State estimation of systems with binary-valued observations

This paper studies problems of state estimation of systems whose outputs are measured by binary-valued sensors. Signal estimation is first explored under an over-sampling method. Strong convergence and convergence rates of signal estimators are established. Algorithms are developed for estimation of initial states based on signal estimation results, when state equations are noise free. It is shown that the algorithms are asymptotically efficient in the sense that they achieve the Cramer-Rao lower bounds asymptotically when over-sampling rates become large. These results are then extended to more general scenarios of smoothing, filtering, and prediction problems.