# Coordinate transformation - NED and ECEF frames

• 9988776655
In summary, the conversation discusses the use of euler angles and rotation matrices to convert from the sensor body frame to the North East Down frame, and then to the Earth Centered Earth Fixed frame. The key question is how to obtain the rotation matrix for the North East Down frame to the Earth Centered Earth Fixed frame. The speaker suggests using the position in latitude and longitude to obtain this rotation matrix. However, there is uncertainty about whether this method is applicable for vectors.
9988776655
Hi,

I have a reference device that outputs euler angles, which are angles that relate the sensor body frame to the north east down frame. These angles are called pitch roll and yaw. The sensor is an accelerometer. I know how to get the rotation matrix that will put accelerations from the accelerometer sensor body frame to the north east down frame. Call this rotation matrix R(Body to North East Down).

How do I get the rotation matrix that will rotate from Body frame to Earth Centered Earth Fixed frame? I need to do this as all of my other calculations use the Earth Centered Earth Fixed frame. I can see that:

R(Body to Earth Centred Earth Fixed) = R(Body to North East Down) * R(North East Down frame to Earth Centered Earth Fixed).

How do I get R(North East Down frame to Earth Centered Earth Fixed)?

To get acceleration in the Earth centered Earth fixed frame, would I use:
Acceleration(Earth Centred Earth Fixed) = R(Body to Earth Centred Earth Fixed)*Acceleration(Body frame) ?

I have access to the position in latitude and longitude (radians). Also note that acceleration is a vector not a coordinate.

Thanks.

Latitude and longitude give you the rotation angles to convert from NED to ECEF. I am working from vague memory, but I think that the latitude gives the rotation angle needed even when you are using the accurate WGS84 Earth model. If you have magnetic north, don't forget to rotate to true north.

R(North East Down frame to Earth Centered Earth Fixed) =

[ sinLatitude*cosLongitude; -sinLongitude; -cosLatitude*cosLongitude]
[-sinLatitude*sinLongitude; cosLongitude; -cosLatitude*sinLongitude]
[cosLatitude; 0; -sinLatitude; ]

I am unsure if this is correct for my application because this may only be relevant for coordinates not vectors. Please comment.

## 1. What is the difference between NED and ECEF coordinate frames?

The NED (North, East, Down) frame is a local-level coordinate system that is oriented with respect to the local horizontal plane and the direction of gravity. It is commonly used in aircraft navigation and geodesy. On the other hand, the ECEF (Earth-Centered, Earth-Fixed) frame is a global coordinate system that is fixed with respect to the Earth's center of mass. It is commonly used in satellite navigation and geodesy.

## 2. How do you convert coordinates from NED to ECEF?

To convert coordinates from NED to ECEF, you will need the latitude, longitude, and altitude of the point in the NED frame. You can then use a set of transformation equations to convert these coordinates to the ECEF frame. These equations take into account the orientation and rotation of the Earth, as well as the altitude of the point relative to the Earth's surface.

## 3. What is the purpose of using coordinate transformations?

Coordinate transformations are used to convert coordinates from one reference frame to another. This is necessary when working with different coordinate systems, such as NED and ECEF. They allow us to accurately represent and analyze data in different coordinate frames and to compare data from different sources.

## 4. Are there any limitations to coordinate transformations?

Yes, there are limitations to coordinate transformations. The accuracy of the transformation depends on the accuracy of the input data, as well as the complexity and accuracy of the transformation equations used. In addition, some transformations may not be valid for certain regions or locations on the Earth's surface.

## 5. How do you take into account the Earth's rotation when performing a coordinate transformation?

The Earth's rotation can be taken into account by using transformation equations that incorporate the Earth's rotation rate and the time of observation. These equations will adjust the coordinates from the initial frame to the final frame, taking into account the rotation of the Earth during the time interval. This is important for accurate positioning and navigation applications.

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