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In the initialization process of the strapdown initial navigation system (SINS) of a launched weapon before its release, transfer alignment (TA) uses the data from the aircraft SINS or other navigation aids. However, stochastic measurement aid information is unreliable in practical integrated navigation system. The paper is the filtering stability for a class of nonlinear stochastic systems with intermittent measurements when the arrival of the observations is described by Bernoulli independent and identically distributed process. The stochastic stability of the a novel Gaussian filter through presenting Gaussian approximate about one step posterior predictive probability density function (PDF) of the state and intermittent measurements is investigated. The estimation errors remain bounded if the system satisfies some sufficient conditions, and its error covariance matrices are statistically convergent by providing the existence of a super-threshold value for the intermittent measurement probability. Finally, a nonlinear integrated navigation method based on the proposed filter is presented, and the ground vehicle test of missile-board SINS is given to illustrate the effectiveness of the investigated techniques.