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This paper analyzes stochastic stability and performance of discrete-time Cubature Kalman Filtering (CKF). The main contribution is (1) Boundedness analysis based on the constructor is proposed. Through Taylor expansion and simplifications of the non-linear transfer function, the constructor expression based on the variance and the structure error can be got. Through boundedness analysis on various subitems of the constructor expression, it is proved that when the initial error and variance are small enough, the estimation error remains bounded. (2) It is shown that the performance difference between CKF (Cubature Kalman Filtering) and Unscented Kalman Filtering (UKF) is the capture ability of the high items in the Taylor expansion. The performance is also related to the dimensions. Simulations are conducted to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]