Re: [Orekit Developers] status on second order derivatives

[Evan Ward <evan.ward@nrl.navy.mil>]

Hi Luc, Paul,

If I understand correctly this issue only affects propagators that do
not use Cartesian representation of the state. When a non-Cartesian
representation is used the propagator's position is combined with the
Keplerian velocity and the resulting combination is not locally tangent
(osculating) to the propagator's orbit. Am I understanding the issue
correctly?

Could this issue be solved by using the propagator's complete state to
determine the instantaneous P/V and use that to build a CartesianOrbit?
Then we wouldn't have to modify the existing set of Orbit classes, and
the user would see the correct osculating P/V. (This might be equivalent
to your second approach.)

As far as where to put the code, it seems like the conversion code would
be specific to the internal state representation used by the propagator,
so I think it makes sense to keep the code as private to the propagator.
Though if you think there would be other uses for the conversion, I
think a public static factory method would work well.

Thanks Luc for finding this issue and doing the analysis. I can see how
this would be an issue when computing the Doppler as well as time shifting.

Best Regards,
Evan

On 10/29/2014 06:57 AM, MAISONOBE Luc wrote:
> Hi Paul,
>
> paulcefo <paulcefo@buffalo.edu> a écrit :
>
>> Luc,
>>
>> Do I correctly understand that your concern is that Keplerian
>> transformations do apply outside the osculating space?
>
> The problem I had was that we did use Keplerian-only expression
> to set up local Taylor expansions around the current point (a few
> seconds away). This was slightly wrong when all the parameters were
> time-dependent and not only the anomaly was time-dependent. Of course,
> the error increasing with the time offset with respect to the central
> date at which the Taylor expansion is built. The fix was simply to
> not forget the derivatives of these other parameters.
>
> This Taylor expansion feature is a built-in feature available in all
> Orekit orbits, it typically allows to do computation in the vicinity of
> an already computed point without needed to trigger a complete
> propagator.
> It can even be used for some computation inside the run of a propagator,
> as for example when the higher level propagator takes care of the long
> term propagation and at each step we need some additional points
> surrounding the current step to compute attitude evolution in some
> specific modes.
>
> My concern was how to implement this fix in our current architecture,
> and more precisely were to put the code: in an existing class or in
> a dedicated class which would be used only by propagators.
>
> best regards,
> Luc
>
>>
>> Paul
>>
>> -- 
>> Dr. Paul J. Cefola
>> Consultant in Aerospace Systems, Spaceflight Mechanics, & Astrodynamics
>> Adjunct Faculty, Dept. of Mechanical and Aerospace Engineering,
>> University at Buffalo (SUNY)
>>
>> 4 Moonstone Way
>> Vineyard Haven, MA 02568
>> USA
>>
>> 508-696-1884 (phone on Martha's Vineyard)
>> 978-201-1393 (cell)
>>
>> paulcefo@buffalo.edu
>> paul.cefola@gmail.com
>>
>> On 10/29/2014 6:02 am, MAISONOBE Luc wrote:
>>> Hello,
>>>
>>> As some of you may be aware, I have been working for a few months on
>>> second order derivatives in the git branch
>>> position-velocity-acceleration. This work is still ongoing but I hope
>>> to finish it for 7.0 and merge the branch back to master soon. For
>>> now, there are still failing tests so I can't do it.
>>>
>>> This change should allow us to reach several goals :
>>>
>>> - improved accuracy in shiftedBy methods
>>> - improved accuracy in interpolators (with user-defined
>>>   choices to use or not first and second derivatives
>>>   from the sample)
>>> - improved accuracy in attitude
>>> - removal of ugly hidden finite differences in some classes
>>>   (most notably attitude modes) with hard-coded steps
>>> - hopefully faster Earth transforms, by replacing Hermite
>>>   interpolation with single point extrapolation
>>> - availability of non-Keplerian acceleration everywhere
>>> - availability of angular acceleration in attitude and frames
>>> - proper composition of dynamics in frames
>>> - possibility to propagate orbits in non-inertial frames
>>> - possibility to propagate orbits without a central body
>>>   (interplanetary missions, Lagrange point missions, ...)
>>>
>>> There is one point that bothers me right now. As I removed some of the
>>> ugly finite differences, some non-regression tests started to fail. I
>>> finally found the raw cause of these failures and was surprised to
