Local tangent plane coordinates
Local tangent plane coordinates (LTP), also known as local ellipsoidal system, local geodetic coordinate system, or local vertical, local horizontal coordinates (LVLH), are a spatial reference system based on the tangent plane defined by the local vertical direction and the Earth's axis of rotation. It consists of three coordinates: one represents the position along the northern axis, one along the local eastern axis, and one represents the vertical position. Two right-handed variants exist: east, north, up (ENU) coordinates and north, east, down (NED) coordinates. They serve for representing state vectors that are commonly used  in aviation and marine cybernetics. Axes. These frames are location dependent. For movements around the globe, like air or sea navigation, the frames are defined as tangent to the lines of geographical coordinates: Local east, north, up (ENU) coordinates. In many targeting and tracking applications the local "East, North, Up" (ENU) Cartesian coordinate system is far more intuitive and practical than ECEF or Geodetic coordinates. The local ENU coordinates are formed from a plane tangent to the Earth's surface fixed to a specific location and hence it is sometimes known as a "Local Tangent" or "local geodetic" plane. By  convention the east axis is labeled formula_1, the north formula_2 and the up formula_3. Local north, east, down (NED) coordinates. In an airplane, most objects of interest are below the aircraft, so it is sensible to define down as a positive number. The "North, East, Down" (NED) coordinates allow this as an alternative to the ENU. By convention, the north axis is labeled formula_4, the east formula_5 and the down formula_6. To avoid confusion between formula_1 and formula_4, etc. in this article we will restrict the local coordinate frame to ENU. The origin of this coordinate system is usually chosen  to be a point on the surface of the geoid below the aircraft's center of gravity. However, care must be taken since, if the aircraft is accelerating (turning or accelerating linearly), then the NED coordinates are no longer inertial coordinates. NED coordinates are similar to ECEF in that they're Cartesian, however they can be more convenient due to the relatively small numbers involved, and also because of the intuitive axes. NED and ECEF coordinates can be related with the following formula: where formula_10 is a 3D position in a NED system, formula_11 is the corresponding ECEF position, formula_12  is the reference ECEF position (where the local tangent plane originates), and formula_13 is a rotation matrix whose columns are the north, east, and down axes. formula_13 may be defined conveniently from the latitude formula_15 and longitude formula_16 corresponding to formula_12: Note that this is actually a rotation matrix for the ENU local tangent plane. Refer to the link below for a more detailed method and explanation.