Jointly Deterministic and Stochastic Identification of Linear Systems Using Binary-Valued Observations

In this paper, identification of systems with binary-valued observations is investigated. Rather than estimating parameters under deterministic and stochastic frameworks separately, we introduce a joint framework in which the two frameworks play complementary roles in improving identification accuracy. It is shown that when uncertainty on the unknown parameter is large, the stochastic method may fail, but the worst-case method is effective in uncertainty reduction. On the other hand, the worst-case method becomes ineffective when the uncertainty becomes small, in fact it leaves an irreducible error and hence consistency is lost. This is where the stochastic framework becomes effective in achieving consistency and efficiency. This paper fully utilizes the strength of each framework to overcome shortcomings. Input design, threshold selection, and criteria for switching from one framework to another are developed.