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In the application of navigation system, networked system, and manufacturing process, incomplete data is unavoidable, which may reduce the performance and stability of the systems. It is a crucial and challenging task when the nonlinear fractional-order system is under incomplete data. As a kind of incomplete data, missing measurements assume that the missing rates of multiple sensors are independent of each other. In order to provide a more reliable and robust state estimation algorithm, a nonlinear fractional-order Kalman filtering algorithm considering both the missing measurements and stochastic nonlinearities is proposed in this paper. Then, the convergence and stability of the proposed filter are analyzed. In addition, sufficient conditions have been investigated to guarantee the stochastic stability. Finally, the effectiveness of the state estimator is verified by two numerical examples.