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Ram Chand
August 23, 2021

Trilateration is a surveying method used to determine the horizontal positions, in addition to other methods like triangulation, intersection, resection and satellite positioning. Trilateration is a method that work with distances and is the major working principle followed in Global Positioning System (GPS) Surveying.

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Trilateration employs electronic distance measuring instruments (EDMs) to measure the lengths of the triangle sides rather than horizontal angles in triangulation. Trilateration consist of series of joined or overlapped triangles that forms polygons or quadrilaterals, with a supplemental horizontal angle observation to provide azimuth control or check the angles.

Trilateration has become more practical with the development of EDMIs, as it is highly accurate and precise for expanding and establishing horizontal control.

- Trilateration measures distance and not angles unlike triangulation method. Initially, the area to measured is turned into triangles and the length of all the sides of the triangles are measured. It can also be polygons, or quadrilateral or any combination of them. The distances are measured using an electronic instrument or a suitable instrument.
- The angles of the triangles and the coordinates of their vertices are determined using trigonometric computations. Sine rule and cosine rule are used to determine the angles.
- This means, the method, does not involves measurement of angles.
- In order to check the accuracy of determined angles from the trigonometric observations, horizontal angles are sometimes measured.
- Once the angles of the triangles are computed, the trilateration is adjusted and the coordinates of the stations are determined.
- When trilateration is used for navigation, astronomy, engineering or mapping, azimuths are also determined. Azimuth is an angular measurement in a spherical coordinated system, that is measured in degrees. Watch Explained v

Trilateration is an alternative to triangulation that rely only on distance measurement. EDMs make trilateration a cost-effective positioning technique for control surveys.

1. If a point A exists, another point B is established using open traverse. Using a total station with EDM device, the distance AB is measured and its azimuth ( Î±) is determined. This like AB becomes the **baseline** for trilateration purpose.

This is performed by placing the total station on A by an operator and a reflector on B. Based on the requirements of control survey, the accuracy of the calculated position B may be conformed by the astronomical observation.

2. The distance AC and BC is measured using total station. Both forward and backward measurements are taken. After the measurements, the slope distances are converted into horizontal distances.

After this, cosine rule is used to determine the interior angles of the triangle, and the coordinates of C can be fixed.

3. The accuracy of the fixed coordinated is checked by plotting triangle ABC nd evaluating the error of closure.

4. Next, the trilateration network is extended to measure the distance CD and BD, and then fix the coordinates of location D. (Fig.3) Watch Explained Video

- In areas that is subjected to seismic activity, trilateration is employed to study the gradual and secular movement in earth's crust. This study helps to construction high-precision engineering projects with defense and scientific facilities.
- Trilateration is also used in control expansion or densification for future metropolitan growth; coastline control; inland waterways; control extension; densification for land subdivisions and construction; and deformation surveys of dams, geothermal areas, structures, regional/local tectonics, and landslides.
- Used for simple low-order topographic survey
- Used for global positioning surveying systems
- Used to extend topographic mapping control from small local tracts to regional areas
- Accuracy increase with the use of EDMs making it suitable for special-purpose precise surveys.

- Achieve rapid control expansion with utmost accuracy
- Earns good cost-benefit ratio and potential
- Less expensive compared to triangulation
- Accurate for most conditions
- Permits control over large and small geographical areas with minimum number of personnel.
- Provide necessary scale control that is lacking in triangulation
- Proper execution make it superior than triangulation and traversing method

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- Ram Chand
- Hi, I am Ram Chand. I am a structural engineering professional. Prodyogi is a blog started to share knowledge on civil engineering for constructors around the world. Each article in Prodyogi is explained precisely to make it simple for everyone to understand. Kindly support Prodyogi and Join the community so that we can learn together.

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