A new identification problem of estimating parameters of linear dynami
c systems from random threshold binary observations of its output and
input is stated, The only available data are collected as a result of
checking whether a signal reached a randomly specified threshold at a
randomly chosen instant of time. The proposed estimation algorithm is
based on the celebrated von Neumann theorem, which was earlier used ma
inly for generating random numbers. Strong consistency of parameters e
stimate from few-cost output binary observations is proved, assuming d
eterministic input signal of a finite duration, Possibilities of relax
ing the assumption used in the theoretical part of the paper are consi
dered by means of simulations.