This thesis examines issues associated with the integrity risk over-bounding in INS/GNSS integration. The integrity risk over-bounding requires three issues to be considered: Modeling and over-bounding of inertial sensor output errors; modeling and over-bounding of GNSS signal errors; and the over-bounding of the output of nonlinear transformations of random variables. While considerable amaount of work has been done in modeling and over-bounding GNSS errors, this thesis explored the other two relatively new issues. This thesis develops a methodology for doing this whereby the varying and higher order process in the actual navigation solution are over-bounded using a lower-order, stationary time-domain model that is a conservative approximation of the actual noise process. This requires developing and validating unified mathematical models for over-bounding the behavior of the post calibration residual errors of inertial sensors. The mathematical models of the INS are a set of nonlinear stochastic differential equations. The nonlinearities of the system come from two parts which need to be handled in the over-bounding: the nonlinear transformation of the sensor errors, and the nonlinear transformation of the previous navigation states. A methodology for analyzing and over-bounding nonlinear transformations of random variables which occur in INS systems is developed. It is shown that the INS system output errors can be over-bounded by Gaussian distributions with an inflated variance. How this approach can be used to over-bound errors in simple vehicle navigation and guidance applications is shown by examples.