As I didn't find the existing answers to this problem on StackExchange to be satisfying, I will add my own solution here. This uses geosphere package to calculate distance between two polar (latitude, longitude) coordinates.
For a data frame:
> head(coordinates)
lat lng distance
21 51.73832 10.72805 6
31 51.76656 10.85404 6
64 51.67559 10.82135 5
70 51.75592 10.85369 5
80 51.70379 10.79743 2
89 51.68976 10.88211 6
use
n <- nls( distance ~ distm(data.frame(lng, lat), c(lng_solution, lat_solution), fun=distHaversine),
data = coordinates, start=list( lng_solution=10.9278778, lat_solution=51.6675738 ) )
Substitute the coordinates in the last line with your start-point estimate.
(Note that the geosphere package uses the uncommon convention of writing longitude before latitude.)
You can use the following code to plot the confidence ellipse:
c <- confidenceEllipse(n, levels=0.95)
ellipse_line <- c[1, ]
ellipse_line <- rbind(ellipse_line, coef(n))
lines(ellipse_line)
text(x = mean(ellipse_line[, 1]), y = mean(ellipse_line[, 2]),
labels=format(distm(ellipse_line[1,], ellipse_line[2,]), nsmall=1))
[![enter image description here][1]][1] [1]: https://i.sstatic.net/VhzZW.png