I'm trying to understand well the kalman filter, as a result i'm having this question : Why do we represent noise with a Gaussian ? what does this really mean intuitively ?
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$\begingroup$ This may be more ontopic on Signal Processing. Do you want us to migrate your question there? Either way, I think you can improve your question by including some of your own thoughts, and which resources you have consulted. (This does sound like a rather basic question, so I assume it's covered in the pertinent textbooks.) $\endgroup$– RaphaelCommented Apr 27, 2017 at 19:08
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$\begingroup$ Yeah it is a basic question I think, I read the original paper of kalman 1960 where it's written that this is an assumption, but I can't figure out why I don't find it that intuitive. And yeah thanks for proposing to migrate the question i would like it if you do ! $\endgroup$– Mohamed BenmahdjoubCommented Apr 28, 2017 at 12:56
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1$\begingroup$ General remark: original research articles are usually a poor learning resource. In particular, assumptions common to the field won't be discussed. Textbooks on the matter (often written decades later) will discuss such things, so I recommend you check one out. $\endgroup$– RaphaelCommented Apr 28, 2017 at 13:39
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1$\begingroup$ I might have some intuitions on Gaussian noise in general to share, but I'd like to know that you want Gaussian noise definition in Kalman filtering context only? $\endgroup$– MimSaadCommented Apr 28, 2017 at 17:38
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1$\begingroup$ this answer helped me understand why. But more of a data based answer than intuition. $\endgroup$– harshknCommented Apr 29, 2017 at 2:46
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1 Answer
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The Gaussian assumption in the case of the Kalman Filter assists with solving the problem.
Since a Gaussian Random Vector stays Gaussian after any linear operator it means for the Kalman model if the initialization is Gaussian the whole process is Gaussian.
Since the Gaussian distribution is defined by the 1st and the 2nd moments it also means that if we solve the the Least Squares problem we get the optimal solution.