8 May 2017; Accepted: 21 June 2017; Published: 24 June 2017 Abstract: Terrestrial laser scanning is an efficient technique in providing highly accurate point clouds for various geoscience applications. The point clouds have to be transformed to a well-defined reference frame, such as the global Geodetic Reference System 1980. The transformation to the geocentric coordinate frame is based on estimating seven Helmert parameters using several GNSS (Global Navigation Satellite System) referencing points. This paper proposes a method for direct point cloud georeferencing that provides coordinates in the geocentric frame. The proposed method employs the vertical deflection from an external global Earth gravity model and thus demands a minimum number of GNSS measurements. The proposed method can be helpful when the number of georeferencing GNSS points is limited, for instance in city corridors. It needs only two georeferencing points. The validation of the method in a field test reveals that the differences between the classical georefencing and the proposed method amount at maximum to 7 mm with the standard deviation of 8 mm for all of three coordinate components. The proposed method may serve as an alternative for the laser scanning data georeferencing, especially when the number of GNSS points is insufficient for classical methods. Keywords: terrestrial laser scanning; georeferencing; reference frame transformation; GNSS positioning; spatial directional intersection; Earth gravity model; deflection of the vertical 1. Introduction Terrestrial laser scanning is one of the most efficient methods for providing the highly accurate and dense point clouds that can subsequently be used for measuring Earth surface processes [1], monitoring the deformations caused by natural hazards [2,3] or generating three-dimensional spatial models, e.g., [4–8]. The point clouds collected by a terrestrial laser scanner require georeferencing [9,10], i.e., the collected points have to be transformed to a reference frame that has a well-defined origin, orientation and scale. The reference ellipsoids of the Geodetic Reference System 1980 (GRS80) [11] or the World Geodetic System 1984 (WGS84) are commonly used as the geocentric coordinate frames for georeferencing of spatial data, because, e.g., the GPS coordinates are directly measured and estimated in WGS84. In terrestrial laser scanning, the point cloud is typically transformed into the geocentric coordinate frame using a 7-parameter Helmert transformation [6]. Three coordinate components of the laser scanner’s origin, the scale, and three orientation angles with respect to the geocentric reference frame are needed to perform such a transformation. The set of seven transformation parameters Sensors 2017, 17, 1489; doi:10.3390/s17071489 www.mdpi.com/journal/sensors Sensors 2017, 17, 1489 2 of 12 is determined using the least squares method on a basis of several georeferencing points whose coordinates are measured both by the laser scanner and a global navigation satellite system (GNSS) receiver. Alternatively, the optical head of a laser scanner may be equipped with several mounted GPS antennas [12–14]. Other methods of georeferencing of terrestrial scanner data comprise back-sighting, sensor-driven, and data-driven approaches [10,15] which also rely on control point targets. In some cases, for instance in city corridors, the availability of control points determined by GNSS can be limited due to deteriorated GNSS signal. Therefore, additional terrestrial measurements may be needed in order to ensure the sufficient number of control points in such situations. To avoid this possible additional effort, we propose a method for direct georeferencing of point clouds obtained using terrestrial laser scanning that allows for providing coordinates in the geocentric frame using a minimum number of GNSS measurements. In the proposed method, three coordinate components of the laser scanner’s measurement origin, two components describing the vertical deflection of the scanner’s rotational axis and one angle of the horizontal orientation of the scanner’s measurement reference frame provide a minimum set of parameters that are needed for georeferencing and are entirely sufficient for a transformation to the geocentric reference frame. To apply the proposed method, the scanner must be levelled. The transformation parameters are estimated using the least