Three dimensional adjustments in a local reference system

Abstract. This paper attempts to quantify geometric considerations in observations and observe trends in solutions to free network solutions. The method of investigation will be utilizing 2D observations to determine how each measurement affects the overall solution and the location of the observations relative to the other nodes. A local reference system will be determined using the Gauss-Markov model with constraints by fixing the largest range observation to the y-axis to give a relative orientation. Further solutions will be calculated by fixing additional points to generate multiple least squares solutions relative to the local reference system. The resulting final points will be modeled using the Gauss-mixture model and compared to a simulated dataset generated by adding random error to the observations. Different weight matrices will be tested to demonstrate the effect on the overall solution. These methods were chosen because of prior experimentation by different research groups studying geometric considerations for UAS and ground surveying conditions. The major contribution will be the trends observed in the modeling and the correlation of the fixed local solutions to the geometry of the points.

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A Practical Procedure to Integrate the First 1:500 Urban Map of Valencia into a Tile-Based Geospatial Information System

ISPRS International Journal of Geo-Information ◽

10.3390/ijgi8090378 ◽

2019 ◽

Vol 8 (9) ◽

pp. 378 ◽

Cited By ~ 1

Author(s):

Villar-Cano ◽

Jiménez-Martínez ◽

Marqués-Mateu

Keyword(s):

Reference System ◽

Geospatial Information ◽

Practical Procedure ◽

Second Stage ◽

Local Reference System ◽

Local Reference ◽

Terrestrial Reference System ◽

Three Stages ◽

The City ◽

Early Maps

The use of geographic data from early maps is a common approach to understanding urban geography as well as to study the evolution of cities over time. The specific goal of this paper is to provide a means for the integration of the first 1:500 urban map of the city of València (Spain) on a tile-based geospatial system. We developed a workflow consisting of three stages: the digitization of the original 421 map sheets, the transformation to the European Terrestrial Reference System of 1989 (ETRS89), and the conversion to a tile-based file format, where the second stage is clearly the most mathematically involved. The second stage actually consists of two steps, one transformation from the pixel reference system to the 1929 local reference system followed by a second transformation from the 1929 local to the ETRS89 system. The last stage comprises a map reprojection to adapt to tile-based geospatial standards. The paper describes a pilot study of one map sheet and results showed that the affine and bilinear transformations performed well in both transformations with average residuals under 6 and 3 cm respectively. The online viewer developed in this study shows that the derived tile-based map conforms to common standards and lines up well with other raster and vector datasets.

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Accounting for the effects of global tectonic processes on the precise positioning in the state reference system or local reference system with the help of GPS NAVSTAR

Geodesy and Cartography ◽

10.22389/0016-7126-2014-888-6-2-7 ◽

2014 ◽

Vol 888 (6) ◽

pp. 2-7

Author(s):

A.V. Voytenko ◽

◽

V.L. Bykov ◽

Keyword(s):

Reference System ◽

The State ◽

Precise Positioning ◽

Tectonic Processes ◽

Local Reference System ◽

Local Reference ◽

State Reference

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Arbitrary-order intrinsic virtual element method for elliptic equations on surfaces

CALCOLO ◽

10.1007/s10092-021-00418-5 ◽

2021 ◽

Vol 58 (3) ◽

Author(s):

Elena Bachini ◽

Gianmarco Manzini ◽

Mario Putti

Keyword(s):

Arbitrary Order ◽

Surface Geometry ◽

Virtual Element Method ◽

Anisotropic Character ◽

Local Reference System ◽

Local Reference ◽

Local Parametrization ◽

Manufactured Solution ◽

Virtual Element ◽

Element Method

AbstractWe develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in covariant form using an appropriate local reference system. The knowledge of the local parametrization allows us to consider the two-dimensional VEM scheme, without any explicit approximation of the surface geometry. The theoretical properties of the classical VEM are extended to our framework by taking into consideration the highly anisotropic character of the final discretization. These properties are extensively tested on triangular and polygonal meshes using a manufactured solution. The limitations of the scheme are verified as functions of the regularity of the surface and its approximation.

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IMAGE-BASED ORIENTATION DETERMINATION OF MOBILE SENSOR PLATFORMS

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences ◽

10.5194/isprs-archives-xliii-b1-2021-215-2021 ◽

2021 ◽

Vol XLIII-B1-2021 ◽

pp. 215-220

Author(s):

O. Hasler ◽

S. Nebiker

Keyword(s):

Sensor Fusion ◽

Pose Estimation ◽

Reference System ◽

Laser Scanner ◽

Relative Orientation ◽

Robotic Platform ◽

Sensor Platforms ◽

Local Reference ◽

The Absolute ◽

Additional Approach

Abstract. Estimating the pose of a mobile robotic platform is a challenging task, especially when the pose needs to be estimated in a global or local reference frame and when the estimation has to be performed while the platform is moving. While the position of a platform can be measured directly via modern tachymetry or with the help of a global positioning service GNSS, the absolute platform orientation is harder to derive. Most often, only the relative orientation is estimated with the help of a sensor mounted on the robotic platform such as an IMU, with one or multiple cameras, with a laser scanner or with a combination of any of those. Then, a sensor fusion of the relative orientation and the absolute position is performed. In this work, an additional approach is presented: first, an image-based relative pose estimation with frames from a panoramic camera using a state-of-the-art visual odometry implementation is performed. Secondly, the position of the platform in a reference system is estimated using motorized tachymetry. Lastly, the absolute orientation is calculated using a visual marker, which is placed in the space, where the robotic platform is moving. The marker can be detected in the camera frame and since the position of this marker is known in the reference system, the absolute pose can be estimated. To improve the absolute pose estimation, a sensor fusion is conducted. Results with a Lego model train as a mobile platform show, that the trajectory of the absolute pose calculated independently with four different markers have a deviation < 0.66 degrees 50% of the time and that the average difference is < 1.17 degrees. The implementation is based on the popular Robotic Operating System ROS.

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