Linear systems identification from random threshold binary data

A new identification problem of estimating parameters of linear dynamic 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 mainly for generating random numbers. Strong consistency of parameters estimate from low-cost output binary observations is proved, assuming deterministic input signal of a finite duration. Possibilities of relaxing the assumption used in the theoretical part of the paper are considered by means of simulations