ECEF and Local frames

There are two functions that can be used to convert a vector between the Earth-Centered, Earth-Fixed (ECEF) reference frame and a local reference frame. Currently, only the NED local frame is supported. This frame is defined as follows at the observer position:

• The X axis points toward the North;
• The Y axis points toward the East; and
• The Z axis points downward.

Converting from ECEF to NED

We can convert a vector in ECEF to NED using the following function:

ecef_to_ned(r_ecef::AbstractVector, lat::Number, lon::Number, h::Number; translate::Bool = false) -> SVector{3}

where a vector r_ecef represented in the Earth-Centered, Earth-Fixed (ECEF) frame is converted to a vector represented in the local reference frame NED (North, East, Down) at the geodetic position lat [rad], lon [rad], and h [m].

If translate is false, this function computes only the rotation between ECEF and NED. Otherwise, it will also translate the vector considering the distance between the Earth's center and NED origin.

julia> r_ecef = [
            2.7189672586353812e6
           -3.608191420727525e6
           -4.487701255149731e6
       ];
julia> ecef_to_ned(r_ecef, -45 |> deg2rad, -53 |> deg2rad, 500; translate = true)3-element StaticArraysCore.SVector{3, Float64} with indices SOneTo(3):
  1.000000000073973
 -1.346480016848351e-10
 -6.608675073698631e-11
julia> ecef_to_ned(r_ecef, -45 |> deg2rad, -53 |> deg2rad, 500; translate = false)3-element StaticArraysCore.SVector{3, Float64} with indices SOneTo(3):
 21385.655604819105
    -2.4815366958196177e-10
    -6.3679536345163295e6

Converting from NED to ECEF

We can convert a vector in NED to ECEF using the following function:

ned_to_ecef(r_ned::AbstractVector, lat::Number, lon::Number, h::Number; translate::Bool = false) -> SVector{3}

where a vector r_ned represented in the local reference frame NED (North, East, Down) at the geodetic position lat [rad], lon [rad], and h [m] is converted to the Earth-Centered, Earth-Fixed (ECEF) frame.

If translate is false, then this function computes only the rotation between NED and ECEF. Otherwise, it will also translate the vector considering the distance between the Earth's center and NED origin.

julia> ned_to_ecef([1, 0, 0], -45 |> deg2rad, -53 |> deg2rad, 500; translate = true)3-element StaticArraysCore.SVector{3, Float64} with indices SOneTo(3):
  2.7189672586353812e6
 -3.608191420727525e6
 -4.487701255149731e6
julia> ned_to_ecef([1, 0, 0], -45 |> deg2rad, -53 |> deg2rad, 500; translate = false)3-element StaticArraysCore.SVector{3, Float64} with indices SOneTo(3):
  0.4255474838907525
 -0.5647205848508179
  0.7071067811865475