>>> discover an old bug in the way we use the osculating orbits produced
>>> by the Eckstein-Hechler analytical propagator. This propagator takes
>>> zonal terms into account, and produces directly circular parameters a,
>>> ex, ey, ... When we compute anything related to geometry, we compute
>>> Cartesian coordinates using the Orbit getPVCoordinates method. As the
>>> Orbit classes do not know anything about the perturbation, the (P, V)
>>> pair does in fact implicitly relies on Keplerian-only expressions. So
>>> the velocity part is *not* consistent with the derivative of the
>>> position. The real derivative of the position takes the non-Keplerian
>>> effects into account which are ignored by getPVCoordinates. The
>>> difference is small, but as the tests threshold were deliberatly very
>>> tight, the tests started to fail when the various pointing directions
>>> were not computed anymore from finite differences mainly involving
>>> position and when they relied on the computed velocity. So the problem
>>> already happens in the master branch, it is not specific to the
>>> introduction of acceleration (it was just detected here during
>>> testing).
>>>
>>> The solution is in fact quite simple. If an orbit has been produced by
>>> a non-Keplerian propagator, the propagator already knows about the
>>> derivatives of the orbital elements (which are circular in the
>>> Eckstein-Hechler model case but can be any kind of parameters for
>>> other propagators). The propagator should therefore provide these
>>> derivatives to the orbit so they can be used in the PVCoordinates
>>> conversion. The code is very simple and straightforward. I have
>>> checked this and got very interesting results with
>>> Eckstein-Hechler/Circular, as for example a simple interpolation over
>>> a 900s arc with proper velocity/acceleration has a 88m error with two
>>> base points now whereas it was 5162 m before (and 0.02m vs 650m for 3
>>> points, 1.0e-5m vs 259m for 4 points).
>>>
>>> Here is what bothers me:
>>>
>>> Should we create specialized classes for perturbed orbits or should we
>>> simply add a constructor to the existing orbits with the parameters
>>> derivatives and set them to 0 when they are not known?
>>>
>>> For my tests, I created PerturbedCircularOrbit which extends
>>> CircularOrbit and override the protected initPVCoordinates method and
>>> the public shiftedBy and interpolate methods. I could also have simply
>>> moved everything into CircularOrbit with a new constructor.
>>>
>>> I do not like much the PerturbedXxxxOrbit approach, as it forces to
>>> create also additional entries in the OrbitType enum with additional
>>> converters and it becomes awkward if for example a user configures a
>>> NumericalPropagator to generate XxxxOrbit, despite this propagator
>>> will in fact really generate PerturbedXxxOrbit because it is what a
>>> Numerical propagator is for. So there should be either an internal
>>> modification of the user setting from OrbitType.XXXX to
>>> OrbitType.PERTURBED_XXXX or an error triggered which would invalidate
>>> *all* current user code as it would become forbiddent to generate XXXX
>>> orbits now.
>>>
>>> On the other hand, the drawback of modifying the existing classes to
>>> hold the non-Keplerian derivatives is that they will consume more
>>> memory. I don't think it is a problem with current computers.
>>>
>>> In any case, initial orbits created directly from user code or by
>>> reading files would not include the derivatives and therefore will be
>>> built as usual (by calling the unmodified classes in the first
>>> approach, or by using the already existing constructors in the second
>>> approach, assuming these constructors will automatically set the
>>> derivatives to Keplerian-only values). In any case, full-blown
>>> perturbed orbits will be created internally by Orekit propagators,
>>> which can easily be modified to provide the derivatives they know (by
>>> creating instances of the new derived classes in the first approach,
>>> or by using new constructors with additional parameters in the second
>>> approach).
>>>
>>> My humble opinion would be to use the second approach to solve this
>>> bug. I will probably do this in the position-velocity-acceleration
>>> branch so it will include accelerations right from the start and will
>>> be merged to master at the same time as the rest of the branch. Of
>>> course, this will be a dedicated commits (Git branches are great!).
>>>
>>> What do you think ?
>>>
>>> best regards,
>>> Luc
>>>
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