Orbit Simulation with Estimated Force Parameters

[GiuliaSchievano]

Dear developers,
First of all, I would like to thank you for the great job and the effort you are doing to develop, improve and maintain GROOPS!

Then, I have few questions regarding orbit simulation with estimated force parameters.

I based my analyses on the scenario GROOPS - GNSS satellite orbit determination and station network analysis (with some small modifications).
I want to compare the estimated orbit, obtained via GnssProcessing (reduced dynamic approach), with a simulated one, via SimulateOrbit.

To be consistent, I am using the very same force models that are used in the 020groopsGnssPreProcessing.xml for the integration of the variational equations and the initial position of the estimated orbit file.
I fed in input the ECOM5 parameters that I got as output from TransmitterDynamicOrbits parametrization (disabled stochastic pulses) and the estimated Earth rotation parameters.

However, I get ~30m orbit difference when I add the ECOM5 parameters, while without these corrections is ~2m.

I would expect to reach a very low orbit difference (around millimetres) between simulated and estimated, since everything is consistent (force models, parameters).

My questions are:

1. Am I applying the corrections in the right way?
2. How is the orbit propagated during the estimation steps and/or at the end GnssProcessing? Is it integrated or the transition matrix from the variational equations is used to compute the orbit corrections at each timestep?

Below you can find 2 screenshots with the Estimation set up and the Simulation set up.

Best
Giulia Schievano

(Estimation)

(Simulation)

[tmayerguerr]

Hi Giulia,

Hmm, your idea and your scripts look plausible. I don't see any mistakes at first glance.

Two suggestions for identifying the problem

• Try using the original Earth rotation instead of the estimated one.
• Or use PreprocessingVariationalEquation instead of SimulateOrbit. PreprocessingVariationalEquation does basically the same thing as SimulateOrbit, but additionally adjusts the initial state to the inpufileOrbit.

Best regards
Torsten

[GiuliaSchievano]

Dear Torsten,

I wanted to follow up on your previous suggestion to use PreProcessingVariationalEquations, which has significantly improved my residuals as shown in the plot.

However, I have a few additional questions:

• I'm observing non-zero residuals at t = 0. (if the apriori initial state is taken from the inputFileOrbit at timeStart, I expect the orbital difference to be zero). Could you clarify why this is the case? I've reviewed the documentation and understand that there are two steps for orbit and forces propagation, but it is not clear on how this process works. Specifically, what does it mean when it says "The orbit is corrected to be self-consistent" in the GROOPS - PreprocessingVariationalEquation documentation?

• To validate the accuracy of the models I used, I'd expect to reach numerical noise levels to ensure that my results are sensible for the next step (orbit prediction). Do you think there are any additional steps or adjustments I can make to achieve this level of simulation accuracy?

Thanks again for your support!
Best regards,
Giulia Schievano

[tmayerguerr]

Dear Giulia,

I agree with you: the orbits should fit together perfectly on numerical level.

The orbit is corrected to be self-consistent: Orbit integration is solving a differential equation: You need a force to compute position r (and velocity) but you need position r before to evaluate the force f(r). In our approach we start with approximate positions r_0 (inputfileOrbit). To get the corrected force a linearized term like
f(r) = f(r_0) + df/dr * (r-r_0)
is applied, where df/dr is the gradient/gradientfield. If the approximate orbit is too far away you should run PreprocessingVariationalEquation once more with the output orbit from the previous PreprocessingVariationalEquation as new input orbit. This usually not needed. In the process also the initial state of the satellite is adjusted to follow the approximate orbit as close as possible (not only at t=0). Therefore you are observing non-zeros at t = 0.

To find the source of your inconsistency you can make the test the other way around:
Estimate the parametrizationAcceleration within PreprocessingVariationalEquationOrbitFit with the orbit from GnssProcessing and compare the estimated forces and the output orbit with the input orbit.

Bets regards
Torsten

[AndreHauschild]

I had a look at this I believe that at least part of the inconsistency is because SimulateOrbit does not use a starcamera file for the attitude modelling and applies all forces in the orbital frame. This is not correct for all forces which depend on the satellite's surface properties. GnssProcessing and PreprocessingVariationalEquation use the satellite attitude from a starcamera and thus apply the estimated SRP parameters consistently.

[Hanbing59]

Hi Andre,

I did not inspect the source code yet, but I found your point is interesting.

If SimulateOrbit just applies all forces in the orbit frame and does not consider the satellite alltitude, it must model erroneously some non-conservative forces like SRP and Albedo.

Did I get your point correctly?

[AndreHauschild]

Yes, I think your understanding is correct.