Distributed moving horizon estimation via dual decomposition

This paper presents a distributed moving horizon estimator (DMHE) based on dual decomposition. The DMHE is equivalent to a centralized Kalman filter and allows the distributed implementation of any centralized controller. This equivalence is achieved by formulating the estimation problem as a suitable convex optimization problem. The cost function is defined on a sliding window involving a finite number of past measurements. These measurements are allocated to the estimators without requiring local observability of the complete state. The communication topology of the estimators is represented by a graph and reflected in the optimization problem by additional consensus constraints. A subgradient method is used for solving the decoupled dual optimization problem. The resulting distributed algorithm alternates between updating and transmitting the primal and dual variables. Simulation results of a closed-loop weir system are provided in order to show the main features of the proposed method.