Relation between Wiener and Kalman filtering What is the relationship from an historical point of view between Kalman and Wiener filtering? Can the first be logically seen a consequence of the latter?
 A: Dan Simon, in his book Optimal State Estimation, discusses this quite comprehensively.

Until 1960, Wiener filtering was the state of the art in signal estimation. The paradigm of signal estimation was shattered with the publication of Rudolph Kalman’s work and related papers in the early 1960s, but it is still worthwhile understanding Wiener filtering because of its historical place in the history of signal estimation. Furthermore, Wiener filtering is still very useful in signal processing and communication theory.

And, in a later chapter:

Wiener filtering addresses the problem of designing a linear, time invariant filter to extract a signal from noise, approaching the problem from the frequency domain perspective. Norbert Wiener invented his filter as part of the World War I1 effort for the United States. He published his work on the problem in 1942, but it was not available to the public until 1949 [Wie64]. His book was known as the “yellow peril” because of its mathematical difficulty and its yellow cover [Deu65, page 1761. Andrey Kolmogorov actually solved a more general problem earlier (1941), and Mark Krein also worked on the same problem (1945). Kolmogorov’s and Krein’s work was independent of Wiener’s work, and Wiener acknowledges that Kolmogorov’s work predated his own work [Wie56]. However, Kolmogorov’s and Krein’s work did not become well known in the Western world until later, since it was published in Russian [Ko141]. A nontechnical account of Wiener’s work is given in his autobiography [Wie56]. [...] The Wiener filter is based on frequency domain analyses, whereas the Kalman filter that we derive later is based on time domain analyses. Nevertheless, both filters are optimal under their own assumptions. Some problems are solvable by both the Wiener and Kalman filter methods, in which case both methods give the same result.

And finally, in the appendix:

Wiener and Kolmogorov’s work in the 1940s was similar to the Kalman filter (see Section 3.4). However, their work did not arise within the context of state-space theory. It is more statistical in nature than Kalman filtering, and requires knowledge of covariances such as E(ziz7) and E(yiz7). In order to implement a Wiener filter in a closed form, the theory assumes that the state and measurements are stationary random processes. Furthermore, Wiener filtering is a steady-state process; that is, it assumes that the measurements have been generated from the infinite past. The 1950s saw a lot of work on relaxing the assumptions of the Wiener filter [Zad50, Boo521. NASA spent several years investigating Wiener theory in the 1950s, but could not see any practical way to implement it in space navigation problems [Sch81].
Later in the 1950s, work began on replacing the covariance knowledge required by the Wiener filter with state-space descriptions. The results of this work were algorithms that are very close to the Kalman filter as we know it today. Work in this direction at Johns Hopkins University was motivated by missile tracking and appeared in unpublished work as early as 1956 [Spa88]. Peter Swerling’s work at the RAND Corporation in the late 1950s was motivated by satellite orbit estimation [Swe59]. Swerling essentially developed (and published in 1959) the Kalman filter for the case of noise-free system dynamics. Furthermore, he considered nonlinear system dynamics and measurement equations (because of his application). Similar to the dispute between Gauss and Legendre regarding credit for the development of least squares, there has been a smaller dispute regarding credit for the development of the Kalman filter.

...and then he goes on to discuss all the people who essentially developed the Kalman filter before Kalman.
