# Triangulation: Estimate a location using lat/long coordinates and bearings

I would like to get an estimated location using lat/long coordinates and bearings at each of those coordinates using R.

In this case I would be approximating the location of a turkey nest that I have marked using radio telemetry by taking 5-8 bearings around the nesting hen so that the nest can be found after the hen has completed the incubation period and left.

Here is an example of what this might look like when plotted in google earth (northern most point not visible):

Full list of coordinates and bearings for the above example:

``````   Coord.(UTMs)......Bearing.(Aizmuth).
``````

1....473789, 4485636.......26

2....473755, 4485659.......50

3....473728, 4485717.......80

4....473730, 4485788.......134

5....473848, 4485866.......196

6....473926, 4485796.......236

7....473925, 4485702.......291

8....473850, 4485660.......326

• Those coordinates are not lat/long but projected, metrical UTM coordinates. This means that you could use any common mathematical triangulation methods you find without caring for geodetic specialities. But since you have more than 3 measurements, you will need to fit them, maybe via Least Squares Regression. Nov 1, 2016 at 21:36
• You may want to have a look at the `sigloc` package. Nov 1, 2016 at 22:02

Here's one (probably very naive) way of doing it using the `sigloc` package.

Once the `sigloc` package is installed the following should work

``````library("sigloc")

df <- data.frame(
Date = '1/11/2016',
Observers = 'MickyT',
GID = 1,
Time = c(1,2,3,4,5,6,7,8),
Easting = c(473789,473755,473728,473730,473848,473926,473925,473850),
Northing = c(4485636,4485659,4485717,4485788,4485866,4485796,4485702,4485660),
Azimuth = c(26,50,80,124,196,236,291,326)
)

``````         X       Y BadPoint Var_X Var_Y Cov_XY AngleDiff Date Time
• This is great and just what I was looking for. The only thing I might add is a line with `nest_location <- data.frame(x=mean(turkeynest\$X),y=mean(turkeynest\$Y))` since the coordinates themselves is also part of what I was going for. Nov 3, 2016 at 3:33