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). In particular, this includes the V&V of sensors used to operate UAS, including navigation systems, the Air Data System (ADS), the Power Monitoring System (PMS), and Collision Avoidance Systems (CAS). The model-based techniques offered in this toolset provide advanced statistical modeling of UAS 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) and combat regions. Overbounds are used to encompass the probability of rare system events, especially system failures, and have traditionally been determined using Gaussian Overbound (GO) uncertainty models. However, GO requires large error measurement datasets to characterize a system’s sensors, and therefore long lead times to process and analyze data for integrity risk assessment, and results in overly-conservative error bounds that do not model the asymptotic characteristics of the error uncertainty. In this program, the novel GPO approach for overbounding unknown distribution functions will be utilized to significantly reduce the amount of data and time needed to ensure the resilience and reliability of the vehicle sensor systems, while providing accurate, data-efficient, and minimally-conservative error bounds. GPO hybridizes Gaussian distributions with Generalized Pareto Distributions using Extreme Value Theory, providing a procedure for determining error probabilities for sensors that displays biases, auto-correlation, heavy-tails, and multivariate correlation. A key objective of the proposed work will be to produce a GPO V&V software toolset that includes algorithms to generate GPO models, overbound conservatism, and analyze statistical data efficiency for characterizing sensor errors of eVTOL and UAM. The program will perform risk assessment using developed data analysis tools, including clustering and data dependency tests. The comprehensive software toolset will include data efficient methods to map overbounds through common model-based data fusion algorithms. Demonstrations using actual sensor data will show the significant benefits of GPO algorithms compared to traditional methods, with the capability to prevent unpredictable vehicle behavior. Phase II will focus on applying the GPO algorithms to specific UAS-grade sensors, including INS/GNSS navigation, ADS, PMS, and CAS data using the fully developed GPO V&V software toolset. The proposed work has broad applicability to risk assessment and certification of aerial, sea, ground, and space vehicles, and applies to a variety of sensor systems requiring statistical data-driven and model-based methods to ensure safety and reliability.