Kalman filter in quantum language

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.