Adaptive Real-Time Filter For Partially-Observed Boolean Dynamical Systems

Partially-Observed Boolean dynamical systems (POBDS) are a general class of nonlinear state-space models consisting of a hidden Boolean state process observed through an arbitrary noisy mapping to a measurement space. The huge uncertainty present in systems/processes, along with the time-limit constraints necessitate real-time or online joint state and parameter estimation of POBDS. In this manuscript, we present a real-time joint state and parameter estimation framework for POBDS. The proposed framework relies on complete-sufficient statistic of parameters, where joint state and parameter estimation is achieved based on the combination of online expectation-maximization method, and the optimal MMSE state estimator for POBDS, called Boolean Kalman filter. The performance of the proposed method is assessed through a POBDS model for Boolean gene regulatory networks observed through noisy measurements.