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It seems that IMUs suffer from integration errors that build up over time, so they are not the most accurate means of determining the attitude of your spacecraft.

So what then would be the most accurate system for this? GPS? Star trackers? Other?

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  • $\begingroup$ also see What will be the accuracy of an Atomic (Quantum) Inertial Sensor used in spaceflight? and Using what technology one can keep a spacecraft truly non rotating $\endgroup$
    – uhoh
    Mar 18, 2021 at 23:13
  • $\begingroup$ You're asking this as an either/or question. The correct answer is yes. Modern spacecraft use sensor fusion, typically implemented in terms of a Kalman filter of some sort. $\endgroup$
    – David Hammen
    Mar 19, 2021 at 16:34
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    $\begingroup$ A note that I didn't see addressed while skimming the existing answers: when thinking about orientations, it's worth keeping in mind what you want to be oriented relative to. Are you trying to align to a docking port? Point a telescope at a star? Orient for an interplanetary transfer burn? Prepare for atmospheric entry? The answer will change depending on what you're trying to do. $\endgroup$
    – Erin Anne
    Mar 20, 2021 at 1:27

4 Answers 4

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TL;DR

Star trackers are by far the most precise. Sun sensors are used for coarse knowledge and IMUs only for estimating the attitude during a maneuver.

Details

Attitude determination typically relies on several sensors. Most (all?) spacecraft have at least two modes: coarse and fine attitude determination. The first is to have a general idea of your attitude and the second is to have a very precise knowledge of your attitude.

For fine attitude determination, nothing beats star trackers. One of the most used STA (Star Tracker Assembly) is manufactured by Adcole and achieves an accuracy of 10 arcseconds, or 0.0027 degrees. That is the precision at which the star tracker will tell your spacecraft how well it is pointed compared to a reference.

Star trackers require the spacecraft to be relatively stable before they can spit out a good attitude estimate (e.g. Adcole needs the spacecraft to rotate at less than 2 degrees per second. That's where coarse sun sensors (CSS) come into play: they tell the spacecraft whether they can see the sun. That is sufficient to have coarse attitude knowledge and to determine a tumbling/angular rate of your spacecraft. The angular rate (also called "body rates") is all you need to know to stabilize your spacecraft (I won't derive it here, but Schaub and Junkins derive in their book, which is one of the references on attitude control).

So far, we know that star trackers provide the most precise attitude determination, and that sun sensors allow for imprecise attitude. In practice, that's what a lot of spacecraft fly: use the sun sensors to detumble/stablize your spacecraft, then turn on the star trackers to achieve the correct attitude pointing.

Where do the IMUs come into play? Typically they're used for high thrust maneuvers (not an attitude control maneuver). During a maneuver, the spacecraft may spin at a rate larger than what the star trackers can follow. So the IMUs are used to track the acceleration imparted on the spacecraft. With a good knowledge of the inertia tensor of the spacecraft and the location and orientation of each thruster, it is possible to determine what kind of spin rate that maneuver has caused. Spacecraft will then use that attitude estimate from the IMUs to guarantee a specific spin rate at the end of the maneuver (typically by modulating the thrusters during the burn), and then again use the star trackers to acquire precise attitude position. Hence, their drift rate isn't a deal breaker because they are re-initialized from star tracker data before a maneuver. Note that for very long burns (over 5 minutes), that drift rate may become problematic.

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    $\begingroup$ Thank you, ChrisR! This is exactly what I was looking for. I suspected star trackers would be it from things I'd read, but I really couldn't say for sure. Thanks for writing all this down. $\endgroup$
    – user39728
    Mar 19, 2021 at 1:03
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    $\begingroup$ @user39728 please check the three links about the use of GPS for attitude that I included in my answer. In short, no! Also, if this answer is exactly what you are looking for, then that's exactly what the up vote button is for; consider up voting this answer? I did! $\endgroup$
    – uhoh
    Mar 19, 2021 at 1:29
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    $\begingroup$ @DavidHammen, happy to hear more! All the Earth orbiters and cislunar spacecraft I've worked on relied only on star trackers for their fine attitude determination. Edit: From nasa.gov/content/goddard/…, seems like the star trackers are the most precise ADC of Hubble apart from its mirrors (which one probably wouldn't fly). Further, the Hubble STs are 6 times less precise than modern Adcole. $\endgroup$
    – ChrisR
    Mar 19, 2021 at 4:36
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    $\begingroup$ @ChrisR that's mentioned in my answer too, look for FGS. You just have to attach two more Hubbles to your spacecraft is all... :-) $\endgroup$
    – uhoh
    Mar 19, 2021 at 7:58
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    $\begingroup$ I mistyped. I should have written that the Hubble Space Telescope would not work if it had to rely on star trackers alone. I added an answer where I mentioned the use of guide stars, which @uhoh also mentioned in his answer. $\endgroup$
    – David Hammen
    Mar 19, 2021 at 16:35
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The most accurate attitude determination depends very much on the needs of the vehicle. It is important to remember that perfection is the enemy of good enough. Different spacecraft have different requirements for what "good enough" is. Going beyond "good enough" is not very smart.

