The aviation community has very stringent navigation integrity requirements that apply to a variety of manned and Unmanned Aerial Vehicle (UAV) operational tasks. This paper presents the results of the research activities carried out by the Italian Air Force Flight Test Centre (CSV-RSV) in collaboration with the Nottingham Geospatial Institute (NGI) and Cranfield University (CU) in the area of Avionics-Based Integrity Augmentation (ABIA) for mission- and safety-critical Global Navigation Satellite System (GNSS) applications. Based on these activities, suitable models were developed to describe the main causes of GNSS signal outage and degradation in flight, namely: antenna obscuration, multipath, fading due to adverse geometry and Doppler shift. Adopting these models in association with suitable integrity thresholds and guidance algorithms, the ABIA system delivers integrity caution (predictive) and warning (reactive) flags, as well as steering information to the pilot and electronic commands to the aircraft/UAV flight control system. These features allow real-time avoidance of safety-critical flight conditions and fast recovery of the required navigation performance in case of GNSS data losses. This paper presents the key ABIA concepts, architecture and mathematical models. A successive paper will address the ABIA integrity thresholds criteria and detailed results of a TORNADO simulation case-study.