GPS is the most widely used satellite navigation system. By design, there is no provision for real time integrity information within the Standard Positioning Service (SPS). However, in safety critical sectors like aviation, stringent integrity performance requirements must be met. This can be achieved using special augmentation systems or at the user sensor level through Receiver Autonomous Integrity Monitoring (RAIM) or both. RAIM, which is considered as the most cost effective method relies on data consistency, and therefore requires redundant measurements for its operation. An external aid to provide this redundancy can be in the form of an Inertial Navigation system (INS). This should enable continued performance even during RAIM holes (when no redundant satellite measurements are available). However, the integrated system faces the risk of failures generated at different levels of the system, in the operational environment and at the user sensor (receiver) level. This thesis addresses integrated GPSIINS architectures, the corresponding failure modes and the sensor level integrity algorithms used to protect users from such failure modes. An exhaustive literature review is conducted to identify the various failure modes. These are then grouped into classes based on their characteristics and a mathematical (failure) model is specified for each class. For the analysis of failures, a simulation of a typical aircraft trajectory is developed, including the capability to generate raw measurements from GPS and the INS. The simulated GPS and INS measurements for the aircraft are used to evaluate the performance of the current integrity algorithms. Their performances are assessed for the most difficult case of failures; slowly growing errors (SGE), and shown to be inadequate (i.e. a considerable period of time is required for detection). This is addressed by developing a new algorithm based on the detection ofthe growth rate ofa typical test statistic (assuming a single failure at a time). Results show that the new algorithm detects slowly growing ramp-type errors faster than the current methods, with a forty percent improvement in the time it takes to detect the worst case SGE. The algorithm is then extended to include detection of multiple SGEs for which a new tightly coupled method referred to as the 'piggyback architecture' is proposed. This method provides the novel capability of detecting all failures including those affecting the INS. The proposed algorithms are validated with real GPS and INS data. In this way, the integrity performance of the integrated system is enhanced against the worst case failures with a detection time that is beneficial for the achievement of stringent time-to-alert requirements. A practical implementation would then comprise of the use of the rate detector algorithm alongside the current methods.