But what if the "good enough" requirement is less than 1/10 of an arcsecond in terms of accuracy, 1/100 of an arcsecond in terms stability? (That describes the Hubble Space Telescope and the James Webb Telescope, BTW.) If that is the case, sensors are only one of the concerns. Other concerns include

  • Vehicle structure. Flimsy spacecraft have flex modes that can be large in magnitude, which goes very much against the high accuracy pointing and stability requirements of a space telescope. Space telescopes with those very high accuracy and stability need to be beefed up a bit in terms of structure, and that is not cheap as every added kilogram adds expense.
  • Liquids, such as propellants and coolants. Liquids slosh. It's what they do. Slosh can be just as bad as vehicle flex in terms of making a mess of high precision pointing and pointing stability. Baffles and other passive techniques can battle slosh, but once again, every added kilogram adds expense.
  • Effectors. Bursty attitude control thrusters are not the solution to those very strict pointing and stability requirements. Something else is needed. Magnetic torquers are out of the question given the mass of a large space telescope that is burdened with extra mass to combat flex and slosh. That limits fine attitude control to reaction wheels or control moment gyros. The Hubble and Webb space telescopes both use reaction wheels.
  • Ball bearings. Reaction wheels and control moment gyros use finely milled ball bearings. Finely milled ball bearings are not cheap, and the technology is dual purpose. The Soviet Union used to make rather lousy ball bearings for its submarines, thereby making them easy to hear underwater. International incidents occurred when European companies thought it would be a good idea (it wasn't) to sell their finely milled ball bearings to the Soviet Union.

What about sensors?

No single sensor does the job. Star trackers do not quite have the accuracy needed, and they are slow, nominally once a second per update, but sometimes with significantly larger gaps. Magnetometers reply on a closely planet with a well-mapped magnetic field, and aren't all that precise. Rate gyros have a dead reckoning problem.

These problems can be overcome by using multiple kinds of sensors. The drift that is inherent in rate gyros can be rectified by using the slow updates from a star tracker. Kalman filters do exactly that. Star trackers are telescopes, very good telescopes, but they do not qualify as "good enough" for the extremely precise attitude requirements of the Hubble and the Webb. While both the Hubble and the Webb do use star trackers for coarse attitude control, they use their own space telescopes for fine grain attitude. In particular, once coarse attitude control has aimed the telescope in more or less the right direction, those spacecraft look for a suitable guide star in the telescope's field of view and rotate so as to keep that guide star's position in the field of view fixed.

Both the Hubble and the Webb use gyros to estimate attitude between star tracker / guide star updates. The use of a Kalman filter addresses issues associated with bias, drift, and noise. Neither the Hubble nor the Webb use microelectromechanical systems (MEMS) gyros; they're nowhere close to "good enough", at least not yet. Neither use ring laser gyros or fiber optic gyros. Both have bias, stability, and accuracy issues. The Hubble uses gas bearing gyros while the Webb uses hemispherical resonator gyros. These are not cheap (not by a long shot), but when it comes to spacecraft as expensive as the Hubble or the Webb, cheaping out on gyros is a bad idea.

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    $\begingroup$ Great answer! Thanks for all those details $\endgroup$
    – ChrisR
    Mar 19, 2021 at 17:13
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GPS?

Yes but basically you have to have several (at least three) antennas that are widely spaced apart. You can either have separate GPS systems at each antenna and use simple trigonometry to calculate your attitude, or feed the the signals from all antennas to a fancy receiver that solves the whole problem at once.

