Attitude sensor noise

I want to simulate attitude sensor's noise in attitude control of a
three axis stabilized spaecraft.
In attitude sensor's catalog the noise of sensor is whritten in term
angle, for example (2'). I dont know what this means and how i should
use this information in simulation for my attitude parameters (Euler
angles or Quaternions).
If i use a sun sensor and an earth sensor whit specified noise as
mentioned above what is the noise in three attitude parameters.
In attitude sensor's catalog we see phrases "1 sigma" or "3 sigma",
what is the meaninig and difference between this two phrase?
Thancks.

Amir Hosein Tavakoli wrote:
I want to simulate attitude sensor's noise in attitude control of a
three axis stabilized spaecraft.
In attitude sensor's catalog the noise of sensor is whritten in term
angle, for example (2'). I dont know what this means and how i should
use this information in simulation for my attitude parameters (Euler
angles or Quaternions).

What sort of attitude sensor?
' is the abbreviation for "minutes" (or is is seconds), 1/60th of a degree.
Seconds is 1/3600th of a degree.

--
http://inquisitor.i.am/ | | Ian Stirling.
---------------------------+-------------------------+--------------------------
"Don't count the humans out until the last one is dead and you have
hacked its body to bits and eaten it" -- John Ringo.

Amir Hosein Tavakoli wrote:
I want to simulate attitude sensor's noise in attitude control of a
three axis stabilized spaecraft.
In attitude sensor's catalog the noise of sensor is whritten in term
angle, for example (2'). I dont know what this means and how i should
use this information in simulation for my attitude parameters (Euler
angles or Quaternions).
If i use a sun sensor and an earth sensor whit specified noise as
mentioned above what is the noise in three attitude parameters.
In attitude sensor's catalog we see phrases "1 sigma" or "3 sigma",
what is the meaninig and difference between this two phrase?
Thancks.


Take the raw sensor output, and add a "random" signal to is that
averages out to 0. Almost any attitude sensor that gives an absolute
angle of something relative to something else (an "observer") will have
some sort of filter to reduce this noise's effect on the attitude estimate.

The single "tick" - ' means arc-minutes. Divide by 60 to get
degrees. The double tick - " means arc-seconds. Divide by 3600 to get
degrees.

Assuming that the noise is described as a "normal" distribution,
sigma is the accepted symbol for standard deviation. 1 sigma refers to
one standard deviation. This is a typical way of describing noise
level. If your attitude sensor has a noise level of 2 arc-minutes
1-sigma, that means that the standard deviation of the angle
measurements the sensor gives will be .03333 degrees. 3-sigma is just
three times this. If it says the sensor is 2 arc-minutes, 3-sigma, this
is a much "cleaner" with a standard deviation of the measurement of
..01111 degrees. This would be a pretty respectable noise level for a
geosynchronus Earth sensor, actually. Maybe I ought to get the catalog
you're looking at...


Of course, while this sort of specification is typically a good
starting place, in reality the noise characteristics need to be known in
more detail. For instance, the frequency spectrum of the noise signal
can be of interest. At some point, low-frequency "noise" stops looking
like "noise" and starts looking like a bias. And this is just the tip of
the iceberg when you get down to the nitty-gritty of design and
performance analysis.


Any good book with a good section on spacecraft attitude
determination (sorry, I have no publically-available references handy)
will be able to elaborate on this to whatever degree you want. Books on
statistics will give you the information, but it will take a long time
to wheedle out the three or four things you need out of a generalized
statistics book.

I would also caution you, if you are analyzing something that will
actually end up being built (instead of a study or a homework problem),
to keep real tight oversight on your sensor vendor. Most of the attitude
determination problems that I have experienced, or heard about, revolve
around observers not meeting their stated specifications. You would
think the Earth, or the Sun, would be pretty easy to find and point at,
but apparently it's the hardest thing in the world!


Brett

Brett Buck wrote in message ...
Amir Hosein Tavakoli wrote:
I want to simulate attitude sensor's noise in attitude control of a
three axis stabilized spaecraft.
In attitude sensor's catalog the noise of sensor is whritten in term
angle, for example (2'). I dont know what this means and how i should
use this information in simulation for my attitude parameters (Euler
angles or Quaternions).
If i use a sun sensor and an earth sensor whit specified noise as
mentioned above what is the noise in three attitude parameters.
In attitude sensor's catalog we see phrases "1 sigma" or "3 sigma",
what is the meaninig and difference between this two phrase?
Thancks.


Take the raw sensor output, and add a "random" signal to is that
averages out to 0. Almost any attitude sensor that gives an absolute
angle of something relative to something else (an "observer") will have
some sort of filter to reduce this noise's effect on the attitude estimate.

The single "tick" - ' means arc-minutes. Divide by 60 to get
degrees. The double tick - " means arc-seconds. Divide by 3600 to get
degrees.

Assuming that the noise is described as a "normal" distribution,
sigma is the accepted symbol for standard deviation. 1 sigma refers to
one standard deviation. This is a typical way of describing noise
level. If your attitude sensor has a noise level of 2 arc-minutes
1-sigma, that means that the standard deviation of the angle
measurements the sensor gives will be .03333 degrees. 3-sigma is just
three times this. If it says the sensor is 2 arc-minutes, 3-sigma, this
is a much "cleaner" with a standard deviation of the measurement of
.01111 degrees. This would be a pretty respectable noise level for a
geosynchronus Earth sensor, actually. Maybe I ought to get the catalog
you're looking at...


Of course, while this sort of specification is typically a good
starting place, in reality the noise characteristics need to be known in
more detail. For instance, the frequency spectrum of the noise signal
can be of interest. At some point, low-frequency "noise" stops looking
like "noise" and starts looking like a bias. And this is just the tip of
the iceberg when you get down to the nitty-gritty of design and
performance analysis.


