  In this paper, we present a new approach to distributed moving horizon
estimation for constrained nonlinear processes. The method involves
approximating the arrival costs of local estimators through a recursive
framework. First, distributed full-information estimation for linear
unconstrained systems is presented, which serves as the foundation for deriving
the analytical expression of the arrival costs for the local estimators.
Subsequently, we develop a recursive arrival cost design for linear distributed
moving horizon estimation. Sufficient conditions are derived to ensure the
stability of the estimation error for constrained linear systems. Next, we
extend the arrival cost design derived for linear systems to account for
nonlinear systems, and a partition-based constrained distributed moving horizon
estimation algorithm for nonlinear systems is formulated. A benchmark chemical
process is used to illustrate the effectiveness and superiority of the proposed
method.
