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This work presents distributed predictor and filter without feedback for nonlinear stochastic uncertain system with correlated noises. Firstly, for the problem that the process noise and measurement noise are correlated, the two-step prediction theorem based on projection theorem is used to replace the one-step prediction theorem, and the two-step prediction value of a single sensor is obtained. Secondly, the two-step prediction value of each sensor state is used as the measurement information to modify the distributed fusion predictor to obtain the distributed fusion prediction value. Then, according to the projection theorem, the prediction value of distributed fusion is used as measurement information to modify the filtering value of distributed fusion. Finally, the Cubature Kalman filter (CKF) algorithm is used to implement the algorithm proposed in this paper. By comparison with existing methods, the algorithm proposed in this paper solves the problem that existing methods cannot handle state estimation and prediction problems for nonlinear multi-sensor stochastic uncertain systems with correlated noises.