Any good book with a good section on spacecraft attitude
determination (sorry, I have no publically-available references handy)
will be able to elaborate on this to whatever degree you want. Books on
statistics will give you the information, but it will take a long time
to wheedle out the three or four things you need out of a generalized
statistics book.

I would also caution you, if you are analyzing something that will
actually end up being built (instead of a study or a homework problem),
to keep real tight oversight on your sensor vendor. Most of the attitude
determination problems that I have experienced, or heard about, revolve
around observers not meeting their stated specifications. You would
think the Earth, or the Sun, would be pretty easy to find and point at,
but apparently it's the hardest thing in the world!


Brett


Thancks for your answer to my questions.
My question wasn't the meaning of "thick". see the characteristics
of some attitude sensor at "http://www.optecs.ru/senser_e.htm" and my
questions a
What sensors i should use for full attitude determination of a
spacecraft; three attitude parameters for example euler angles or 3 of
quaternions ?
If i use one or two of these sensors how i should use the noise of
these sensors in simulation? What is the noise in attitude parameters
( euler angles or ...) in control law that includes three attitude
parameters?

Amir Hosein

Amir Hosein Tavakoli wrote:
Brett Buck wrote in message ...

Amir Hosein Tavakoli wrote:

I want to simulate attitude sensor's noise in attitude control of a
three axis stabilized spaecraft.
In attitude sensor's catalog the noise of sensor is whritten in term
angle, for example (2'). I dont know what this means and how i should
use this information in simulation for my attitude parameters (Euler
angles or Quaternions).
If i use a sun sensor and an earth sensor whit specified noise as
mentioned above what is the noise in three attitude parameters.
In attitude sensor's catalog we see phrases "1 sigma" or "3 sigma",
what is the meaninig and difference between this two phrase?
Thancks.


Take the raw sensor output, and add a "random" signal to is that
averages out to 0. Almost any attitude sensor that gives an absolute
angle of something relative to something else (an "observer") will have
some sort of filter to reduce this noise's effect on the attitude estimate.

The single "tick" - ' means arc-minutes. Divide by 60 to get
degrees. The double tick - " means arc-seconds. Divide by 3600 to get
degrees.

Assuming that the noise is described as a "normal" distribution,
sigma is the accepted symbol for standard deviation. 1 sigma refers to
one standard deviation. This is a typical way of describing noise
level. If your attitude sensor has a noise level of 2 arc-minutes
1-sigma, that means that the standard deviation of the angle
measurements the sensor gives will be .03333 degrees. 3-sigma is just
three times this. If it says the sensor is 2 arc-minutes, 3-sigma, this
is a much "cleaner" with a standard deviation of the measurement of
.01111 degrees. This would be a pretty respectable noise level for a
geosynchronus Earth sensor, actually. Maybe I ought to get the catalog
you're looking at...


Of course, while this sort of specification is typically a good
starting place, in reality the noise characteristics need to be known in
more detail. For instance, the frequency spectrum of the noise signal
can be of interest. At some point, low-frequency "noise" stops looking
like "noise" and starts looking like a bias. And this is just the tip of
the iceberg when you get down to the nitty-gritty of design and
performance analysis.


Any good book with a good section on spacecraft attitude
determination (sorry, I have no publically-available references handy)
will be able to elaborate on this to whatever degree you want. Books on
statistics will give you the information, but it will take a long time
to wheedle out the three or four things you need out of a generalized
statistics book.

I would also caution you, if you are analyzing something that will
actually end up being built (instead of a study or a homework problem),
to keep real tight oversight on your sensor vendor. Most of the attitude
determination problems that I have experienced, or heard about, revolve
around observers not meeting their stated specifications. You would
think the Earth, or the Sun, would be pretty easy to find and point at,
but apparently it's the hardest thing in the world!


Brett



Thancks for your answer to my questions.
My question wasn't the meaning of "thick".



????? I don't understand this at all.


see the characteristics
of some attitude sensor at "http://www.optecs.ru/senser_e.htm" and my
questions a
What sensors i should use for full attitude determination of a
spacecraft; three attitude parameters for example euler angles or 3 of
quaternions ?


Depends. Since the you link to sun, star, and earth sensors, I have
no idea at what you want to point.

Assuming you want to point at the Earth, a standard system would be
a inertial reference assembly using gyros, integrated to get a
continually-updated reference (in say, quaternion notation). This
reference would then be compared to Earth sensor output, a difference
calculated, some sort of filter applied, and then an reference update
quaternion formed. This would then be used to update the reference
quaternion with a quaternion multiplication. Pitch would update pitch,
and roll would update roll. Roll times orbit rate would be used to
update the yaw reference in classical gyrocompassing. If you are clever,
you can also determine the pitch and yaw gyro drift - proof is left to
the reader.

The filtering style is up to you, and depends on the noise
characteristics of the sensors, and the rewuired performance.

If you just use the observers raw, it helps to formulate a
quasi-intertial reference using conservation of angular momentum to
estimate the rates by keeping track of the actuator activity and mass
properties to estimate the rate changes. Integrate these like they were
real gyro data, and then you can still apply a filter to the observers.
This can be made to work acceptably well for low-performance systems,
but it couples controls performance, actuator modeling, and attitude
knowledge together, which is generally not the best way to go.

If i use one or two of these sensors how i should use the noise of
these sensors in simulation? What is the noise in attitude parameters
( euler angles or ...) in control law that includes three attitude
parameters?


How noise effects it depends entirely on the detailed system
design. Without a detailed design, it's not possible to analyze the
noise effects.

Brett