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, the Gaussian belief is represented by their moments, whereas in Information Filter, the Gaussian belief is represented by the canonical form. The canonical form is comprised of an information matrix ($\Omega$) and an information vector ($\xi$).
As we all know, the name Kalman Filter is after Rudolf E. Kálmán, one of the primary developers of this theory.
Now I want to know where the name information filter came from? Why it is called information filter? What type of information is attached to this filter? Is there any significance behind the nomenclature?
I have the same question about the information matrix and information vector. Is there any significance behind the nomenclature?
I already read Probabilistic Robotics by Sebastian Thrun. Chapter 3 Gaussian filter, in subsection 3.4 The Information Filter. There are many equations and theories but that does not tell us about the nomenclature.