Coordinate transformations

[ShujuanGeng0227]

Discussed in #1

^{Originally posted by pgrebolt May 29, 2023}
Hi all,

I am working with the DFN darkflight modelling code and, looking deep into it, I think there are some conversions between frames that are not done properly. I have seen that when converting from ECI coordinates to LLH, a transformation involving ECEF->LLH is applied, thus neglecting any Earth rotation effect. For example, this occurs in df_functions.py, in line 77 (AtmosphericModel). In my opinion, the steps should be ECI->ECEF->LLH. I have made the conversion as:

Pos_ECEF = ECI2ECEF_pos(Pos_ECI, t_jd)
Pos_LLH = ECEF2LLH(Pos_ECEF)

Similarly, this also happens in df_functions when converting the wind vector (in ENU) to ECI or in trajectory_utilities.py when computing gravity_vector(). In the case of the wind vector I am now conducting the following conversion:

lat = float(Pos_LLH[0]); lon = float(Pos_LLH[1]) # (rad)
ENU2ECEF_matrix = ENU2ECEF(lat, lon)
Wind_ECEF = np.dot(ENU2ECEF_matrix, Wind_ENU)
Wind_ECI = ECEF2ECI(Pos_ECEF, Wind_ECEF, t_jd)[1] + v_rot

However, I am still wondering if in this case v_rot should be added.

Has anyone wondered the same? Is it possible that I am missing some approximations between ECI and ECEF?

Thank you

[ShujuanGeng0227]

Hello, I have asked the same question to one of the author and we would like to repo his answer here:

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You may notice I've put an ECI position vector into a ECEF2LLH conversion. From memory, I believe that was because I wanted to save computational time and also because we don't have access to timing information at that point in the code to do the proper conversions from ECI -> ECEF -> LLH. I think the +-40m was calculated by me and is due to the small difference between Earth's ECEF z-axis and Earth's ECI z-axis. If I pretend those z-axes are the same (as I've done in the code), I'm actually shifting the Earth's ellipsoid in one of those frames very slightly, changing heights on the ground.

If I pretend those z-axes are the same (as I've done in the code), we end up with a possible height difference on the ground (height between the blue and green ellipses) of about 40m.

That said, I don't think this is a problem at all because (1) the meteoroid is probably travelling almost vertically by that point anyway so the impact site in lat/long would be almost the same, and (2) as far as I'm aware, we are not yet including proper ground height information, besides a constant height above sea-level set in a config file somewhere.

You are welcome to change it to use the proper conversions, i.e. ECI -> ECEF -> LLH, but you will slow down the code quite a bit and you will need to pass it the timing information somehow.

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That's the answer. Hope this will help you.