Determine target point coordinates from distances to known points

Usage

multilaterate(
  distances,
  ref_points,
  crs = NULL,
  ellipse_conf = 0.95,
  plot = TRUE,
  ...
)

Arguments

distances: A named vector containing the distances from at least 3 ref_points to the target point.
ref_points: An sf object containing the reference point geometry and a 'Name' column.
crs: A projected coordinate reference system to use in the distance calculations if ref_points does not already have a projected CRS.
ellipse_conf: The confidence level for the uncertainty ellipse (0, 1).
plot: Logical, whether to plot the multilateration solution.
...: Additional options passed to sf::plot()

Value

A list, with xy coordinates in coords, measures of coordinate and positional uncertainty in se, and the mean ellipsoidal height of the reference points in mean_ellipsoid_height.

Details

This function performs 2D multilateration via optimization. The optimization will fail or give nonsensical results if the units of distances and crs are not identical. It is strongly recommended to use a projected coordinate system. The standard errors for the x coordinate, y coordinate, and xy positional uncertainty are calculated from the Hessian of the objective function.

Examples

d <- c(A = 10.1, B = 7.7, C = 8.0, D = 13.8)
ref <- sf::st_as_sf(data.frame(
 Name = c("A", "B", "C", "D"),
 x = c(0, 10, 0, 18),
  y = c(0, 0, 10, 18)
), coords = c("x", "y"), crs = 32613)
multilaterate(distances = d, ref_points = ref, ellipse_conf = 0.95)

#> $coords
#>        x        y 
#> 7.753330 7.532022 
#> 
#> $se
#>      se_x      se_y     se_xy 
#> 0.5623134 0.5609161 0.7942438 
#>