An approach of Bayesian filtering for stochastic Boolean dynamic systems

This paper introduces an approach to estimate the true states for stochastic Boolean dynamic system (SBDS), where the state evolution is governed by Boolean functions with additive binary process noise while the measurement is an arbitrary function of the state yet with additive binary measurement noise. The problem of figuring out the true state using the only available noisy outputs is crucial for practical applications of Boolean dynamic system models, however, for such Boolean systems with wide background, there are no ready-to-use convenient tools like Kalman filter for linear systems. To resolve this challenging problem, an approach based on Bayesian filtering called Boolean Bayesian Filter (BBF) is put forward to estimate the true states of SBDS, and an efficient algorithm is presented for their exact computation. An index to evaluate the filtering performance, named estimation error rate, is put forward in this paper as well. In addition, extensive simulations via actual examples have illustrated the effectiveness of the proposed algorithm based on BBF.