Posted on December 24, 2022 (Updated on July 22, 2025)

Position from LLA to NED and vice-versa

Hiking & Activities

Decoding Location: From GPS to Local Views (LLA to NED and Back)

Ever wondered how your phone knows exactly where you are, or how a drone manages to navigate so precisely? It’s all about coordinate systems – ways of pinpointing locations. Two of the big players are Latitude, Longitude, Altitude (LLA) and North, East, Down (NED). Think of LLA as your global address and NED as your neighborhood map. Knowing how to translate between them is key in fields like aerospace, surveying, and even robotics. So, let’s dive in and make sense of it all.

LLA vs. NED: Global Address vs. Local Map

  • LLA (Latitude, Longitude, Altitude): This is the familiar GPS setup. Latitude tells you how far north or south you are from the equator, longitude tells you how far east or west you are from the Prime Meridian, and altitude tells you how high you are above sea level (or, more accurately, a reference ellipsoid called WGS84). It’s a global system.
  • NED (North, East, Down): Now, imagine you’re standing in a park. NED is like describing everything relative to you. North is straight ahead, East is to your right, and Down is, well, down. It’s a local coordinate system, perfect for describing things nearby. This is super useful when you only care about positions relative to a close-by starting point.

Why Bother Converting?

Why not just stick with one system? Because different jobs call for different tools!

  • Aerospace: Imagine a drone trying to land on a moving platform. Using NED, the drone can figure out its position relative to the landing pad much more easily than if it were using raw GPS coordinates. It simplifies flight control and path planning.
  • Robotics: I once worked on a project where we had a robot navigating a field. GPS gave us the robot’s LLA coordinates, but to make sense of where it was relative to obstacles, we needed NED. It made the robot’s “thinking” much simpler.
  • Surveying: Surveyors use LLA for the big picture, but when they’re focusing on a specific construction site, NED helps them with the fine-grained details.

LLA to NED: From Global to Local

Okay, let’s get a little technical, but I’ll keep it as painless as possible. Converting from LLA to NED involves a few steps:

  • LLA to ECEF (Earth-Centered, Earth-Fixed): First, we need to translate our GPS coordinates into a different Cartesian system called ECEF. Think of ECEF as a 3D coordinate system with its origin at the Earth’s center. The x-axis points towards the Prime Meridian, the y-axis points 90 degrees east, and the z-axis points towards the North Pole. It’s a necessary stepping stone. The formulas look like this:

    • x = (N + h) * cos(latitude) * cos(longitude)
    • y = (N + h) * cos(latitude) * sin(longitude)
    • z = ((1 – e^2) * N + h) * sin(latitude)

    Where:

    • latitude and longitude are in radians
    • h is the altitude
    • N is the radius of curvature in the prime vertical
    • e is the eccentricity of the ellipsoid

  • Calculate the ECEF difference vector: Now, subtract the ECEF coordinates of your reference point (the origin of your NED system) from the ECEF coordinates of the point you’re interested in. This gives you a vector pointing from the origin to your point.

  • Rotate to NED: This is where the magic happens. We use a rotation matrix to transform the ECEF vector into the NED frame. This rotation depends on the latitude and longitude of your origin. The rotation matrix looks like this:

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