The position of B (typically body) relative to E (typically Earth) is given as cartesian position vector p_EB_E, in meters ("ECEF-vector").

## Arguments

- p_EB_E
Cartesian position vector from E to B, decomposed in E (3x1 vector) (m)

- a
Semi-major axis of the Earth ellipsoid (m, default [WGS-84] 6378137)

- f
Flattening of the Earth ellipsoid (no unit, default [WGS-84] 1/298.257223563)

## Value

n-vector representation of position B, decomposed in E (3x1 vector) (no unit) and depth of system B relative to the ellipsoid (z_EB = -height)

## Details

The function converts to n-vector, n_EB_E and its depth, z_EB.

The calculation is exact, taking the ellipticity of the Earth into account. It is also nonsingular as both n-vector and p-vector are nonsingular (except for the center of the Earth). The default ellipsoid model used is WGS-84, but other ellipsoids (or spheres) might be specified.

## References

Kenneth Gade A Nonsingular Horizontal Position Representation.
*The Journal of Navigation*, Volume 63, Issue 03, pp 395-417, July 2010.

## Examples

```
p_EB_E <- 6371e3 * c(0.9, -1, 1.1)
(n_EB_E <- p_EB_E2n_EB_E(p_EB_E))
#> $n_EB_E
#> [1] 0.5170890 -0.5745433 0.6344439
#>
#> $z_EB
#> [1] -4702060
#>
```