Over-Bounding Integrated Ins/Gnss Output Errors. (Paperback)

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 overbounding 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.