ISS position and AMS 02 pointing accuracy study

On March 27th, 2011 Grange Obs. contacted NASA JPL since an indipendent technology research on AMS 02 orientation was in progress.
At the time, it was noticed the JPL tool HORIZONS (on-line ephemerides calculator) provided ISS orbital prediction for a short period of time (the service was canceled on January 2011).
The AMS 02 payload has been mounted on May 19th, 2011 on ISS during the STS-134 Shuttle mission, but 2 months earlier it was clear that the Space Station orbit accuracy needed to be studied.

Dr. Jon Giorgini (JPL SSD Group senior analyst) replied the day after (cc'd Dr. Donald K. Yeomans, senior research scientist at JPL - CALTECH) that the service was temporarily provided since the ISS Crew wanted to observe an asteroid's close approach, so station-centered predictions were needed for a limited amount of time.
The AMS 02 problem was deemed fairly similar; in fact, the payload has the possibility to select the studied uncharged particles (gamma rays) incoming direction, so in principle it performs like an optical telescope observing the celestial sphere, and needing to be precisely pointed.
AMS 02 has a built-in star trackers (having a pointing accuracy of several arcsec), but ISS cannot orientate itself like the Space Telescope, in fact the station manouvers are due mainly for the orbit circularization purpose, and are not intended for pointing a fixed celestial object.
Dr. Giorgini also offered the JPL support for re-activating the ISS service on Grange Obs. demand, while justified and clearly referenced.
A reply was then sent for investigating the ISS position accuracy and the involved algorithms to solve its orbit decay needed corrections on orbital elements.
Here is the Dr. Giorgini reply:

"As to uncertainties of the result, there is no general
answer, being a function of the target's orbit and
measurement dataset. Accuracy data is not distributed.

The models and solutions are relatively low accuracy
however, and you should expect km-level error even for
the "latest" set of elements, at least for low-Earth
orbit cases."

Why ISS orbit (thus position) seems so uncertain, considering celestial bodies position is known with high accuracy?
First of all, an astronomer would notice the sky rotation rate as seen from ISS is about 16 times faster than that observed on Earth, since our planet spins once a day; instead ISS Crew withnesses 16 sunrises and sunsets during 24 hours, speeding considerably faster.
Consequently, on ISS stars rise and set at high speed, and space station footages show for example how fast the Moon is setting or how short is the dusk duration.
That is due to the ISS orbital speed (about 28000 km/h) so in one second the position of a payload like AMS 02 changes by 8 km, and its pointing precision shall vary accordingly (about 4 arcmin/s). Telescopes on ground have mounts which counterbalance Earth rotation, but AMS 02 is firmly fixed on station Truss.

Secondarily, in astrometry the higher is the target speed (like during a fast asteroid Earth fly-by), the highest is the rate of the measures obtained for having a good approximation on position and velocity.
Using optical methods, from target single positions (at least three, 2 components on celestial sphere times 3 equal six numbers, see over) the orbital elements can be calculated; fast targets simply need more measures to reach a given accuracy.
On the contrary, having the orbital elements of a fast object close to Earth it is important to predict the effect of its velocity decay (due to our planet difference in mass distribution and the presence of the atmosphere remnant, actually acting as a motion resistence, or drag).
That prediction is called orbit propagation.

The orbital elements are six conic geometry, length and angular parameters (plus a seventh one, i.e. the time or epoch), and can be provided also in a form called Two-Line Elements (TLE), frequently used by state-of-the-art orbital tools like AGI Satellite Tool Kit (STK), which propagate orbits using the SGP 4 and SGP 8 (Earth satellites) or SDP 8 (deep space probes) algorithms.
The SGP4 algorithm limit is the air drag effect variation is linearly applied during discrete time periods (based on power spectral density evaluations), but solar effect on atmosphere dimensions and drag effectiveness is actually unpredictable over the time.
Have a look of the ISS orbit decay statistics from the CalSky website based on distributed TLEs; the station period is mainly depending on the atmospheric drag and the decay appears linear, in reality being highly non-linear like solar activity (so the station position errors could be very high from time to time):

The AMS 02 local position and resolution is described in this paper to be purchased, where ISS tracking is mentioned.
The ISS orbital positional accuracy is discussed in this other paper, see page 1 and page 2.
A discussion about satellites orbit determination methods and the involved timing errors can be found in Bill Gray's website; the late MIR station (as well as the current ISS) precision would be about 700 meters.

It is concluded that since position numbers on computers appear changing once a second or two, the first impression in the audience is that involves a great accuracy; in reality, they simply propagate the USSPACECOM distributed ISS TLE and daily published State Vectors (i.e. 3 components for the target position in space and 3 for its velocity at a given epoch, again six numbers in total), updated every 36 hours nominally, by the aid of the SGP above mentioned algorithms, and selected co-variance methods.
The point remains the poor knowledge of the atmospheric drag effect, as well as time formats digit limitation.

Accuracy is a well know concept for the observatories certified in astrometry, having instruments and tools capable to estimate objects position on celestial sphere better than half arcsecond (at the ISS typical 350-400 km minimum distance from Earth, the station position approximation shall be theoretically equal to 1 meter in the best conditions).

Dr. Roberto Battiston, the former Deputy Spokeperson of AMS 02 consortium involving 16 Counries and leaded by Samuel Ting, the Boston MIT professor winner of the Nobel Prize, (now heading ASI) replied to a Grange Obs. offer to link the present page into the project website; he pointed out the payload, along with star trackers can use modern GPS receivers aboard ISS which could potentially lead to a precision of 5 meters, see this paper.

Indeed, reading info on the web and contacting experts in the aerospace sector, the AMS 02 GPS receivers are only used for timing purposes; moreover, reading the AMS website page you can read:

"A comparison between the taken picture and stellar maps could reveal the orientation of AMS in the sidereal reference frame. Star Tracker acquires a picture of the sky every 10 seconds, to describe finely the AMS orientation along the 90 minutes ISS orbit"

In 10 s the ISS position accuracy for AMS 02 changes by 80 km and the pointing angles heavily vary in accordance.
And if the exercise is having the AMS 02 position at the given microsecond a gamma ray count was received, the interpolation (of which type?) between the restricted accessed 1 Hz ISS state vectors (from JSC consoles) basically means having a fish every second, but using Station's accurate TLEs is like to be thaught fishing.
My impression is those notes have helped the AMS 02 Team for the ISS tracking purposes (but nothing seems transpire).

The Grange Obs. with its telescopes expertize and astrometry methodology applications could indipendently teach derive and validate the Station TLEs using optical methods at every visible passage with an accuracy of about 8 m (using GPS timing) in Space Awareness Optical Centers, and can calculate accurate ephemerides of de-orbiting space debris.

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