  Recently, we proposed measurement theory ( or. quantum language) as a
linguistic turn of quantum mechanics (with the Copenhagen interpretation). This
theory has a great power of scientific descriptions. In fact, we have continued
asserting that even statistics can be described in terms of measurement theory.
Thus, we believe that quantum language is future statistics (i.e., statistics
will develop into quantum language). However, now we think that our arguments
were too abstract and philosophical, that is, we should have presented concrete
examples much more. Thus, in this paper, we show that the calculation of Kalman
filter is more understandable in terms of quantum language than in terms of
usual statistics. For this, we devote ourselves to statistical measurement
theory, in which the Bertrand paradox is discussed.
