Though precise, most LiDARs are vulnerable to position and pointing; errors as deviations from the expected principal axis lead to projection; errors on target. While fidelity of location/pointing solutions can be; high, determination of uncertainty remains relatively limited. As a; result, NASA’s 2021 Surface Topography and Vegetation Incubation Study; Report lists vertical (horizontal, geolocation) accuracy as an; associated parameter for all (most) identified Science and Application; Knowledge Gaps, and identifies maturation of Uncertainty Quantification; (UQ) methodologies on the STV Roadmap for this decade. The presented; generalized Polynomial Chaos Expansion (gPCE) based method has wide; ranging applicability to improve positioning, geolocation uncertainty; estimates for all STV disciplines, and is extended from the bare earth; to the bathymetric lidar use case, adding complexity introduced by entry; angle, wave structure, and sub-surface roughness.; This research addresses knowledge gaps in bathy-LiDAR measurement; uncertainty through a more complete description of total aggregated; uncertainties, from system level to geolocation, by applying a gPCE-UQ; approach. Currently, the standard approach is the calculation of the; Total Propagated Uncertainty, which is often plagued by simplifying; approximations (e.g. strictly Gaussian uncertainty sources) and ignored; covariances. gPCE intrinsically accounts for covariance between; variables to determine uncertainty in a measurement, without manually; constructing a covariance matrix, through a surrogate model of system; response. Additionally, gPCE allows arbitrarily high order uncertainty; estimates (limited only by the one-time computational cost of computing; gPCE coefficients), accurate representation of non-Gaussian sources of; error (e.g. wave height energy distributions), and direct integration of; measurement requirements into the design of LiDAR systems, by; trivializing the computation of global sensitivity analysis.
