My Math Forum Spacecraft attitude estimation

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 May 23rd, 2017, 12:41 AM #1 Newbie   Joined: May 2017 From: Belgium Posts: 1 Thanks: 0 Spacecraft attitude estimation Hi all, I'm studying aeronautical engineering and I'm making an error assessment of a star tracker (https://en.wikipedia.org/wiki/Star_tracker). I have made a simulation in matlab, this simulation generates a star image. This star image is used to estimate the attitude of the satellite after a pixel error has been added. Now I want to retrieve this added error from the attitude. I'm trying to do this with matlab by using the function fsolve. I need to create a cost function to use it in the fsolve function. This is were I'm stuck. Let me try to clarify this: 1- star image is generated 2- pixel error is added to these 2D star coordinates (error is a normal distribution) 3- these 2D star coordinates are transformed to 3D position vectors. 4- The 3D position vectors are used to calculate the estimated attitude. 5- trying to retrieve the added error from step 2, by using fsolve function in matlab. There are 2 star trackers, this means that their are 2 images generated and 2 attitudes are determined with the same error added. My plan to retrieve the error from the attitude: 1- find relative error between star trackers (done)(attitude quaternion 1 * attitude quaternion 2) 2- find the mean relative error (done) 3- find the standard deviation of the relative error (done) (this has to be used in step 4). 4- iterative approach (fsolve) a- choose standard deviation for startracker (guess) b- create Star tracker attitude c- calculate Star tracker relative error d- compare with step 3. and iterate. Step 4 is were i'm having trouble and I would like some help in creating this step and cost function. If you need extra information, please let me know. Kind regards, Sam Last edited by skipjack; May 23rd, 2017 at 09:57 AM.
May 25th, 2017, 02:54 AM   #2
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 Originally Posted by samcam Hi all, I'm studying aeronautical engineering and I'm making an error assessment of a star tracker (https://en.wikipedia.org/wiki/Star_tracker). I have made a simulation in matlab, this simulation generates a star image. This star image is used to estimate the attitude of the satellite after a pixel error has been added. Now I want to retrieve this added error from the attitude. I'm trying to do this with matlab by using the function fsolve. I need to create a cost function to use it in the fsolve function. This is were I'm stuck. Let me try to clarify this: 1- star image is generated 2- pixel error is added to these 2D star coordinates (error is a normal distribution) 3- these 2D star coordinates are transformed to 3D position vectors. 4- The 3D position vectors are used to calculate the estimated attitude. 5- trying to retrieve the added error from step 2, by using fsolve function in matlab. There are 2 star trackers, this means that their are 2 images generated and 2 attitudes are determined with the same error added. My plan to retrieve the error from the attitude: 1- find relative error between star trackers (done)(attitude quaternion 1 * attitude quaternion 2) 2- find the mean relative error (done) 3- find the standard deviation of the relative error (done) (this has to be used in step 4). 4- iterative approach (fsolve) a- choose standard deviation for startracker (guess) b- create Star tracker attitude c- calculate Star tracker relative error d- compare with step 3. and iterate. Step 4 is were i'm having trouble and I would like some help in creating this step and cost function. If you need extra information, please let me know. Kind regards, Sam
You have explained the situation well, but i'm not sure what exactly you are stuck on with applying fsolve. Is it that you aren't sure how to select the right data to be used with the function? Or are you having programming difficulties in general?

Likely you will need to use a couple of for loops to first populate your vectors, and then use those within your equation before working with fsolve, is this the tricky part? A snippet of code may be helpful .

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