This paper considers a distributed state estimation problem for multi-agent systems under state inequality constraints. We first give a distributed estimation algorithm by projecting the consensus estimate with help of the consensus-based Kalman filter (CKF) and projection on the surface of constraints. The consensus step performs not only on the state estimation but also on the error covariance obtained by each agent. Under collective observability and connective assumptions, we show that consensus of error covariance is bounded. Based on the Lyapunov method and projection, we provide and prove convergence conditions of the proposed algorithm and demonstrate its effectiveness via numerical simulations.
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