Re: Is Gauss Method really so inputs sensitive? (Orbit Determination with Starlink observations from GoPro)

From: Andreas Hornig via Seesat-l <>
Date: Thu, 28 May 2020 22:27:42 +0200
Hi Cees,

first things first, thank you! :)
Your answer helps a lot.

On Tue, May 26, 2020 at 11:37 PM C. Bassa <> wrote:

> Hi Andreas,
> Thank you for sharing your interesting analysis.

You are welcome. I just try to share a bit back into this community.

> Though I have no (recent) experience with Gauss' method, I am not
> surprised you are seeing noise in your orbital parameters. With 3
> positions you have 6 measurements to fit 6 orbital parameters, meaning
> that you have no degrees of freedom. Hence, noise in your position and
> time measurements will directly lead to noise in the orbital
> parameters, as the orbital parameters do not average over additional
> observations.
> I've taken a closer look at your IOD measurements, and identify the
> Starlink satellite as Starlink-1207 [45380/20019W]. See
> for a skymap at your location. Comparing
> against the TLE with epoch 20111.00001157, the object
> was about 1.5 seconds late compared to the TLE, which is reasonable
> since it is still raising its orbit and hence expected to be late (the
> TLE was about 0.81 days old at the time of your observations).

Thank you very much! That was not so easy for me because of so many TLEs :).

When I understand you correctly, you took my IODs and plotted that on the
starmap. Then you found the right satellite and took the TLE and also
plotted that on the starmap. What I did not understand yet is how you
calculated thte 1.5 seconds. You selected one of my points and checked when
the satellite on the TLE propagation path is closest to my point, and then
checked the timestamp of the TLE and compared it to my IOD timestamp?

> Fitting a circular orbit against your 20 measurements yields (using
> satfit from to fit an SGP4 orbit
> directly):
> 1 45380U 20019W   20111.81342593  .00000000  00000-0  50000-4 0    04
> 2 45380  53.0004  91.2433 0001000   0.0000  70.4781 15.63581426    05
> # 20200420.81-20200420.81, 20 measurements, 0.400 deg rms
> This places the orbit at 379 km, so very similar to your result. The
> TLE for Starlink-1207 also was a 380 km altitude.

Oh, cool! :) That boost my hope!
Why did you use a circular orbit? Just for a quick check?

> The rms of the fit is about 0.4 degrees, which is not very good.
> Comparing the measurements against predictions from the circular orbit
> shows a large spread in errors along the track, which indicates timing
> errors. These vary from -1.3 to 1.0 seconds. The errors perpendicular
> to the track are better, at maximum 0.05 deg, which corresponds to 3
> arcminutes.

When I will be at this point, I will try to get a fit with an
eliptical orbit.
Did you directly take Ra/Dec for your fitting? I intend to use the position
vectors I get from the Gauss Method.

> What is the pixel scale of your setup? should provide
Pixel scale: 108.24 arcsec/pix.

> it. How do you compute the timestamps for the images?

I tested, that the timstamp is stored with the end of saving the image to
the sd card. So I calculate the start time with the integration time of 10
seconds before the storage timestamp.
Then I check the streaks in the image and check the flight direction with
the following images. So I know which streak pixel is the starting end and
which is the ending end.
I just take 2 measurements per streak in the image. By this, I know which
measurement has which timestamp

> Regards,
>     Cees

Realy a big thanks! :)

Best regards,

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Received on Thu May 28 2020 - 15:29:32 UTC

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