How To...

Triangulation

  • Triangulation refers to the process of determining the location of a point by forming triangles to it from known points, using only angle measurements.
  • Trilateration (True Range Multilateration) is a method of determining the location of a point using multiple known distance measurements from known points.
  • Triangulateration involves the use of both angle and distance measurements to determine the location of a point.
  • Apply the following techniques to find the location of unknown points using only a Garmin GPSr and a creative interpretation of the above methods.

    1. Intersection by Bearing
    2. Intersection by Distance
    3. Intersection of Circle
    4. Midpoint
    5. Equilateral Triangle
 


 


1. Intersection by Bearing


1.1. Find the point of intersection between two bearings from two points


1.1.1. Find the coordinates for a distant landmark within visual range

Landmark (X) in visual range Save current location
as Waypoint (B)		 Project a waypoint beyond
Landmark (X)		 Save Waypoint (A)
       
Move to a new location
and save Waypoint (C)		 Project a waypoint beyond
Landmark (X)		 Save Waypoint (D) Create new route on GPSr...
       
...from Waypoint (A) to (B)... ...add Waypoint (B) to (C)... ...finish Waypoint (C) to (D) Mark Waypoint (X) at
route intersection

 

1.1.2. Find the coordinates for an unknown waypoint where two locations and bearings are known

Move to first location
and save as Waypoint (B)		 Project a waypoint at
specified Bearing		 Save Waypoint (A) Move to second location...
       
Save second location
as waypoint (C)		 Project a waypoint at
specified Bearing		 Save Waypoint (D) Create new route on GPSr...
       
...from Waypoint (A) to (B)... ...add Waypoint (B) to (C)... ...finish Waypoint (C) to (D) Mark Waypoint (X) at
route intersection

 

1.2. Find the point of intersection between two bearings to two points

  • Modify each bearing between 001° and 180° by adding 180°
  • Modify each bearing between 181° and 360° by subtracting 180°

Move to first location
and save as Waypoint (B)		 Project a waypoint at
specified Bearing		 Save Waypoint (A) Move to second location...
       
Save second location
as waypoint (C)		 Project a waypoint at
specified Bearing		 Save Waypoint (D) Create new route on GPSr...
       
...from Waypoint (A) to (B)... ...add Waypoint (B) to (C)... ...finish Waypoint (C) to (D) Mark Waypoint (X) at
route intersection

 

 

 


2. Intersection by Distance


2.1. Find the point of intersection between multiple points with known distances

  • Find the coordinates for an unknown waypoint where two locations and distances are known (Bilateration)
  • Find the coordinates for an unknown waypoint where three locations and distances are known (Trilateration)

Two known locations,
points (A) and (B)		 Create Proximity Alert at
specified distance for point (A)		 Create Proximity Alert at
specified distance for point (B)		 Two solutions exist where
Proximity (A) and (B) intersect
       
Three known locations,
points (A), (B) and (C)		 Two solutions exist where
Proximity (A) and (B) intersect		 Create Proximity Alert at
specified distance for point (C)		 Mark Waypoint (X) where
Proximity (A)(B)(C) intersect

 

 

 


3. Intersection of Circle


3.1. Find the points of intersection on a circle with a line by bearing

Save 'Circle' location
as Waypoint (A)		 Move to 'Bearing' location
and save as Waypoint (B)		 Create Proximity Alert at
specified distance for point (A)		 Project a waypoint at
specified Bearing
       
Save Waypoint (C) Create new route on GPSr... ...from Waypoint (B) to (C) Two solutions exist where
(B)(C) intersects (A)

 

 

 


4. Midpoint


4.1. Find the midpoint between two known points

Two known locations,
points (A) and (B)		 Create new route on GPSr
from waypoint (A) to (B)		 Create Proximity Alert (A) at
½ distance of Route (A)(B)		 Create Proximity Alert (B)
equal to Proximity Alert (A)
       
Adjust both Proximity Alerts
in equal increments if they
do not overlap precisely		 Proximity Alerts (A) and (B)
exhibit correct overlap		 Mark location where
Proximity Alerts (A) and (B)
 intersect Route (A)(B)		 Saved Waypoint (X) is
(A)(B) midpoint

 

4.2. Find the midpoint between three known points

Three known locations,
points (A), (B) and (C)		 Create new route on GPSr
from waypoint (A) to (B)
and record route distance		 Create new route on GPSr
from waypoint (B) to (C)
and record route distance		 Create new route on GPSr
from waypoint (C) to (A)
 and record route distance
       
Solution will be between
longest route (A)(B) and
shortest route (C)(A)		 Create Proximity Alert for
any point using a value
between (A)(B) and (C)(A)		 Create Proximity Alerts for
remaining points using
the same value		 If Proximity Alerts do not
all overlap, increase the
value and repeat process
       
Create a Proximity Alert for
any point using new value		 Create Proximity Alerts for
remaining points using
the same value		 If all Proximity Alerts overlap
but do not intersect at same
point, reduce value and repeat		 Create a Proximity Alert for
any point using new value
       
Create Proximity Alerts for
remaining points using
the same value		 Mark Waypoint (X)
where all Proximity Alerts
intersect at same point		 Saved Waypoint (X) is
(A)(B)(C) midpoint		 Create Proximity Alert (X)
using final (A)(B)(C) value
to verify solution

 

 

 


5. Equilateral Triangle


5.1. Find coordinates to form an equilateral triangle from two known points

Two known locations,
points (A) and (B)		 Create new route on GPSr
from waypoint (A) to (B)		 Find total distance
for Route (A)(B)		 Create Proximity Alert (A)
using distance (A)(B)
       
Adjust Proximity Alert (A)
distance as required for precise
intersection with point (B)		 Create Proximity Alert (B)
equal to Proximity Alert (A)		 Mark Waypoints (X) and (Y)
where Proximity Alerts
(A) and (B) intersect		 (A)(X)(B) and (A)(Y)(B)
form Equilateral Triangles