Star trackers?

Quoting this answer to How are space telescopes stabilised to a perfect standstill which quotes Hubble Space Telescope; Pointing Control

The objects labeled Fine Guidance Sensors use CCDs at the edge of the Hubble's field of view to track stars:

The FGSs use starlight captured by the telescope’s mirrors to find and maintain a lock on guide stars to ensure that the spacecraft’s attitude does not change. One FGS can also be used as a scientific instrument to determine a star’s position with high accuracy. The level of stability and precision that the FGSs provide gives Hubble the ability to remain pointed at a target with no more than 0.007 arcsecond of deviation over extended periods of time. This is the same as holding a laser beam focused on Franklin D. Roosevelt’s head on a dime roughly 200 miles away — which is about the distance from Washington, D.C., to the Empire State Building in New York City — for 24 hours.

It may not be practical for your spacecraft application to have two 2.4 m diameter Hubble Space Telescopes oriented at 90 degrees but that's what I would do if I needed accurate determination of attitude of a spacecraft that wasn't rotating appreciably at all.

See also:

Other?

However, you might opt instead for three fiber optic gyroscopes. According to Wikipedia:

Like all other gyroscope technologies and depending on detailed FOG design, FOGs may require initial calibration (determining which indication corresponds to zero angular velocity).

So you may need at least a pair of modest star cameras to correct the integration errors that may arise.

Originally I'd thought that a ring laser or fiber optic gyroscope would be drift free and have essentially zero integration error because it seems to operate like an interference fringe-counting laser interferometer for linear position measurements (which basically don't gain/lose counts) but apparently their operation is more complex and real-world issues of laser phase noise and coherent backscattering within the fiber and other things I don't understand mean that these will always have a slow drift problem.

You are always going to need a star camera or some other method to "zero" your gyros and compensate for integration error.

Another other?

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    $\begingroup$ Spy satellites tend not to use ring laser gyros, fiber optics gyros, MEMS gyros, or atomic (quantum) inertial sensors. They use other types of gyros that are more reliable and more accurate -- and more expensive. The only difference between spy satellites and space telescopes is where they're looking. Spy satellites spy on the Earth while space telescopes spy on the universe. Turning a space telescope around (and changing its focus) would make for a fantastic spy satellite. Alternatively, turning a spy satellite around (and changing its focus) would make for a fantastic space telescope. $\endgroup$
    – David Hammen
    Mar 19, 2021 at 16:43
  • $\begingroup$ @DavidHammen: Spy satellites also need to be able to rotate fast enough to track a target without the image quality suffering due to vibration; most space telescopes (which generally look at things many orders of magnitude farther away) can't rotate fast enough for spysat use. $\endgroup$
    – Vikki
    Mar 19, 2021 at 22:14
  • $\begingroup$ @DavidHammen in my pranksat I used a collimator to prepare a virtual image for Hubble, but for a few seconds I was gearing up to insist that Hubble wouldn't have to refocus when looking down from its orbit until I got to the comment's author, at which point I decided to stop myself and reconsider. Wow that'a quite a lot of focus travel necessary to refocus on a "foreground" object only 570,000 meters away! $\endgroup$
    – uhoh
    Mar 20, 2021 at 9:35
  • $\begingroup$ @DavidHammen I've just asked Has Hubble ever focused on something close enough that it had to move away from being focused at infinity? $\endgroup$
    – uhoh
    Mar 20, 2021 at 9:44
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    $\begingroup$ @Vikki-formerlySean That's true, but there still are lots of similarities. There are enough similarities that one of the two spy satellites provided by the National Reconnaissance Office (NRO) to NASA is being turned into the Roman Space Telescope. $\endgroup$
    – David Hammen
    Mar 20, 2021 at 11:17
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It's probably the system used by the Gaia mission, which uses the astrometric telescope payload as its most precise sensor.

"The challenges for the AOCS design are to provide attitude control within a restricted pointing domain, due to thermal constraints, and to provide a fine pointing mode with relative pointing error (RPE) of a few milli-arcseconds (mas). The fine pointing mode needs to use the scientific payload as an AOCS sensor in order to measure angular rate to the accuracy required."

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