# Onboard propagator in satellites SGP or J2

The Earth orbit propagator SGP4 (simplified general perturbation) was developed by NORAD to allow users to generate short-term prediction of satellite positions using two line element sets (TLEs) distributed by NORAD. The method is based on mean values.

The satellite would use GPS but since it is power hungry one might use propagator in between the GPS on-off switching. The propagator would be SGP4 or based on the J2 propagator etc. and integrated again and again numerically to estimate position and velocity of the satellite.

Can one use SGP4 as onboard propagator?

## 2 Answers

The first question you need to ask yourself is the following: does the spacecraft need to know its own position? Many, if not most, spacecraft do not need that information. The ground team simply needs to know when to schedule maneuvers, which means that only the ground team needs to know the position of the spacecraft, not the spacecraft itself.

If the spacecraft does need to know its own position, then a propagator in itself is not sufficient for onboard orbital determination (OD). In the subject of orbital determination, as defined in "Statistical orbit determination" by Schutz et al. 2004, the solution to the problem includes not only the position and velocity of a spacecraft, but also the uncertainty of that position and velocity. An example of how this might work is available here: you'll note that the plots include the error between the true spacecraft state and the estimated state (green dots), along with the uncertainty (red line). If using any kind of propagator, may this be the SPG4 which was initially release in 1988, or the latest and greatest models, the "solution" will only be the position and velocity of the spacecraft. As per the above definition, that does not correspond to a fully defined solution of orbital determination. Instead, it corresponds to a "propagated spacecraft state", which may be literally hundreds of kilometers off compared to the truth. For example, the difference between a non-J2 effect and a J2 effect is 0.097 km in just one day. I encourage you to run a few different simulations in NASA's GMAT to compare the final states of spacecraft using different fidelities of the harmonics and of the drag.

More specifically, an SPG4 propagator may give the spacecraft some very rough estimate of where it is, but the real-world spacecraft dynamics are far too complicated to be determined by any propagator by itself without any measurements, and without running an OD filter.

It would need some measurements of the world around it (through GPS readings or ground tracking passes) in order to accurately determine its state, and the uncertainty in its state. Moreover, if a GPS module is considered power hungry, then the computation needed for an SGP4 would also likely be considered too power hungry.

LEO birds may be equipped with a GPS module which can handle the velocities of spacecraft (they are usually ITAR restricted but nothing prevents you from designing your own chip). If equipped with a GPS module, two strategies for OD are possible.

First, the spacecraft could store onboard each of the measurements and downlink them to the ground on request. The ground team would then determine an OD solution independently in order to accurately determine the orbit of the spacecraft. The team will then upload a maneuver file based on ground propagation of the spacecraft's trajectory.

Secondly, if spacecraft needs to know its own position without ground support, then it needs to run an onboard Kalman filter. The Kalman filter will allow the spacecraft to infuse GPS measurements with the expected model of its dynamics (i.e. Earth gravity field, drag model, position of the planets, etc.), and compute an estimate of its position and velocity (and optionally other parameters), along with an uncertainty of its state.

When doing spacecraft navigation in operations, an OD analyst will run many different filters with slight variations in the dynamical model. For example, in the case of the GRAIL mission around the Moon, analysts simulated small maneuvers in their "truth model" in order to account for errors in the gravity field which weren't fully understood by scientists and engineers during the mission.

• "is not sufficient" and "very rough estimate" are really subjective. Since the OP has not specified an application or accuracy requirement, a few kilometers could certainly be sufficient for many applications. Medium magnification camera pointing or medium gain antenna pointing towards Earth or towards the Moon or even a non-LEO spacecraft or body would be fine. I think this answer is currently just a non-supported opinion. I'm pretty sure a spacecraft could perform all of these example tasks using it's own TLE (received from Earth every few days) as long as it had a fairly stable clock.
– uhoh
Commented Aug 15, 2018 at 3:04
• More about "a few kilometers" in this answer.
– uhoh
Commented Aug 15, 2018 at 3:06
• Yes, it is subjective. As my professor of OD would say "orbital determination is more of an art than a science." Moreover, I'd say, from my experience and my job, that the SPG4 would likely not be sufficient by themselves to provide the kind of accuracy that is required by US regulations. The model was published in 1988, and the gravity field of Earth, the drag models, and planetary ephemerides have significantly changed since. Commented Aug 15, 2018 at 3:58
• What US regulation requires a satellite to be able to calculate its own position with better accuracy than SGP4 can provide? I didn't know spacecraft had any requirements at all to perform such local calculations. I think you are confounding several different topics here, or answering a different question than was asked.
– uhoh
Commented Aug 15, 2018 at 5:23
• I think my answer isn't structured well enough, and that may lead to a confusion of the main point. So I'll state it here: orbit propagation is not the same as estimation. Estimation is a branch of statistics. OD is a branch of astrodynamics which mixes propagation and estimation. Commented Aug 15, 2018 at 13:50

Many satellites do not have any position or velocity measurements. Time tag tables including satellite state, magnetic and sun vector are been uploaded from the ground and the satellite uses it for attitude control and orbit control maneuvers.

LEO satellite can use GPS and OD features to obtain the satellite state without being dependent on ground updates. This capability allows the satellite to use closed-loop orbit and attitude control because now it has a real-time feedback.

SGP4 can be used as an onboard propagator either as a backup if GPS fails or as main orbit propagator if there is no requirement to know the exact position of the satellite. Position accuracy of few kilometers is more than enough for many use cases including formation flying applications. GPS receiver consumes a lot of power that might not be available all the time (in 1U CubeSats for example). SGP4 require very limited computing power and the only required input is TLE and time.

Numerical propagation based on TLE will quickly accumulate error with respect to the real satellite position. The error will decrease every time new TLE measurements uploaded to the satellite. NORAD update the TLE catalog almost every day so fresh TLE can be sent to the satellite on a daily bases lowering the accumulated error.

Engineering is all about compromises. If the expected accuracy of SGP4 is good enough for the mission, use it and save the money of space-qualified GPS receiver.