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In this paper, a new distributed Kalman filter scheme is proposed to estimate actuator faults for deep space formation flying satellites. The method can also be applied to large-scale systems such as sensor networks and power systems. For a hierarchical large-scale system, the overlapping block-diagonal state space (OBDSS) representation of the system is transformed into our proposed constrained-state block-diagonal state space (CSBDSS) model. The proposed model becomes purely diagonal which simplifies and allows the distributed implementation of the Kalman filters. The constrained-state condition needs to be satisfied at each Kalman filtering iteration which is shown to be equivalent to solving local constrained optimization cost functions. Simulation results presented confirm the effectiveness of our proposed analytical work.