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Inertial navigation systems (INS) are vital for airplanes, spacecraft, missiles, surface or subsurface vessels operating at sea where continuous, accurate and reliable position information, as well as heading, attitude, acceleration and velocity components of the vehicle are provided. INS have the inherent capability of being autonomous; but however, the errors in position coordinates increase unboundedly as a function of time. On the other hand, satellite navigation systems, as well as advanced radio navigation systems, which are available today and which shall be available in the near future, provide very accurate and frequently updated position information. Unfortunately, these data are prone to jamming or being lost due to the limitations of electromagnetic waves, which form the fundamental of their operation. Also, they are not usable for under-sea or under-Earth applications. To eliminate these deficiencies, INS are integrated with satellite or hyperbolic navigation systems that also obtain intermittent position information. This study gives a mathematical treatise on such an integrated system. As a feasible example, a search and rescue aircraft, involved in an expanding area search operation, equipped with strapdown INS and a Global Positioning System is simulated. The INS use two sets of acceleration and rate of rotation sensors. The model used indicates that the error in position information becomes large in time, otherwise it is limited to acceptably low levels if correction information from Global Positioning System is obtained. Improved performance of the INS by the proposed integration can be utilized to use low-cost sensor elements without the loss of accuracy, thereby making INS a feasible outfit for general purposes.