Abstract (16.0: Kalman filter) The Kalman filter is located as in the following $(\sharp)$:

$(\sharp): \mbox{Statistics} \left\{\begin{array}{l} \mbox{Fisher's maximum likelihood method} &{\;} \xrightarrow[\scriptsize{\mbox{ usually deterministic}}]{\scriptsize{\mbox{$+$causality}}} \mbox{regression analysis} \\ \\ \mbox{Bayes' method} & {\;} \xrightarrow[\scriptsize{\mbox{ non-deterministic}}]{\scriptsize{\mbox{$+$causality}}} \mbox{Kalman filter} \end{array}\right.$

Thus, I can not emphasize too much the importance of the Kalman filter. Though Kalman filter belongs to Bayes' statistics, this fact may not be a common sense. This present state is due to the confusion between Fisher's statistics and Bayes' statistics. I hope that such confusion should be clarified by the above $(\sharp)$ (based on quantum language). This chapter is extracted from the following paper:
 $(\sharp):$ S. Ishikawa, K. Kikuchi: Kalman filter in quantum language,
 $(\sharp):$ S. Ishikawa, Mathematical Foundations of Measurement Theory, arXiv:1404.2664 [math.ST]

Again recall that, as mentioned in $\S$1.1, the main purpose of this book is to assert the following figure 1.1:
Fig.1.1: the location of "quantum language" in the world-views
This(particularly, ⑦--⑨) implies that quantum language has the following three aspects: $$\left\{\begin{array}{ll} \mbox{ ⑦ :the standard interpretation of quantum mechanics} \\ \mbox{ \qquad (i.e., the true colors of the Copenhagen interpretation) } \\ \\ \mbox{ ⑧ : the final goal of the dualistic idealism (Descartes=Kant philosophy) } \\ \\ \mbox{ ⑨ : theoretical statistics of the future } \end{array}\right.$$