Optimal finite-horizon sensor selection for Boolean Kalman Filter

Partially-observed Boolean dynamical systems (POBDS) are large and complex dynamical systems capable of being monitored through various sensors. However, time, storage, and economical constraints may impede the use of all sensors for estimation purposes. Thus, developing a procedure for selecting a subset of sensors is essential. The optimal minimum mean-square error (MMSE) POBDS state estimator is the Boolean Kalman Filter (BKF) and Smoother (BKS). Naturally, the performance of these estimators strongly depends on the choice of sensors. Given a finite subsets of sensors, for a POBDS with a finite observation space, we introduce the optimal procedure to select the best subset which leads to the smallest expected mean-square error (MSE) of the BKF over a finite horizon. The performance of the proposed sensor selection methodology is demonstrated by numerical experiments with a p53-MDM2 negative-feedback loop gene regulatory network observed through Bernoulli noise.