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We all know Information Filter is a dual representation of kalman filter. The main difference between information filter and kalman filter is the way the Gaussian belief is represented. In kalman filter Gaussian belief is represented by their moments where as in Information filter Gaussian belief is represented by canonical form. Canonical form is comprised with a information matrix($\Omega$) and a information vector ($\xi)$.

As we all know the name kalman filter name after Rudolf E. Kálmán, one of the primary developers of its theory.

Now I want to know that from where the name information filter came?Why it is called information filter?what type of information attached with this filter? Is there any signification behind the nomenclature?

I have the same question about information matrix and information vector. Is there any signification behind the nomenclature?

I already read Probabilistic Robotics by Sebestian Thrun. Chapter 3 Gaussian filter ,in the subsection 3.4 The information Filter. There are many equations and theories but that does not tell us about the nomenclature.

Probabilistic Robotics

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  • $\begingroup$ A quick note, namely a Kalman filter is also called a linear quadratic estimator(LQE), which is the dual of the linear quadratic regulator (LQR). $\endgroup$
    – fibonatic
    Nov 3, 2018 at 0:08
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    $\begingroup$ What is the relation between my question and your answer? $\endgroup$
    – Encipher
    Nov 5, 2018 at 20:08
  • $\begingroup$ ai.stackexchange.com/q/8796/1794 $\endgroup$
    – D.W.
    Nov 30, 2022 at 5:49

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I think the answer is that a covariance matrix represents uncertainty. As its singular values grow, uncertainty grows as well. On the other hand, if you look at its inverse you see (of course) the opposite. As singular values of the covariance matrix inverse grow, uncertainty decreases. In other words, uncertainty decreases when more valuable information is gathered. That is why the inverse of the covariance is called information. Since the filter propagates this matrix and its associated vector it is called an information filter.

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  • $\begingroup$ Ok. You have a valid point. But can you explained it more precisely. I am little bit confused with your answer. $\endgroup$
    – Encipher
    Nov 6, 2018 at 21:35
  • $\begingroup$ what are the singular values of covariance matrix? $\endgroup$
    – drerD
    Nov 18, 2018 at 20:08

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