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Summary  This paper deals with state estimation of a spatially distributed system given noisy measurements from pointwise‐in‐time‐and‐space threshold sensors spread over the spatial domain of interest. A  maximum a posteriori probability  (MAP) approach is undertaken and a  moving horizon  (MH) approximation of the MAP cost function is adopted. It is proved that, under system linearity and log‐concavity of the noise probability density functions, the proposed MH‐MAP state estimator amounts to the solution, at each sampling interval, of a convex optimization problem. Moreover, a suitable centralized solution for large‐scale systems is proposed with a substantial decrease of the computational complexity. The latter algorithm is shown to be feasible for the state estimation of spatially dependent dynamic fields described by  partial differential equations  via the use of the  finite element  spatial discretization method. A simulation case study concerning estimation of a diffusion field is presented in order to demonstrate the effectiveness of the proposed approach. Quite remarkably, the numerical tests exhibit a  noise‐assisted  behavior of the proposed approach in that the estimation accuracy results optimal in the presence of measurement noise with non‐null variance.

MAP moving horizon estimation for threshold measurements with application to field monitoring