Gaussian-Pareto Overbounding for Verification and Validation of Safety-Critical eVTOL and UAM Operations

A Gaussian-Pareto Overbounding (GPO) software toolset will be developed for the verification and validation (V&V) of safety-critical Unmanned Aerial Systems (UAS) sensors, including Guidance, Navigation and Control (GNC) and Collision Avoidance Systems (CAS) sensors using time- and data-efficient overbounding solutions. V&V remains a critical attribute of safe operation within active airspace for current aircraft and future autonomous eVTOL vehicles, particularly those designed for operation in dense environments, including Urban Air Mobility (UAM) or combat regions. Overbounds are used to determine the probability of system failure. However, traditional Gaussian Overbounding methods require large datasets of measurements, which leads to long required lead times to process and analyze data for integrity risk assessment, resulting in overly-conservative error bounds. In this program, a novel approach for overbounding unknown distribution functions called Gaussian-Pareto Overbounding (GPO) will be utilized to significantly reduce the amount of data and time needed to ensure the resilience and reliability of the vehicle systems, while providing accurate and minimally conservative error bounds. This method produces overbounds by hybridizing Gaussian distributions with Generalized Pareto Distributions using Extreme Value Theory, providing a procedure for determining error probabilities for multivariate systems which may display biases, auto-correlation, and heavy-tails. The hybridized GPO algorithms will increase data modeling accuracy and statistical efficiency for these systems. A key objective of the proposed work will be to design and develop a GPO V&V software toolset that includes functions and algorithms to generate GPO models, overbound conservatism, and analyze data efficiency. The program will also perform general risk assessment, using developed and available data analysis tools, including clustering and data dependency tests. The comprehensive software toolset will include data efficient methods to map overbounds through linearized systems. Simulations will be performed to demonstrate utility and applicability of GPO algorithms compared to traditional methods. Phase I will focus on applying the GPO algorithms to UAS overbounding, including using existing INS/GNSS navigation and collision-avoidance system data, and incorporating these methods into the prototype GPO V&V software toolset, with extended applications to guidance, control, and power management systems. The proposed work has broad applicability to risk assessment and certification of aerial, sea, ground, and space vehicles, and applies to a variety of systems requiring data-driven methods to ensure safety and reliability. This includes use in surveillance, security, disaster evaluation, humanitarian aid delivery, scientific investigations, package transport, and hobbyist operations.