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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. |
#2
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Attitude sensor noise
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. |
#3
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Attitude sensor noise
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 |
#4
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Attitude sensor noise
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 |
#5
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Attitude sensor noise
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 |
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