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.

NASA’s 2021 STV Incubation Study Report lists vertical (horizontal, geolocation) accuracy as an associated SATM product parameter for all (most) identified Science and Application Knowledge Gaps. The presented generalized Polynomial Chaos Expansion (gPCE) based method has wide ranging applicability to improve positioning, geolocation uncertainty estimates for all STV disciplines, but is presented for the bathymetric lidar use case, due to added complexity introduced by wave structure, roughness, and entry angle. Most LiDARs, though precise, are vulnerable to position, 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 basic. Currently, the standard approach is the calculation of the Total Propagated Uncertainty (TPU), which is often plagued by simplifying approximations and ignored covariances. Additionally, uncertainty sources are often exclusively modeled as Gaussian, inaccurately capturing some variable distributions. Prominently, wave behavior is better described by Gamma distributions (which are supported under gPCE). This research addresses specific 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 uncertainty quantification approach. gPCE intrinsically accounts for covariance between variables to determine the uncertainty in a measurement, without manually constructing a covariance matrix, through a surrogate model of system response. Determining point-wise positioning uncertainty using gPCE is less computationally expensive than Monte Carlo methods and more tractable for most dimensionalities of interest (roughly from 3 to 20+). The method also does not rely on simplifying assumptions used in typical TPU methods. Additionally, a key attribute of this approach is that global sensitivity analysis (GSA), after obtaining gPCE coefficients, is trivial and nearly costless to compute. Furthermore, GSA of system configurations/uncertainty is a powerful tool to design and develop LiDAR systems with the measurement requirements integrated into the design solution.