Formal analysis of the compact positionreporting algorithm

Abstract The Automatic Dependent Surveillance-Broadcast (ADS-B) system allows aircraft to communicate current state information, including position and velocity messages, other in their vicinity ground stations. Compact Position Reporting (CPR) algorithm is the ADS-B protocol responsible for encoding decoding of positions. CPR sensitive computer arithmetic since it relies on functions that are intrinsically unstable such as floor modulus. In this paper, a formal verification presented. contrast previous work, presented here encompasses entire range message types supported by ADS-B. paper also presents two implementations algorithm, one double-precision floating-point 32-bit unsigned integers, which both formally verified against real-number algorithm. proceeds three steps. For each implementation, version CPR, simplified manipulated reduce numerical instability leverage features datatypes, proposed. Then, Prototype Verification System (PVS) used prove real conformance properties, assert ideal counterpart improved mathematically equivalent standard definition. Finally, static analyzer Frama-C verify software say implementation correct with respect its idealized counterpart. concert, properties guarantee meets original specification. will be included revised standards document reference