Trilateration in geodetic control

1. Trilateration Theory
   

• According to the definition, trilateration is the process of determining the position (coordinate) of a point by measure the distance only.
  
• To determine the position of point by using trilateration, there are 3 main factors which needed to ensure the coordinate of the unknown point can be known. The 3 main factors are:
  
  • The distance for every line.
    
  • The coordinate of a known point.
    
  • The azimuth of a line.
    
• By using the sine formula, the coordinate of the unknown point can calculated.
  
• For example:
  

 

 

    
 

 

 

Explanation:

1. By referring to the diagram above, point A is a known point which the coordinate is obtained by using GPS observation.
   
2. The distance from point A to point B, point A to point C and point B to point C are measured by using total station.
   
3. By making the solar observation for any line in the traverse, we can have the azimuth of the line.
   
4. For example, azimuth A to B is known and the distance of a and b are also known.
   
5. By using the cosine formula, we can calculate an angle of station A.
   
6. The cosine formula :
   

   a² = b² + c² – 2bc cos A
   

     A = cos^-1
(a² - b² - c² )

     -2bc    

1. When the angle A is known, then the bearing from A – C can be calculated.
   
2. Thus, the coordinate of point C can be determined by applying the latitude and departure.