Convert ECI to ECEF: A Step-By-Step Guide

In summary, the conversation discusses the process of converting between ECI and ECEF coordinate systems, and then to ENU. The speaker is seeking a direct formula for the conversion, but is met with some confusion and unhelpful responses due to the technical jargon used. Eventually, the speaker solves the issue on their own.
  • #1
Rawls
2
0
I have done a search online to understand how to convert ECI to ECEF. I wanted to learn what the conversion is so I could just create a MATLAB script to make it happen. My problem is that most of the information I find assumes you already have some knowledge about ECI and ECEF. If I had more time I am confident I could learn about each system, make sense of the knowledge found all over the web and construct my own script.

My ultimate goal is to go from ECI to ENU. There are MATLAB toolboxes that can make this easy however I do not have access to those tool boxes so I must create my own.

Step 1: Convert ECI to ECEF. I want to take Matrix A which is in ECI and convert it to matrix A' which is in ECEF. So A'=eci2ecef(A).

Having limited knowledge I would like to know the direct formula (that is explained step by step if possible).

Step 2: Convert ECEF to ENU. Matrix A''=ecef2enu(A'). Maybe there is a way to go from ECI directly to ENU, that would be great but from what I have been reading it does not appear to be the case.

Any help would greatly be appreciated. If you require more information from me please just ask. I cannot yet think of how I can make this question better for those who come across it.
 
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  • #2
Well, ECEF is NOT an inertial frame. This has implications in terms of whether it makes sense to think of the conversion as a matrix multiplication. So, your first step is to understand the difference between an inertial frame of reference and one which is undergoing a (non-linear) acceleration. Step Two is to NOT use jargon such as ECEF and the possibly obsolete ECI. Third is to post this in the appropriate section. Why would you think a question about orbital mechanics belongs in linear and abstract algebra? Sorry, if I could, I would give more specifics - but that isn't in my area of interest/competence. Sorry if my reply isn't helpful - I referred to ESA's navipedia for the little information I used.
 
  • #3
ogg said:
Well, ECEF is NOT an inertial frame. This has implications in terms of whether it makes sense to think of the conversion as a matrix multiplication. So, your first step is to understand the difference between an inertial frame of reference and one which is undergoing a (non-linear) acceleration. Step Two is to NOT use jargon such as ECEF and the possibly obsolete ECI. Third is to post this in the appropriate section. Why would you think a question about orbital mechanics belongs in linear and abstract algebra? Sorry, if I could, I would give more specifics - but that isn't in my area of interest/competence. Sorry if my reply isn't helpful - I referred to ESA's navipedia for the little information I used.
Why did you waste your time responding? I don't recall mentioning anything about ECEF being an inertial frame so step 1 is irrelevant. ECI is not obsolete and if it were it doesn't make a difference. If you don't understand the jargon then clearly this post isn't relevant to you, move onto another. I posted this in this section because this process requires matrix algebra to complete and its relevant. I don't need to understand navigational coordinate systems I need to do math. SOME ADVICE FORE YOU, IF YOU DON'T KNOW WHAT YOU ARE TALKING ABOUT DON'T WASTE YOUR TIME (OR OTHERS') REPLYING WITH SNIDE REMARKS. It isn't helpful or necessary. I solved the issue and this thread is done.
 

Related to Convert ECI to ECEF: A Step-By-Step Guide

What is ECI and ECEF?

ECI (Earth-Centered Inertial) and ECEF (Earth-Centered Earth-Fixed) are two coordinate systems commonly used in satellite and spacecraft orbits. ECI is a non-rotating, fixed coordinate system with its origin at the center of the Earth. ECEF, on the other hand, is a rotating coordinate system that has its origin at the center of the Earth and moves with the Earth's rotation.

Why do we need to convert from ECI to ECEF?

Converting from ECI to ECEF is necessary when working with satellite or spacecraft data, as the data is typically collected and stored in ECI coordinates. However, many applications require the use of ECEF coordinates, such as navigation and mapping systems. Converting between the two coordinate systems allows for the data to be used in a wide variety of applications.

What is the process for converting ECI to ECEF?

The conversion process involves a series of mathematical calculations using the Earth's rotation rate and the time of observation. The first step is to calculate the Greenwich Hour Angle (GHA) of the observer, which represents the angle between the observer's location and the prime meridian. Then, the transformation matrix is calculated using the GHA and the Earth's rotation rate. Finally, the ECI coordinates are multiplied by the transformation matrix to obtain the ECEF coordinates.

What are the benefits of using ECI and ECEF coordinate systems?

ECI and ECEF coordinate systems have different advantages depending on the application. ECI coordinates are useful for representing the position and velocity of objects in space, as they are non-rotating and have a fixed origin at the center of the Earth. ECEF coordinates, on the other hand, are useful for navigation and mapping applications, as they are directly tied to the Earth's surface and its rotation.

Are there any challenges or limitations when converting between ECI and ECEF?

One challenge when converting between ECI and ECEF is the need for accurate time and location data. The calculations are highly sensitive to errors in these parameters, which can result in significant differences in the converted coordinates. Additionally, the transformation matrix can become singular at certain points, making the conversion impossible. However, these limitations can be overcome with careful data collection and processing techniques.

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