  The paper addresses state estimation for discrete-time systems with binary
(threshold) measurements by following a Maximum A posteriori Probability (MAP)
approach and exploiting a Moving Horizon (MH) approximation of the MAP
cost-function. It is shown that, for a linear system and noise distributions
with log-concave probability density function, the proposed MH-MAP state
estimator involves the solution, at each sampling interval, of a convex
optimization problem. Application of the MH-MAP estimator to dynamic estimation
of a diffusion field given pointwise-in-time-and-space binary measurements of
the field is also illustrated and, finally, simulation results relative to this
application are shown to demonstrate the effectiveness of the proposed
approach.