squares method on a basis of the geocentric coordinates of the laser scanner’s origin, the geocentric coordinates of one GNSS point and the components of the vertical deflection of the scanner’s rotational axis determined in the gravitational force field of the Earth Gravity Model 2008 (EGM2008) [16] which gives the components of axis deflection with respect to the reference ellipsoid GRS80. Furthermore, we show results from a field test that proves correctness of the results obtained using proposed method. The paper is structured as follows: First, we introduce laser scanner geocentric orientation parameters, then an adjustment procedure for determination of the orientation parameters is described. In the following section, a field test of the proposed method is provided. Finally the method is discussed in an extended context and conclusions are drawn. 2. Methods 2.1. The Laser Scanner Geocentric Orientation Parameters The external geocentric orientation parameters of the laser scanner’s measurement frame, assuming the equality of the scale in the both reference frames, reads as follows (see Figure1): • X0, Y0, Z0 geocentric GRS80 coordinates of the origin P of the laser scanner’s measurement frame (x, y, z), • S, x, h orientation angles of the measuring frame (x, y, z) with respect to the external reference frame (X, Y, Z). The x, h orientation angles constitute the components of the laser scanner vertical axis deflection with respect to the normal to the GRS80 reference ellipsoid (Figure1), which is caused by the inhomogeneity of the local gravity field due to the local mass distribution. The directional horizontal angle S is called the instrument horizontal orientation constant. The coordinates x, y, z of the point Q measured by a laser scanner can be obtained by (Figure1): 0 1 0 1 x s cos a sin b B C B C x = @ y A = @ s sin a sin b A (1) z s cos b + i − j where s—spatial distance, a—horizontal direction, b—vertical angle (corrected due to refraction), i—height of the laser scanner above ground point P, j—height of the reflector above measured point Q, j = 0 for the point clouds and j > 0 for the georeferencing points. The origin of the laser scanner coordinate system (x, y, z) is usually defined as a point of the electro-optical center of the scanner or a point of the intersection of the horizontal and vertical rotation axes of the scanner or a zero Sensors 2017, 17, 1489 3 of 12 Sensors 2017, 17, 1489 3 of 12 intersection of the horizontal and vertical rotation axes of the scanner or a zero distance measurement point of the scanner [17,18]. The connection of the computed vertical coordinate z scos j with the distance measurement point of the scanner [17,18]. The connection of the computed vertical coordinate z coordinate according to Formula (1) yields as follows: z z i (see Figure 1). z = s cos b − j with the z coordinate according to Formula (1) yields as follows: z = z + i (see Figure1). z – laser scanner rotation axis Z Q(X, Y, Z) plumb line EGM direction j North direction x s in the z – ellipsoid normal horizontal y (x, y) - plane i x y P(X0, Y0, Z0) The WGS84 Z0 reference φ Y ellipsoid λ X0 Y0 X Figure 1. Six parameters of the laser scanner geocentric orientation: X0, Y0, Z0, S, x, h. Figure 1. Six parameters of the laser scanner geocentric orientation: X0, Y0, Z0, Σ, ξ, η. The coordinates (x, y, z) of a particular point Q measured by a laser scanner are converted into the The coordinates (x, y, z) of a particular point Q measured by a laser scanner are converted into (X, Y, Z) external reference frame according to the formula (e.g., [19,20]): the (X, Y, Z) external reference frame according to the formula (e.g., [19,20]): 0 1 0 1 0 1 X X X0X x x 0 T B Y C = B Y0 C + (R(S) · Q(x, h, j) · P(j,Tl)) B y C (2) @ A Y@ Y0A RΣQ ,,P, y @ A (2) Z Z0 z Z Z0 z or equivalently: or equivalently: T X = X0 + (R(S) · Q(x, h, j) · P(j, l)) x (3) T X X0 RΣQ,,P, x (3) where: 0 1 where: − sin j cos l − sin j sin l cos j B C P(j, l) = @ − sin l cos l 0 A (4) sin cos sin sin cos cos j cos l cos j sin l sin j P, 0 sin cos 01 (4) 1 −h tan j −x cosB cos cos sin sinC Q(x, h, j) = @ h tan j 1 −h A (5) x1 tan h 1 0 1 Q ,, costanS sin1S 0 (5) R(S) = B − sin S cosS 0 C1 (6) @ A 0 0 1 cosΣ sinΣ 0 with j, l being the geodetic latitude and longitude of the laser scanner’s or total station’s reference RΣ sinΣ cosΣ 0 (6) frame origin P.
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