Integrity Risk is a quantitative measure of the probability that a positioning system will provide misleading information without timely warning, specifically, the likelihood that the true position error exceeds the calculated protection level or specified alert limit without the system alerting the user. This parameter is fundamental to safety-critical navigation applications where undetected positioning errors could lead to hazardous outcomes.
The mathematical definition of integrity risk relates protection levels, alert limits, and the probability of hazardously misleading information. For a system to meet its integrity specification, the probability that the actual position error exceeds the protection level must remain below the target integrity risk at all times. This relationship, P(error > Protection Level) ≤ Target Integrity Risk, must be demonstrated through analysis, simulation, and testing across all anticipated operating conditions and failure scenarios.
Target Integrity Risk (TIR) values vary depending on application criticality. Aviation precision approach procedures may require integrity risks as low as 10⁻⁷ per approach (one in ten million). Automotive lane-level positioning applications may specify integrity risks between 10⁻⁷ and 10⁻⁸ per hour of operation. These demanding requirements reflect the serious consequences of undetected positioning errors, aircraft flying into terrain or vehicles departing their intended lanes into oncoming traffic or obstacles.
Meeting integrity risk requirements presents significant engineering challenges. Systems must account for all potential error sources and failure modes, including satellite anomalies, atmospheric disturbances, multipath, interference, and hardware or software faults. The integrity risk budget must be carefully allocated across subsystems, with each component (GNSS corrections, receiver processing, sensor fusion, integrity monitoring) contributing only its allocated portion of the total risk. Demonstrating compliance requires extensive analysis, simulation, and testing, often billions of simulated operating hours to statistically validate that rare integrity failures remain below target thresholds.
